Parameterization of the Am1* Semiempirical Molecular Orbital Method for the First-Row Transition Metals and Other Elements

PARAMETERIZATION OF THE AM1* SEMIEMPIRICAL MOLECULAR ORBITAL METHOD FOR THE FIRST-ROW TRANSITION METALS AND OTHER ELEMENTS

Der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg

zur Erlangung des Doktorgrades Dr. rer. nat.

vorgelegt von Hakan Kayi aus Bursa, Türkei

2009

Als Dissertation genehmigt durch die Naturwissenschaftliche Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg

Tag der mündlichen Prüfung: 23.12.2009

Vorsitzender der Promotionskommission: Prof. Dr. Eberhard Bänsch

Erstberichterstatter: Prof. Dr. Timothy Clark

Zweitberichterstatter: Prof. Dr. Nicolai Burzlaff

ACKNOWLEDGMENTS

First of all I would like to express my deepest gratitude to my supervisor Prof. Dr. Timothy Clark for his endless support, patience, full confidence in me and for always encouraging me. Without his understanding and excellent guidance, I could never complete this project. I am also very thankful for his support on personal level, that has been very valuable during many difficult situations.

I would like to thank Prof. Dr. Rudi van Eldik and Prof. Dr. Bernd Meyer for accepting to be examiners at my defense exam, and also Prof. Dr. Nicolai Burzlaff for his expertise.

I am very thankful to Dr. Paul Winget and Anselm Horn for sharing their great experiences in programming and for their help in using of parameterization scripts, and Dr. Nico van Eikema Hommes for his support and advice for solving technical problems related to hardware, software and scripting. Additionally, my thanks go to my officemate Dr. Tatyana Shubina for her fruitful discussions. I am also very thankful for the help and very valuable discussions of Dr. Matthias Henneman. Many thanks go as well to my former and present colleagues for their friendliness and support in many different issues: Dr. Harald Lanig, Dr. Ralph Puchta, Dr. Gudrun Schürer, Dr. Kendall Byler, Dr. Florian Haberl, Dr. Olaf Othersen, Dr. Jr-Hung Lin, Dr. Frank Beierlein, Dr. Mateusz Wielopolski, Dr. Pawel Rodziewicz, Dr. Gül Özpinar, Dr. Adria Gil Mestres, Dr. Ute Seidel, Christian Kramer, Christof Jäger, Sebastian Schenker, Matthias “Döner” Wildauer, Angela Götz, Marcel Youmbi and Alexander Urban. I also would like to say thank you to my friends: Kurtulus Erdogan, Günay Kaptan and Can Metehan Turhan for all the unforgettable moments they shared with me in Erlangen, and those everywhere that stayed friends despite the separations of time and distance.

For the financial support I thank Deutsche Forschungsgemeinschaft (GK312 “Homogeneous and Heterogeneous Electron Transfer” and SFB583 “Redox-Active Metal Complexes”).

And finally, I would like to express my warmest and endless gratitude to my parents and my sister for their lifelong love, support and encouragement.

ZUSAMMENFASSUNG

In dieser Doktorarbeit wird die Parametrisierung der semiempirischen AM1* Molekülorbitaltechnik für einige neue Elemente beschrieben. Dies beinhaltet Resultate und Parameter für Vanadium, Chrom, Mangan, Eisen, Kobalt, Nickel, Kupfer, Zink, Brom, Jod und Gold. Die AM1* Methode ist eine Erweiterung der ursprünglichen AM1 Molekülorbital Theorie. Sie benutzt d-Orbitale für Elemente ab der zweiten langen Reihe des Periodensystems und eine leichte Modifizierung von Voityuk und Rösch’s AM1(d) Parametern für Mo. Unsere ursprüngliche Motivation für die Parametrisierung von AM1* war, die Vorteile von AM1 (gute H-Brücken Energien, höhere Rotationsbarrieren für π-Systeme als MNDO oder PM3) für die Elemente H, C, N, O und F beizubehalten, während die Performanz für P-, S- und Cl- beinhaltende Substanzen verbessert werden sollte. Zusätzlich wollten wir endlich eine Parametrisierung für Übergangsmetalle auf Basis eine MNDO Methode publizieren. Im Laufe der Arbeit stellte sich heraus, dass es auch nötig ist, Brom und Jod zu parametrisieren, um die Bromide und Jodide der Übergangsmetalle in den Parametrisierungsdatensätzen adäquat zu nutzen. Während der Vorbereitung der Parametrisierungsdatensätze wurden experimentelle Daten aus mehreren Quellen gesammelt. Im Falle fehlender experimenteller Daten und um den Bereich des Parametrisierungsdatensatzes zu vergrößern wurden die Eigenschaften wichtiger prototypischer Strukturen auf hoher quantenmechanischer Niveau berechnet. Zusätzlich haben wir experimentelle Daten geringer Qualität mit den Ergebnissen von hochqualitativen quantenmechanischen Rechnungen verglichen und verbessert. In solchen Fällen wurde das B3LYP Hybrid-Funktional mit LANL2DZ Basis Satz und Polarisierungsfunktionen oder Coupled Cluster Rechnungen mit Einzel- und Doppelanregungen und Störungstheoriekorrekturen für Dreifachanregungen (CCSD(T)) mit dem 6-311+G(d) Basissatz benutzt. Nach der Zusammenstellung des Datensatzes wurde die Parametrisierung durchgeführt und die Performanz und typische Fehler von AM1* analysiert. Diese werden im Detail gezeigt und mit der Performanz von anderen Methoden, die die NDDO Nährung benutzen, verglichen. Zusammenfassend lässt sich sagen, dass der AM1* Hamiltonian für energetische, elektronische und strukturelle Eigenschaften den anderen verfügbaren Hamiltonians überlegen ist, insbesondere für die Beschreibung von Übergangsmetallen.

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ABSTRACT

This thesis describes the parameterization of AM1* semiempirical molecular orbital technique for a series of new elements. Parameterization results for vanadium, chromium, manganese, iron, cobalt, nickel, copper, zinc, bromine, iodine and gold are reported. The AM1* methodology is an extension of the original AM1 molecular orbital theory uses d-orbitals for the elements starting from the second long row of the periodic table, and a slight modification of Voityuk and Rösch’s AM1(d) parameters for Mo. Our original motivation in parameterizing AM1* was to retain the advantages of AM1 (good energies for hydrogen bonds, higher rotation barriers for π-systems than MNDO or PM3) for the elements H, C, N, O and F and to improve performance over AM1 for P-, S- and Cl-containing compounds and eventually to produce a published parameterization for an MNDO-like method for the transition metals. Additionally, bromine and iodine have also been parameterized because parameters for these elements became necessary in order to be able to parameterize the transition metals adequately by including their bromides and iodides in the parameterization datasets. In the preparation of parameterization datasets, experimental target data were collected from several sources. In the case of lack of experimental data and also to extend the range of parameterization dataset, prototype compounds were used and their properties derived from high-level calculations. In addition to this, when we have determined that the available experimental data are of insufficient quality, we have also applied corrections to available values using results from high-level calculations. In such cases, the B3LYP hybrid functional with the LANL2DZ basis set including polarization functions or coupled cluster calculations with single and double excitations and a perturbational corrections for triples (CCSD(T)) with the 6-311+G(d) basis set were used and dataset became more reliable. Once the parameterization dataset has been assembled, the parameterization process is performed. After this parameterization process is successfully completed, the performance and the typical errors of AM1* are discussed and also compared with the other available neglect of diatomic differential overlap (NDDO) Hamiltonians. To summarize, the performance of the AM1* for energetic, electronic and structural properties is superior to other available Hamiltonians in many cases, especially for the transition metals.

CONTENTS

1 INTRODUCTION 1 1.1 Historical Development of Semiempirical Methods ...... 1 1.1.1 Hückel (HMO), Pariser-Parr-Pople (PPP) and Extended Hückel Theory (EHT) ..... 1 1.1.2 CNDO, INDO ...... 1 1.1.3 NDDO ...... 2 1.1.4 MINDO ...... 3 1.1.5 MNDO ...... 3 1.1.6 AM1 ...... 4 1.1.7 PM3 ...... 5 1.1.8 MNDO/d ...... 6 1.1.9 SAM1 ...... 6 1.1.10 PM3(tm) ...... 7 1.1.11 AM1(d) ...... 7 1.1.12 PM5 ...... 7 1.1.13 AM1* ...... 8 1.1.14 RM1 ...... 8 1.1.15 PM6 ...... 8 1.1.16 OMx-D ...... 9 1.2 Transition Metals ...... 9

2 THEORY 13 2.1 General Approximations ...... 13 2.2 Methods and Hamiltonians ...... 17 2.2.1 MNDO ...... 17 2.2.2 AM1 ...... 21 2.2.3 PM3 ...... 23 2.2.4 PM6 ...... 25 2.2.5 AM1* ...... 27

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3 PARAMETERIZATION OF SEMIEMPIRICAL METHODS 31 3.1 Introduction to Parameterization Methodology ...... 31 3.2 Reference Data ...... 31 3.3 Relative Weights of the Properties ...... 33 3.4 Parameter Optimization Procedure ...... 34

4 RESULTS OF AM1* PARAMETERIZATIONS 37 4.1 Parameterization Data ...... 37 4.2 Parameterization of Vanadium and Chromium ...... 38 4.2.1 Results ...... 38 4.2.1.1 Vanadium ...... 40 4.2.1.1.1 Heats of Formation of Vanadium Compounds ...... 40 4.2.1.1.2 Ionization Potentials and Dipole Moments of Vanadium Compounds ..... 46 4.2.1.1.3 Geometries of Vanadium Compounds ...... 47 4.2.1.2 Chromium ...... 55 4.2.1.2.1 Heats of Formation of Chromium Compounds ...... 55 4.2.1.2.2 Ionization Potentials and Dipole Moments of Chromium Compounds .... 60 4.2.1.2.3 Geometries of Chromium Compounds ...... 61 4.2.2 Conclusions and Outlook ...... 67 4.3 Parameterization of Manganese and Iron ...... 68 4.3.1 Results ...... 68 4.3.1.1 Manganese ...... 69 4.3.1.1.1 Heats of Formation of Manganese Compounds ...... 69 4.3.1.1.2 Ionization Potentials and Dipole Moments of Manganese Compounds ... 73 4.3.1.1.3 Geometries of Manganese Compounds ...... 74 4.3.1.2 Iron ...... 78 4.3.1.2.1 Heats of Formation of Iron Compounds ...... 78 4.3.1.2.2 Ionization Potentials and Dipole Moments of Iron Compounds ...... 84 4.3.1.2.3 Geometries of Iron Compounds ...... 85 4.3.2 Conclusions and Outlook ...... 93 4.4 Parameterization of Cobalt and Nickel ...... 94 4.4.1 Results ...... 94 4.4.1.1 Cobalt ...... 95 4.4.1.1.1 Heats of Formation of Cobalt Compounds ...... 95

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4.4.1.1.2 Ionization Potentials and Dipole Moments of Cobalt Compounds ...... 100 4.4.1.1.3 Geometries of Cobalt Compounds ...... 101 4.4.1.2 Nickel ...... 108 4.4.1.2.1 Heats of Formation of Nickel Compounds ...... 108 4.4.1.2.2 Ionization Potentials and Dipole Moments of Nickel Compounds ...... 113 4.4.1.2.3 Geometries of Nickel Compounds ...... 114 4.4.2 Conclusions and Outlook ...... 123 4.5 Parameterization of Copper and Zinc ...... 124 4.5.1 Results ...... 124 4.5.1.1 Copper ...... 125 4.5.1.1.1 Heats of Formation of Copper Compounds ...... 125 4.5.1.1.2 Reaction Energies of Copper Compounds ...... 127 4.5.1.1.3 Ionization Potentials and Dipole Moments of Copper Compounds ...... 128 4.5.1.1.4 Geometries of Copper Compounds ...... 129 4.5.1.2 Zinc ...... 133 4.5.1.2.1 Heats of Formation of Zinc Compounds ...... 133 4.5.1.2.2 Ionization Potentials and Dipole Moments of Zinc Compounds ...... 137 4.5.1.2.3 Geometries of Zinc Compounds ...... 139 4.5.2 Conclusions and Outlook ...... 145 4.6 Parameterization of Bromine and Iodine ...... 146 4.6.1 Results ...... 146 4.6.1.1 Bromine ...... 147 4.6.1.1.1 Heats of Formation of Bromine Compounds ...... 147 4.6.1.1.2 Ionization Potentials and Dipole Moments of Bromine Compounds ..... 153 4.6.1.1.3 Geometries of Bromine Compounds ...... 156 4.6.1.2 Iodine ...... 160 4.6.1.2.1 Heats of Formation of Iodine Compounds ...... 160 4.6.1.2.2 Ionization Potentials and Dipole Moments of Iodine Compounds ...... 164 4.6.1.2.3 Geometries of Iodine Compounds ...... 167 4.6.2 Conclusions and Outlook ...... 170 4.7 Parameterization of Gold ...... 171 4.7.1 Results ...... 171 4.7.1.1 Heats of Formation of Gold Compounds ...... 172 4.7.1.2 Ionization Potentials and Dipole Moments of Gold Compounds ...... 174

4.7.1.3 Geometries of Gold Compounds ...... 176 4.7.2 Conclusions and Outlook ...... 181

BIBLIOGRAPHY 183

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INTRODUCTION Chapter 1

1 INTRODUCTION

1.1 Historical Development of Semiempirical Methods

1.1.1 Hückel (HMO), Pariser-Parr-Pople (PPP) and Extended Hückel Theory (EHT)

The history of semiempirical methods started with theories based on purely π-electron treatments in the 1930s. The Hückel Molecular Orbital (HMO) method is the earliest, simplest and the most prominent π-electron theory for treating conjugated molecules [1]. It was used to predict the properties and reactivities of planar conjugated compounds. A great failing of HMO is its treatment of electron repulsion. The first semiempirical π-electron theory that includes formally the effect of electron repulsion between valence electrons and thence improves on HMO is the Pariser-Parr-Pople (PPP) method [2, 3, 4, 5, 6, 7]. Both HMO and PPP methods are only applied to planar conjugated molecules, but PPP allows heteroatoms other than hydrogen. PPP is popular for developing simple parameterized analytical expressions for molecular properties. Today it is still used in the cases that require minimal electronic effects. Extended Hückel Theory (EHT) appeared as a molecular orbital theory that takes into account all valence electrons in the molecule and is applicable to non-planar molecules [8, 9]. Since EHT is applicable to all periodic table elements, today there is still interest in EHT, especially for modeling inorganic compounds in a reasonable CPU time. Currently, EHT is also preferred for computing band structures, which are generally considered to be very computation-intensive calculations. One the other hand, one must consider that EHT is very poor at predicting molecular geometries.

1.1.2 CNDO, INDO

Later, all-valence-electron semiempirical methods using the Zero Differential Overlap (ZDO) approximation, such as Complete Neglect of Differential Overlap (CNDO) [10, 11, 12, 13], Intermediate Neglect of Differential Overlap (INDO) [10, 14] and Neglect of Diatomic Differential Overlap (NDDO) [10, 11] were also proposed by Pople and his collaborators starting from the mid-1960s. These self-consistent field models are related to the extended 1

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Hückel method in much the same manner as the Pople-Pariser-Parr method is related to the Hückel molecular orbital approximation [15]. Simply, in the ZDO approximation, all products of basis functions on the same electron coordinates are neglected when they are located on different atoms. CNDO is the simplest of the all-valence-electron NDO models. In this model, only valence electrons are explicitly treated, the inner-shell electrons are taken as a part of the atomic core [16]. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ab initio calculations on hydrocarbons [17]. In the INDO approximation, the primary modification to the CNDO approximation is that one-center repulsion integrals between atomic orbitals on the same atom are not neglected. However, the INDO approximation shares with CNDO the inadequate representation of electron repulsions involving atomic orbitals with directional properties. Today, the INDO method has largely been superseded by more accurate methods. It is still sometimes used as an initial guess for ab initio calculations. In 1973, the ZINDO program package, which contains INDO/1 to calculate molecular geometries and INDO/S especially designed to calculate electronic spectra of organic molecules and transition metal complexes, was introduced by Zerner’s group [18]. The program also predicts UV transitions well except metals with unpaired electrons. However, it produces generally poor results for geometry optimizations. An interesting intermediate neglect of differential overlap based technique, symmetrically orthogonalized INDO, in short SINDO and later SINDO1, is conceptually and practically superior to the INDO method [19, 20, 21]. The most important features of SINDO are that it explicitly takes ortogonalization transformations of the basis functions into account and treats inner orbitals by a local pseudopotential. SINDO appears to perform well but has not found the wide range of acceptance of the NDDO based methods.

1.1.3 NDDO

The NDDO method is an improvement on INDO, since it neglects differential overlap only when the atomic orbitals are on different atoms. Thus dipole-dipole interactions are retained and expressed in terms of integrals that are calculated either from atomic orbitals or determined empirically [15]. A few attempts were made to parameterize NDDO, but the results were rather disappointing [22].

INTRODUCTION Chapter 1

1.1.4 MINDO

A few years later, several the modified intermediate neglect of differential overlap methods (MINDO/1, MINDO/2, MINDO/3) were introduced by Dewar and coworkers [23, 24, 25]. Dewar aimed to calculate ground-state properties, in particular heats of formation and molecular geometries with chemical accuracy, such as bond lengths of 0.1 pm, bond angles of 0.1°, heats of formation that are correct to 0.1% and so on, taking all valence electrons into account [23]. His motivation for modifying INDO was to remove several deficiencies of INDO, especially in the analytically calculation of the one-electron repulsion integrals. He rather evaluated these integrals by using parameters and fitting these parameters to experimental data. Incorporating the Davidson-Fletcher-Powell geometry optimization routine [26], the parameterization program was able to accept initial geometries as input and derive the associated minimum energy structures. In this way, the MINDO methods became convenient for geometry optimization calculations. Here one can say that MINDO represented a very big step toward encouraging chemists to use molecular orbital calculations in the interpretation of experimental data. The third version of MINDO was by far the most reliable and was accepted to be the first modern semiempirical method. Though MINDO/3 has been superseeded by more accurate methods today, it is still sometimes used to calculate an initial guess for ab initio calculations. MINDO methods had some limitations, such as too positive heats of formation for unsaturated molecules, too large bond lengths and too negative heats of formation for molecules that contain adjacent atoms with lone pairs. Some of these limitations resulted from using the INDO approximation, particularly from the inability of INDO to deal with systems containing lone pairs [27].

1.1.5 MNDO

To overcome these limitations, in 1977 the modified neglect of diatomic overlap (MNDO) method was introduced by Dewar and Thiel [28]. This method is the oldest NDDO-based model that evaluates one-center two-electron integrals based on spectroscopic data for isolated atoms, and evaluates other two-electron integrals using the idea of multipole- multipole interactions from classical electrostatics. In MNDO, various integrals are not determined analytically, rather numerical parameters are adjusted to fit the experimental data as in MINDO. MNDO was mainly parameterized to reproduce heats of formation and the

INTRODUCTION Chapter 1

geometrical properties of stable molecules using ionization potentials and dipole moments as ancillary data. Possibly the most important advantage of MNDO over MINDO/3 is the use of monatomic parameters, while MINDO/3 requires diatomic parameters in resonance integrals and core-core repulsion. There are many articles available that compare the performance of MNDO with different semiempirical methods [29, 30, 31, 32, 33, 34, 35, 36]. MNDO has some known deficiencies, such as its inability to model intermolecular systems containing hydrogen bonds accurately when the atoms are separated by a distance around sum of their van der Waals radii. Additionally, hypervalent molecules are too unstable, four-membered rings are too stable, rotational barriers are often underestimated, activation barriers are too high, electronic excitation energies are underestimated, conformational preferences are sometimes not reproduced [37]. The major problem of MNDO, its tendency to overestimate repulsions between atoms at approximately their van der Waals distance was sought to be solved by modifying the core repulsion function in MNDO.

1.1.6 AM1

In this way, beside the MNDO/H, which was introduced by Burstein and Isaev to investigate H-bonded systems [38], Dewar and coworkers introduced their new method AM1 [39]. AM1 is basically a modification to and a reparameterization of the general theoretical model found in MNDO. Its major difference is the addition of Gaussian functions to the description of core repulsion function to overcome MNDO’s hydrogen bond problem. Additionally, since the computer resources were limited in 1970s, in MNDO parameterization methodology, the overlap terms, βs and βp, and Slater orbital exponents ζs and ζp for s- and p- atomic orbitals were fixed. That means they are not parameterized separately just considered as βs = βp, and

ζs = ζp in MNDO. Due to the greatly increasing computer resources in 1985 comparing to 1970s, these inflexible conditions were relaxed in AM1 and then likely better parameters were obtained. The addition of Gaussian functions significantly increased the numbers of parameters to be parameterized from 7 (in MNDO) to 13-19, but AM1 represents a very real improvement over MNDO, with no increase in the computing time needed. Dewar also concluded that the main gains of AM1 were its ability to reproduce hydrogen bonds and the promise of better estimation of activation energies for reactions [39]. However, AM1 has some limitations. Although hypervalent molecules are improved over MNDO, they still give larger errors than the other compounds, alkyl groups are too stable, nitro compounds are too unstable, peroxide bond are too short [40]. AM1 has been used very widely because of its 4

INTRODUCTION Chapter 1

performance and robustness compared to previous methods. This method has retained its popularity for modeling organic compounds and results from AM1 calculations continue to be reported in the chemical literature for many different applications.

1.1.7 PM3

In 1989, Stewart introduced PM3 [41, 42, 43], which can be considered as a reparameterization of AM1. This method was named as parametric method 3, considering MNDO and AM1 as the methods 1 and 2, respectively, as one of the three NDDO-based methods. In both MNDO and AM1, one-center electron repulsion integrals (g ij , h ij ), which are five parameters gss , gsp , gpp , gp2 , and gsp , are assigned values determined from atomic spectra by Oleari [44]. PM3 differs from MNDO and AM1 and these one-center electron integrals are taken as parameters to be optimized. PM3 also differs from AM1 in the number of Gaussian terms used in the core repulsion function. PM3 uses only two Gaussian terms per atom instead of up to four used by AM1. Another difference is that PM3 uses an automated parameterization procedure, in contrast to AM1. H, C, N, O, F, Al, Si, P, S, Cl, Br, and I parameters were simultaneously parameterized, whereas AM1 parameters were adjusted manually by Dewar with the help of chemical knowledge or intuition. Since his parameter optimization algorithms permitted an efficient search of parameter space, Stewart was able to employ a significantly larger data set in evaluating his penalty function than had been true for previous efforts [45]. Statistically, PM3 was more accurate than the other semiempirical methods available at the time [46], but it was found to have several deficiencies that seriously limited its usefulness. One of the most important of these is the rotational barrier of the amide bond, which is much too low and in some cases almost non-existent. The other one is that PM3 has a very strong tendency to make the environment around nitrogen pyramidal. Thus, PM3 is not suggested for use in studies where the state of hybridization of nitrogen is important [46].

According to a search of “Current Contents” done in 1999, AM1 was the most widely used semiempirical quantum mechanical method and PM3 was second [47].

INTRODUCTION Chapter 1

1.1.8 MNDO/d

The MNDO, AM1 and PM3 methods use only sp -basis sets and do not include d-orbitals in their original implementation. Therefore, these methods are unable to treat most of the transition metal compounds and a large part of the periodic table. Also, from ab initio calculations it is known that d-orbitals are significant for quantitative accuracy in the hypervalent compounds of main group elements. Because of these limitations and deficiencies, an extension of the MNDO formalism to d-orbitals was necessary to investigate transition metals and heavier main group elements. In 1992, Thiel and Voityuk introduced MNDO/d, the first NDDO model with d-orbitals [48, 49, 50]. MNDO/d explicitly contains d- orbitals for heavier atoms starting from the second long row in periodic table. It uses theory and parameters in original MNDO methodology unchanged for the elements where Z<11. In MNDO/d two-center two-electron integrals are calculated using the original point-charge model [51] which is also used in MNDO, AM1 and PM3. These integrals are expanded in terms of semiempirical multipole-multipole interactions. All monopoles, dipoles and quadrupoles of these charge distributions are included, whereas all higher multipoles beyond order 4 are neglected [52]. MNDO/d showed enormous improvements over MNDO, AM1 and PM3, especially for hypervalent molecules. MNDO and AM1 were not designed to treat hypervalent compounds, but in the parameterization of PM3 considerable effort was made to overcome such deficiencies. MNDO/d predicts the point groups of hypervalent compounds more accurately and also predicts the heats of formation of hypervalent compounds with small mean absolute errors compared to MNDO, AM1 and PM3 [34, 48, 49, 50]. Nonetheless one must consider that MNDO/d produces identical results to MNDO for the elements with Z<11.

1.1.9 SAM1

The last semiempirical technique produced by Dewar’s group is Semi-ab initio model 1 (SAM1) [53, 54, 55]. In this method, two-electron repulsion integrals are ab initio integrals that are evaluated from contracted Gaussian basis functions (STO-3G) fit to Slater-type orbitals using standard methods [56]. SAM1 is apparently quite successful for transition metals and vibrational frequencies, but neither the complete method nor a comprehensive analysis of its performance has been published. Due to the need of calculating two-electron repulsion integrals correctly in ab initio fashion, SAM1 is slower than AM1 but much faster

INTRODUCTION Chapter 1

than ab initio methods because it still uses the NDDO approximation. This method is only available within the commercial software package, AMPAC 9 [57].

1.1.10 PM3(tm)

The extension of MNDO formalism to d-orbitals not only formed a basis for MNDO/d but also for the independent PM3(tm) parameterization [58]. PM3(tm) has not been fully described in the literature, so it is one of those unpublished methods, and only available within commercial software package SPARTAN 8.0 [59]. Hehre and coworkers added d- orbitals to Stewart’s PM3 and parameterized only to reproduce the geometries of crystal structures of transition metal complexes. More usual properties, energies, dipole moments and ionization potentials were not taken into account for the parameterization. PM3(tm) appears not to be as reliable as hoped [60] but can be used to generate reasonable molecular geometries, whose energies may then be calculated with more reliable methods.

1.1.11 AM1(d)

In 2000, Voityuk and Rösch introduced the AM1(d) parameterization for molybdenum [61]. They extended AM1 to an spd -basis by adding d-orbitals to molybdenum. The core-repulsion function was also modified. They excluded Gaussian functions from the core-core repulsion term and included two new bond-specific parameters. The established AM1 formalism and all the parameters for all-main group elements were taken unchanged. Due to this fact, AM1(d) produces identical results to the original AM1 method for non-transition metal elements.

1.1.12 PM5

In addition to PM3(tm), another extension of PM3 molecular orbital technique, namely PM5, has also been produced by Stewart. PM5 is a reparameterization of PM3 to improve its performance. It has been parameterized for all main group elements and many of transition metals. This method is available within the commercial software LinMopac2002 [62]. The complete method has never been published. However, some articles that include the results from PM5 calculations and compare its performance are available [63, 64, 65, 66, 67, 68]. Today this method has been superseded by PM6.

INTRODUCTION Chapter 1

1.1.13 AM1*

In 2003, Clark and coworkers introduced AM1* [69], as an extension to AM1 molecular orbital method. AM1* is based on AM1, rather than MNDO or PM3, because AM1 reproduces the energies of hydrogen bonds relatively well and generally performs better for rotational barriers of partial double bonds than the other two methods. AM1* uses the parameters and theory of original AM1 method unchanged for the elements H, C, O, N and F, and adds d-orbitals to other elements using a modified core-repulsion function. The use of these original AM1 parameterization elements obviously limits AM1*’s ultimate accuracy in some cases. On the other hand, the recent parameterizations for AM1*, in particular transition metal parameterizations [66, 68, 70], have shown that AM1* performs very well compared to other available modern methods, PM5 and PM6.

1.1.14 RM1

In 2006, RM1 (Recife Model 1, which takes its name from the city Recife, Brazil) was introduced [71]. Without making any changes to original AM1 formalism and to the set of approximations used in original AM1 methodology, ten elements, H, C, N, O, F, P, S, Cl, Br, and I were reparameterized. This resulted with improved accuracy over all other NDDO methods for organic compounds.

1.1.15 PM6

Stewart introduced his most recent model, PM6, in 2007 [72]. He made several modifications to the core-core interaction term and also to the method of parameter optimization. Additionally, d-orbitals were used. PM6 has been parameterized for 70 elements and so provides very large application area. Modification of core-core interaction term has resulted in a significant improvement for main group elements and also the use of d-orbitals has allowed this method to be extended to the transition metals.

INTRODUCTION Chapter 1

1.1.16 OMx-D

Thiel and coworkers have continued to modify MNDO over the years, using effective core potentials for the inner orbitals and adding orthogonalization corrections as in SINDO1. They have introduced OM1, OM2 and OM3 models (OMx) [73, 74, 75, 76, 77, 78]. These corrections are important especially to describe torsional angles correctly. In 2008, they added dispersion correction terms taken from density functional work without modifying the standard OMx parameters and achieved significant improvements for non-covalent interactions in biochemical systems [79]. McNamara and Hillier [80] also incorporated dispersion terms into AM1 and PM3 just before OMx-D, taking the parameters for dispersion functions from the BLYP-D parameterization. And method performs well for the non- covalent complexes.

Other semiempirical methods exist than the models only presented here. Other methods and variations of these models or many of hybrid-models are also available today. Semiempirical methods keep developing steadily. The availability of different methods with a large variety of parameters provides a good starting point for future developments and reaction-specific local parameterizations and also comparison calculations.

1.2 Transition Metals

Transition metals are distinguished from the other elements by the presence of filled or partially filled d-orbitals in their valence shell in one or more of their oxidation states. For the first row transition metals, 3d -orbitals are filled, whereas 4d - and 5d -orbitals are filled for second row and third row transition elements, respectively. They are the elements of the groups 3-12 of the periodic table. However, especially group 12 and to some extent group 3 show significant analogy to main-group elements. Although scandium and zinc are in the d- block, they are not considered to be transition elements, generally. Because they have no ion that has a partially filled d-orbital. Electronic configurations of transition metals given below in Table 1.1.

INTRODUCTION Chapter 1

Table 1.1: The electronic configurations of transition metals 1st Row 2nd Row 3rd Row Scandium [Ar]3d l4s 2 Yttrium [Kr]4d l5s 2 Lanthanum [Xe]5d 16s 2

Titanium [Ar]3d 24s 2 Zirconium [Kr]4d 25s 2 Hafnium [Xe]4f 14 5d 26s 2

Vanadium [Ar]3d 34s 2 Niobium [Kr]4d 45s l Tantalum [Xe]4f 14 5d 36s 2

Chromium [Ar]3d 54s 1 Molybdenum [Kr]4d 55s 1 Tungsten [Xe]4f 14 5d 46s 2

Manganese [Ar]3d 54s 2 Technetium [Kr]4d 55s 2 Rhenium [Xe]4f l4 5d 56s 2

Iron [Ar]3d 64s 2 Ruthenium [Kr]4d 75s l Osmium [Xe]4f 14 5d 66s 2

Cobalt [Ar]3d 74s 2 Rhodium [Kr]4d 85s 1 Iridium [Xe]4f 14 5d 76s 2

Nickel [Ar]3d 84s 2 Palladium [Kr]4d l0 5s 0 Platinum [Xe]4f 14 5d 96s 1

Copper [Ar]3d 10 4s 1 Silver [Kr]4d 10 5s 1 Gold [Xe]4f l4 5d l0 6s l

Zinc [Ar]3d 10 4s 2 Cadmium [Kr]4d l0 5s 2 Mercury [Xe]4f 14 5d 10 6s 2

The chemistry of the transition metals has been examined for about two centuries and experimentalists and theoreticians have had a growing interest in the past three decades. Transition metals are very widely used in many important areas of chemistry. Especially coordination compounds (or complexes) of transition metals with organic reagents play a very important role in organometallic chemistry. These compounds behave differently to both ionic and covalent compounds in organic chemistry. Because of their complicated constitution, these compounds are considered to be complexes [81]. Compounds containing transition metals are also very important in biochemistry and they are generally responsible for the specific functionality of many enzymes. Transition metals are the active sides in many molecules relevant in catalytic processes, and also clusters of transition metals mediate catalytic surface processes in many reactions [82].

Calculations of transition metals are important to test the performance of the available quantum chemical theories. Many of the transition metals contain unpaired electrons in their valence shell. The determination of the correct spin states, which directly affects the properties, makes the calculation of transition metals difficult [83]. Generally the most common methods for calculating transition metal compounds are classical ab initio techniques and DFT. The use of effective core potentials for describing transition metals has become popular [84]. Although relativistic effects can be considered very conveniently and the number of electrons to be calculated is reduced, these methods are still very demanding and expensive for the calculation of transition metal compounds. Hartree-Fock-based ab initio

INTRODUCTION Chapter 1

methods are often used in the calculation of transition metals, but the HF approximation has been recognized as being in error for the first row transition metals with partly filled d-orbitals [85], while d 0 and d 10 transition metal compounds are reliable [86]. On the other hand, in using of DFT methods, the choice of the proper basis set, exchange and correlation functionals is a very critical point and directly affects the quality of the results.

There are also several semiempirical methods available for the treatment of transition metals efficiently. One of the oldest of those, INDO/S [18] was especially designed to calculate electronic spectra of the transition metal complexes beside organic compounds. However, it is not used in the prediction of energetic and geometrical properties since it is not reliable for these properties. SINDO1 [19, 20, 21] has been extended to some transition metals. This method is not able to treat open shell systems and its accuracy is within the limits of classical INDO [10, 14] approximation.

Today most of the available semiempirical methods to treat transition metals are the ones based on the NDDO [10, 11] approximation. An extension of MNDO [28] method to d- orbitals, MNDO/d [48, 49, 50], was the first method to include d-orbitals that were necessary to investigate transition metals. However, only zinc, cadmium and mercury parameters were published for MNDO/d method [34]. An unpublished method, Semi-ab initio model 1 (SAM1) with a different theoretical basis, is quite successful for transition metals and vibrational properties, but the only transition metals available for SAM1 are iron and copper [53, 54, 55]. As an extension of PM3 to d-orbitals, PM3(tm) was parameterized to reproduce the geometries of transition metal compounds [58]. PM3(tm) parameters are available for Ti- Zn, Zr, Mo, Ru-Pd, Cd, Hf, Ta, W, Hg and Gd. But this method is not able to reproduce energetic and electronic properties, which are very important. AM1(d), which is an extension of the AM1 method to d-orbitals, is also available for molybdenum [61]. Another one of the unpublished method, PM5 [62] was parameterized for many of the transition metals, but has been superseded by PM6 [72]. PM6 contains all d-block elements and therefore provides a very wide application area. And finally, AM1*, which is again as an extension of AM1 to d- orbitals, has been parameterized for all first row transition metals plus gold [66, 67, 68, 69, 70, 87]. Today the parameterization of AM1* for the new d-block elements still continues. Comparisons of the AM1*, PM6 and PM5 methods for the transition metals are given in detail in the following sections.

INTRODUCTION Chapter 1

THEORY Chapter 2

2 THEORY

2.1 General Approximations

The most important goal of many approaches made in quantum chemistry is to solve the time- independent, non-relativistic Schrödinger equation [88] approximately.

= (2.1) where H is the Hamiltonian for a system (a molecule), E is the energy of the system and Ψ is the wavefunction containing all information that can possibly be known about the quantum chemical system. Mathematically, H is considered to be an operator, Ψ is an Eigenfunction and E is an Eigenvalue that is a scalar value.

The Hamiltonian for M nuclei and N electrons can be written as

1 1 1 = − − − + + (2.2) 2 2 where the indices i and j indicate electrons and A and B indicate nuclei. MA is the mass of nucleus A, RAi is the distance between atom A and electron i, rij is the distance between electrons i and j, RAB is the distance between atoms A and B, and ZA and ZB are the nuclear charges of atoms A and B, respectively. 2 is the Laplacian operator which is specific to each particle, and if we work in Cartesian coordinates it is defined as

= + + (2.3) The first and second terms of Equation (2.2) are the kinetic energy terms of the electrons and the nuclei A, respectively. The remaining three terms are the potential energy terms. The first indicates nucleus-electron attraction, the second electron-electron repulsion and the third nucleus-nucleus repulsion.

THEORY Chapter 2

Here we can apply some simplification to Schrödinger equation. Since the mass of the nucleus is much heavier than that of the electron, nuclei move much slower than the electrons. Thus, electrons can be considered to be moving in the field of fixed nuclei. Since the nuclei are considered to be stationary in the space, their kinetic energy becomes zero and nuclei-nuclei interaction term that indicates potential energy becomes a constant value. This approximation is known as the Born-Oppenheimer approximation [89]. By applying this approximation, the Hamiltonian operator can be separated into nuclear and electronic Hamiltonian parts and written as

1 1 = + = − ∇ − + (2.4) 2 This approximation also allows us to write the total energy as the sum of electronic energy and the constant nuclear repulsion term.

= + = + (2.5)

Then we just need to calculate the electronic energy, Eelec , using the electronic wavefunction,

Ψelec , and the electronic Hamiltonian, Helec , only.

= (2.6)

The electronic wavefunction Ψelec is a function of the electron coordinates and the spins of N electrons of the system. However, nuclear coordinates only join parametrically and do not explicitly appear in Ψelec [90].

= (, , , , … , ) (2.7) and

= , (2.8)

THEORY Chapter 2

where ri is the vector position of electron i and ωi indicates its spin. Thus, the electronic wavefunction becomes a function of 4N variables consisting of the three coordinates and the spin for each electron.

Since the Schrödinger equation is exactly soluble only for one electron systems, it is not possible to solve Equation (2.6) searching through N-electron wavefunction. At this point, making of some approximations again become necessary. Here we utilize from Hartree-Fock approximation (also known as Self-Consisted Field , SCF approximation) [91, 92, 93, 94] that approximates the many-particle solution of N-electron wavefunction by N one-electron wavefunctions, . Then Hartree product, as an approximation for N-electron wavefunction, Ψelec is defined as

(, , , … , ) = ()()() … () (2.9) where one-electron wavefunctions, are the spin orbitals. The Hartree scheme allows the approximation that

≈ ℎ (2.10) where hi is the one-electron Hamiltonian for electron i, and

= (2.11) where the summation of the Eigenvalues εi of the one-electron wavefunctions give the electronic energy. Thus, the Schrödinger equation based on the Hartree approximation becomes

= (2.12) However, since electrons have spin, they must obey the Pauli exclusion principal which states wavefunction must be antisymmetric with respect to exchanging any two electrons [95]. That 15

THEORY Chapter 2

is, the electronic wavefunctions must change sign whenever the coordinates of two electrons are interchanged. Fock postulated that the wavefunction defined as the Hartree product does not obey the antisymmetry condition [94]. Then Slater [96, 97] expressed the wavefunction according to Fock’s suggestion as a determinant as follows

() () .... ()

1 () () .... () = : : : (2.13) ! .... : : .... : () () () where indicate spin orbitals that each is a function of spatial coordinates and a spin function, N is the total number of electrons and the term is a normalization factor. ΨSlater is known as Slater determinant that indicates a Hartree-Fock! or SCF wavefunction. However, the definition of spin orbitals remains a problem. At this stage, Hückel’s linear combination of atomic orbitals (LCAO) [1, 98, 99, 100] approximation helps to represent molecular orbitals as linear combinations of atomic orbitals for the constituent atoms. This approximation is shown as

= (2.14) where NAOs is the number of atomic orbitals in the system, φj is an atomic orbital in a molecular orbital , and is the coefficient of atomic orbital φj. According to the variational principle, there are no solutions with a lower energy than the correct wavefunction. At this point, the wavefunction still cannot be solved directly, but solutions can be found by using a set of guessed molecular orbitals, and then iterations are done until the energy converges to its minimum while the electron density does not vary. Detailed discussions of this procedure are available in several textbooks [27, 45, 47, 90].

THEORY Chapter 2

2.2 Methods and Hamiltonians

Semiempirical methods, in general, distinguished from each other by the electrons being treated (e.g., models based on π-electron or all valence-electron treatment), the systems to which they can be applied (e.g., non-planar, planar conjugate systems), the differential overlap being neglected (e.g., CNDO, INDO, NDDO approximations), the treatment of core- core repulsion term (e.g., using of element-specific or element-pair specific parameters in the core repulsion function), the parameterization strategy (e.g., by chemical intuition or fully automated), values of the parameters (e.g., methods using the same formalism and the same set of approximations such as AM1 and RM1). There are many of semiempirical methods available in the literature that are distinguished by these differences, and also several hybrid methods exist.

In the following sections, we examine the NDDO methods, or in other words MNDO-like methods, in a more detailed theoretical frame for the most widely used and most popular semiempirical methods.

2.2.1 MNDO

Since MNDO is the first and the oldest of the NDDO-based techniques, and the theory and the approximations used in MNDO are very significant to the following methods, we will examine it very closely.

MNDO, in a general sense, evaluates one-center two-electron integrals based on spectroscopic data for isolated atoms, and evaluates other two-electron integrals using the idea of multipole- multipole interactions from classical electrostatics. In MNDO, various integrals are not determined analytically, rather numerical parameters are adjusted to fit the experimental data.

For closed-shell molecules and the valence electrons in them, the MNDO formalism uses the frozen core approximation (electrons move in the field of a fixed core composed of the nuclei and inner shell electrons) and the valence shell molecular orbitals χi and the corresponding orbital energies εi are obtained from the solution of the secular equations.

THEORY Chapter 2

= (2.15) where φi represents atomic orbitals of valence electrons. The coefficients cµi are calculated from the Roothaan-Hall [101, 102] equations which take the form given below in the NDDO approximation (the overlap matrix S µν = δµν for NDDO).

0 = ( − ) (2.16) where εi is the Eigenvalue of the molecular orbital χi, and δµν is the Kronecker-delta (equal to one if µ = ν and zero otherwise).

Considering the atomic orbitals φµ and φν centered at atom A, and the atomic orbitals φλ and

φσ at atom B (A ≠ B), the NDDO Fock matrix elements for MNDO are defined as below [28, 37].

For the most complex element, the diagonal element, it is written as

1 = + (| ) − (| ) + (|) (2.17) 2 where Hµµ and Pµµ are elements of one-electron core Hamiltonian and Hµµ is given as

= + , (2.18) The off-diagonal elements when two basis functions µ and ν are on the same atom A, are represented as

1 = + 3(| ) − (| ) + (|) (2.19) 2 where

THEORY Chapter 2

= , (2.20) and the off-diagonal elements when the basis function µ is on atom A and λ is on atom B are given by

1 = − (|) (2.21) 2 where

1 = = + (2.22) 2

Here, Hµλ (and so βµλ ) represents two-center one-electron core resonance integrals, which mainly contribute to the bonding energy of a molecule, Sµλ are called overlap integrals, and

Pλσ is the density matrix. βµ is an adjustable parameter that is characteristic of φµ atomic orbital at atom A, and βλ is an adjustable parameter of φλ atomic orbital at atom B. For the first-row elements there are at most only two different β parameters (βs and βp) to be optimized since these atoms contain only s- and p-orbitals. On the other hand, for nitrogen and oxygen atoms these two parameters are set equal and not optimized separately ( βs = βp for N and O atoms).

Vµµ ,B and Vµν ,B are two-center one electron attractions between an electron distribution φµφµ or

φµφν, respectively, on atom A and the core of atom B. These terms are given by the expressions below.

, = −(|) (2.23) , = −(|) (2.24) If we summarize, the energy terms and interactions given below are included in MNDO methodology [28, 37]:

- one-center one-electron energies Uµµ (as part of Hµµ ), which present the sum of kinetic

energy of an electron in AO φµ at atom A and its potential energy due to the attraction by core of atom A.

THEORY Chapter 2

- one-center two-electron repulsion integrals, i.e., Coulomb integrals ( µµ |νν ) = gµν and

exchange integrals ( µν |µν ) = hµν ,

- two-center one-electron core resonance integrals βµλ = Hµλ , - two-center one-electron integrals representing electrostatic core-electron attractions

Vµν ,B , between an electron in the distribution φµφν at atom A and the core of atom B, - two-center two-electron repulsion integrals ( µAνA|λBσB), - two-center core-core repulsions

In the MNDO methodology, one must consider that Slater-type orbital exponents ( ζs and ζp), which are not shown above explicitly, for the s- and p-orbitals for each element are set equal to one another ( ζs = ζp). Additionally, one-center two-electron repulsion integrals gss , gpp , gdd , gsp , hsp are taken from atomic spectra provided by Oleari [44] and not optimized.

The total energy of a molecule, Etot , is represented by the sum of its electronic energy, Eel , and the repulsion energy, , between the cores of atom A and B.

= + (2.25) and the electronic energy is given as

1 = ( + ) (2.26) 2 where Hµν is the one-electron part of core Hamiltonian.

The core-core repulsion energy term, , of the MNDO method has the form of

= (|) + ( ) (2.27) where the net electrostatic repulsion between two neutral atoms f(RAB ) is defined as

( ) = (|) + (2.28)

THEORY Chapter 2

Additionally, for the pairs N-H and O-H interactions are treated separately as follows since Dewar found it advantageous.

( ) = (|) + (2.29) And finally, in MNDO the core-core repulsion terms, , becomes

= (|)1 + + (2.30) and (if A = N, O and B = H)

= (|)1 + + (2.31) where ZX (X = A, B, H) is the effective (valence only) charge of the element, (where X = B, H) is a two-center integral of type ( ss|ss ), αX (X = A, B, H) is the( adjustable | ) element specific parameter, and RAB is the distance between atoms A and B (or H, if B = H).

Beside these parametric functions and description of the approximations presented above, MNDO was the first method that could represent lone-pair lone-pair interactions which had been ignored by the previous methods. This made MNDO very popular and very accurate comparing to previous methods. However, over the years, some deficiencies of MNDO became apparent. The most important of those was its inability to model systems containing hydrogen bonds accurately. It was almost not able to reproduce hydrogen bonds. A second deficiency was related to hypervalent compounds, i.e., difficulties in accurately predicting of energies, geometries and correct point groups.

2.2.2 AM1

AM1 [39] is currently one of the most commonly used of the Dewar-type methods. It was the next semiempirical method introduced by Dewar and coworkers in 1985 following MNDO. It is simply an extension, a modification to and also a reparameterization of the MNDO method. AM1 differs from MNDO by mainly two ways. The first difference is the modification of the core repulsion function. The second one is the parameterization of the overlap terms βs and βp,

THEORY Chapter 2

and Slater-type orbital exponents ζs and ζp on the same atom independently, instead of setting them equal as in MNDO. MNDO had a very strong tendency to overestimate repulsions between atoms when they are at approximately their van der Waals distance apart. To overcome this hydrogen bond problem, the net electrostatic repulsion term of MNDO, f(RAH) given by Equation (2.29), was modified in MNDO/H [38] to be

( ) = ( | ) (2.32) where α was proposed to be equal to 2.0 Å -2 for all A-H pairs. On the other hand, the original core repulsion function of MNDO was modified in AM1 by adding Gaussian functions to provide a weak attractive force [39].

The core-core repulsion energy term in AM1 is given by

= (1 + + + + 2.33 where Gaussian functions F(A) and F(B) are expressed by

, , = , 2.34

, , = , 2.35 And finally AM1 core-repulsion function becomes

, , , , , , = + + 2.36

In this equation, K, L and M are the Gaussian parameters. The remaining parameters have the same meaning as in the previous section. L parameters determine the widths of the Gaussians and were not found to be critical by Dewar. Therefore, a common value was used for many of

THEORY Chapter 2

the L parameters. On the other hand, all K and M parameters were optimized. Each atom has up to four of the Gaussian parameters, i.e., K 1, …, K 4, L 1, …, L 4, M 1, …, M 4. Carbon has four terms in its Gaussian expansion whereas hydrogen and nitrogen have three and oxygen has two terms (only K 1, K 2, L 1, L 2, M 1, M 2). Because in AM1, for carbon, hydrogen and nitrogen both attractive and repulsive Gaussians were used whereas for oxygen only repulsive ones considered. Addition of Gaussian functions into the core-repulsion function significantly increased the number of parameters to be optimized and made the parameterization process more difficult. As for original MNDO, one-center two-electron repulsion integrals gss , gpp , gdd , gsp , hsp are assigned to atomic spectral values and not optimized.

In contrast to MNDO, in which parameters were first optimized for carbon and hydrogen together and then other elements added one at a time, by increased computer resources and improved optimization procedure a larger reference parameterization dataset was used in the parameterization of AM1. All the parameters for H, C, N and O were optimized at once in a single parameterization procedure. Optimization of the original AM1 elements was performed manually by Dewar using chemical knowledge and intuition. He also kept the size of the reference parameterization data at a minimum by very carefully selecting necessary data to be used as reference. Over the following years many of the main-group elements have been parameterized keeping the original AM1 parameters for H, C, N and O unchanged. Of course, a sequential parameterization scheme caused every new parameterization to depend on previous ones, which directly affects the quality of the results.

AM1 represented a very considerable improvement over MNDO without any increase in the computing time needed. AM1 has been parameterized for many of the main-group elements and is very widely used, keeping its popularity in organic compounds’ modeling due to its good performance and robustness. Although many of the deficiencies in MNDO were corrected in AM1, it still has some important limitations as outlined in the historical development section.

2.2.3 PM3

Both MNDO and AM1 had been parameterized by hand with the help of chemical knowledge and intuition using few reference data. Stewart had a more mathematical philosophy for the parameterization procedure and thought automated search of parameter space using complex 23

THEORY Chapter 2

optimization algorithm might be more successful to obtain better parameters. He made an optimization process by deriving and implementing formulae for the derivative of a suitable error function with respect to the parameters.

= − 2.37 where S is defined as the sum of the squares of the differences between calculated or predicted ( ) and reference values ( ) for reference functions. The parameter set is modified to minimize the value of S, and parameters are considered as optimized when for a given set of parameters, the sum square of errors, S, is a minimum.

In PM3, for each of the element’s parameter set consists of 18 parameters ( Uss , Upp , βs, βp, ζs,

ζp, α, gss , gpp , gsp , gp2 , hsp , K1, K 2, L 1, L 2, M 1, M 2) except for hydrogen, which has 11 parameters only since parameters related to p-orbitals are not included. As different from

MNDO and AM1, in PM3 the one-center electron repulsion parameters are ( gij , hij ) optimized instead of assigning to atomic spectral values. PM3 also shares the same core-repulsion function with AM1 which is given as

, , , , , , = + + 2.38 but it uses only two Gaussian terms ( i = 1, 2 and j = 1, 2 above) for each atom instead of four in AM1 ( i = 1,...,4 and j = 1,…,4).

In the initial parameterization of PM3, twelve elements (H, C, N, O, F, Al, Si, P, S, Cl, Br and I) were optimized simultaneously and then following parameterizations were carried out keeping the parameters for these elements fixed. PM3 may have global minimum in comparing with MNDO and AM1, but this global minimum is obtained for a specific penalty function used and it is heavily affected by the type of compounds included in the parameterization dataset. Thus, it does not necessarily supersede MNDO and AM1 especially for any particular type of problem. Known deficiencies of PM3 have been given in detail in the historical development section. 24

THEORY Chapter 2

2.2.4 PM6

PM6 uses most of the approximations used in AM1 and PM3 but also several modifications have been made. After Voityuk and Rösch [61] proposed using diatomic parameters within the core-core interaction term has, this modification was tested for couple of element pairs in PM3 and in every case the average error decreased. Voityuk and Rösch’s modification to core-repulsion function that they used in molybdenum parameterization for AM1(d) [61] was,

= 1+ 2.39

In this equation, δAB and αAB are element-pair specific parameters.

Further examination also showed that inclusion of diatomic parameters into the core-repulsion function always resulted with an increase in accuracy. Thus, Stewart decided to use Voityuk and Rösch’s approximation instead of those used in MNDO and AM1 for the core-core interaction in PM6 [72]. At increasing interatomic distance, RAB , the AM1(d) core-repulsion function converges to the exact point-charge interaction. However, Stewart found that especially for rare gas interactions the addition of a small perturbation to the core-repulsion function results in an increase in the accuracy and it is generally beneficial [72]. So, the general form of the core-repulsion function used in PM6 is given as

. = 1+ 2.40 For small interatomic distances, and have very similar behavior. But for large distances longer than about 3 Å, PM6 core-repulsion function becomes significantly smaller than the AM1(d) approximation.

For several diatomic interactions, the general form of the PM6 core-repulsion function presented above was modified when a specific fault was detected and existing approximation was inadequate.

After optimizations, it was found that the calculated hydrogen bond interaction energy was too small and to correct this fault the core-repulsion function was modified only for the C-H and O-H interactions as 25

THEORY Chapter 2

= 1+ 2.41 where A represents carbon or oxygen atom. Especially at hydrogen bonding distances around 2 Å this expression becomes important. By a decrease in the value of the exponential term, hydrogen bond energy increases and the fault is corrected.

Additionally, compounds containing –C≡C– groups were found to be about 10 kcal mol -1 too stable per –yne group by using the general form of the PM6 core-repulsion function. To overcome this fault, only for C-C interactions the core repulsion function was modified to give

. . = 1+ + 9.28 2.42 where indices A and B represent different carbon atoms in the interaction.

After optimization of all parameters, during the test process, Stewart noticed that neutral silicate layers of the type found in talc (H 2Mg 3Si 4O12 ) were slightly repulsive instead of being slightly bound. To correct this fault again a perturbation was added for Si-O interactions.

. . = 1+ − 0.0007 2.43 where indices A and B represent silicon and oxygen atoms.

Additionally in PM6, d-orbitals were also added to many of the main-group elements and transition metals due to their well-known effect which results with a significant increase in the accuracy of the predictions as proved before [34, 48, 49, 50].

Stewart followed a different parameterization strategy during the parameterization of PM6 that can be considered as another difference between PM6 and the previous methods. First, H, C, N and O were parameterized simultaneously. Then the parameters for these elements were held constant and F, P, S, Cl, Br and I were optimized one at a time. The parameters for all these elements were then reoptimized simultaneously. Once parameters were obtained for these 10 elements, the remaining main group elements were parameterized following the same

THEORY Chapter 2

sequence and procedure. In this way, parameters for all 39 main-group elements plus Zn, Cd and Hg (that behave like main group elements) were obtained. This was followed by the parameterization of 27 transition metals and lanthanide Lu. At this stage, the parameters for previous 42 elements were held constant and only transition metal and Lu parameters were optimized. They were not optimized simultaneously with the main group elements later, just to prevent any possible corruptive effect of transition metals on the main group-elements, because the reference data for transition metals was of poor quality. The performance of PM6 is generally better than or comparable to previously available methods for the main-group elements. However, a statistical analysis [72] showed that a recent reparameterization of AM1 method, namely RM1 [71], performed more accurately than PM6 and any of the other NDDO methods for organic compounds. The performance of PM6 for heats of formation of common organic compounds, including H, C, N, O, F, P, S, Cl and Br atoms, is better than both B3LYP and HF methods at the 6-31G(d) level. However, in prediction of geometries PM6 is somewhat worse, and for electronic properties, i.e., ionization potentials and dipole moments, it performs significantly worse than B3LYP and HF.

Stewart interestingly did not compare the performance of PM6 for transition metals with any of available methods, particularly PM5 which was almost the only available method for many of transition metals at that time. In the following sections we will examine it in detail.

2.2.5 AM1*

AM1* [66, 67, 68, 69, 70, 87] was introduced as an extension to original AM1 technique. AM1* uses standard MNDO approximations for all integrals involving s- and p-orbitals and MNDO/d approximations for those including d-orbitals. While the original AM1 parameterization was retained for the elements H, C, N, O and F, new elements have been parameterized with the addition of d-orbitals. AM1* also uses Gaussian functions in the core- repulsion functions that are also common for AM1, PM3 and PM5 for the elements H, C, N, O and F. Therefore, AM1* is identical to AM1 for the compounds that only contain these five elements.

The core-repulsion function of AM1* for H, C, N, O and F core-core interactions is given as

THEORY Chapter 2

∗ , , , , , , = + + 2.44 where A, B = H, C, N, O and F.

However, AM1* uses another core-core interaction formalism for the rest of the elements that was introduced by Voityuk and Rösch [61]. This formalism with element-pair specific parameters in the core-repulsion function was found to be more effective. However, using these parameters brings the disadvantage of requiring specific parameterization of these terms for every pair of elements. Fortunately, core-repulsion functions with these element-pair specific parameters does not lead to false minima as Gaussian functions can.

Thus, for the newly parameterized elements, the core-repulsion energy used in AM1* is given as

∗ = 1+ 2.45 where αAB and δAB are the element-pair specific parameters to be optimized, ZA and ZB are the effective (valence only) core charges of elements A and B, RAB is the distance between the atoms A and B, and is two-center integral which was defined in original MNDO/d [34, 48, 49, 50, 52, 103] method as follows:

/ = , = + + 2.46 where are the independent adjustable element specific parameters so that the balance between and attractive and repulsive Coulomb interactions is determined.

Additionally, in AM1* core-core interactions of hydrogen with the elements starting from second long row are represented as

∗ = 1+ 2.47 where A ≠ H, C, N, O, F.

THEORY Chapter 2

Details related to parameterization techniques, preparation of parameterization dataset etc. are given in the following sections and will not be described further here.

THEORY Chapter 2

PARAMETERIZATION OF SEMIEMPIRICAL METHODS Chapter 3

3 PARAMETERIZATION OF SEMIEMPIRICAL METHODS

3.1 Introduction to Parameterization Methodology

There are three main objects that directly affect the performance of semiempirical methods. These are the set of the approximations used within methodology, the quality and the reliability of the data used as reference for parameterization, and the parameterization itself [104]. Parameterization is a very important part of the development of a new method and the accuracy of the method heavily depends on the quality of the parameters generated. The main purpose of parameterization is to generate set of optimum values for parameters to fit predicted values to reference data. This process allows the assignment of specific values to quantities that are not experimentally available.

There are three main stages in the parameter optimization: Collecting reference data, relative weights of the properties, and optimization of parameters.

3.2 Reference Data

Construction of a valid reference data set is very important in the parameterization because the training data set is required to be sufficiently diverse to allow the parameters used in the method to be defined. This data set should also reflect the main characteristics of the method that it is designed for. Thus, the data must be as accurate as possible and it must represent a wide range of chemical systems and properties. It must also be suitable to be manipulated by mathematical tools and the parameter optimization program. Reference data may be based on either experimental data or results obtained from high-level ( ab initio or DFT) calculations. Also, as in our case, the data may be a well combination of experimental data and high-level calculation results. Using only experimental data, e.g., as used in the AM1 parameterization, has the advantage of circumventing any theoretical inadequacy of high-level methods [105]. If a semiempirical method is parameterized mostly using high-level reference results, then any possible errors in that model will be reproduced by the semiempirical method, too. On the

PARAMETERIZATION OF SEMIEMPIRICAL METHODS Chapter 3

other hand, lack of experimental data or presence of unreliable experimental data, especially as in the case of transition metals, makes the use of reference results obtained from high-level calculations necessary. One must consider that results obtained from ab initio methods are sufficiently accurate and reliable to be able to challenge experimental results in many areas [106].

Heats of formation, molecular geometries, dipole moments and ionization potentials are the most important properties used in parameterization. Heats of formation and molecular geometries provide information about the energy hypersurface, whereas dipole moments and ionization potentials provide information on the electronic structure. Bond lengths between the atoms that are chemically bonded and non-covalently bonded, i.e., hydrogen bonds, bond angles including dihedral and torsion angles, are used as geometrical properties in parameterization. Generally, the largest source for the geometric data is X-ray measurements. The Cambridge Structural Database (CSD) [107] is one of the best-known and the largest sources available for crystal structures. Using data from microwave measurements is also possible but they are limited to the vapor phase. High-level ab initio or DFT calculations are always the savior in the absence or unreliability of experimental data.

Beside heats of formation, other properties such as reaction enthalpies, conformational energies and also rotational barriers may be used in parameterization as energetic data. Since semiempirical calculations model isolated molecules, the reference energetic data used for parameterization should apply to gas-phase systems at 298 K and one atmosphere. Cox and Pilcher [108] for organic and organometallic compounds, the JANAF tables [109] for inorganic compounds, and the NIST Webbook [110] as general, are good thermochemical data sources. Again, ab initio and DFT calculations serve as good sources. Clark and Winget have published an atom-additive scheme for producing formation enthalpies accurately at 298 K using density functional theory [111].

Dipole moments are probably the least accurate ones within all types of reference data used [104]. Since no single large source is available for dipole moments, data are collected from various individual articles and determined using the Stark effect, and high-level calculations. Levin and Lias [112] have provided a large source for ionization potentials beside the NIST Webbook [110]. In the parameterization of semiempirical methods, mostly the first ionization

PARAMETERIZATION OF SEMIEMPIRICAL METHODS Chapter 3

potential is used. And this can also be determined using ab initio calculations from Koopmans’ theorem.

3.3 Relative Weights of the Properties

After all reference data, i.e., heats of formation, geometric properties, dipole moments, ionization potentials, etc., are collected, they must be rendered into dimensionless quantities. This step is called as weighting and once data is weighted it can easily be manipulated. The weighting factors to make properties dimensionless are listed in Table 3.1.

Table 3.1: Weighting factors for reference quantities [28] Reference Data Weight Factor Heat of Formation 1.0 mol kcal −1 Bond Length 100 Å −1 Bond Angle 2/3 degree −1 Dipole Moment 20 debye −1 Ionization Potential 10 eV −1

In addition to this, Stewart has shown unusual weighting factors for geometries, in that the quantity that is being fitted is not the reference data itself, it is not the geometry, but the calculated forces acting on the reference geometry [104]. They are given in Table 3.2.

Table 3.2: Weighting factors for reference quantities Reference Data Weight Factor Heat of Formation 1.0 mol kcal −1 Bond Length 0.7 Å mol kcal −1 Bond Angle 0.7 Å mol kcal −1 Dipole Moment 20 debye −1 Ionization Potential 10 eV −1

By using forces instead of geometries, saving in computation time has been aimed, and this aim has been achieved without any loss in generality. Though everything seems very automated, sometime personal intervention, in other words some restrictions, may be necessary especially in the using of weighting factors.

PARAMETERIZATION OF SEMIEMPIRICAL METHODS Chapter 3

3.4 Parameter Optimization Procedure

In the optimization of parameters, the error function plays the most crucial role. The error function is defined as the sum of the squares of the weighted difference between calculated values and reference values of a quantity obtained for a set of adjustable parameters. It is formulated as

= − 3.1 where S is the error function, is calculated and is reference value for a reference quantity, and wi is the weighting factor.

For optimization, parameters are modified to minimize the value of the error function, S. Then parameters are considered as optimized when two conditions are satisfied. The first derivative of the error function with respect to all parameters must be zero, and the second derivative is positive.

= 0, > 0 3.2 To prove that second condition is valid, it is necessary to show that the lowest eigenvalue, ε, of the matrix of second derivatives of the error function with respect to all parameters (considering there are n different parameters) is positive [46].

⋯ ⋮ ⋮ ⋱ ⋮ = , > 0 3.3 ⋯ Several decades ago in the first days of the development of the new semiempirical methods, to make an initial guess for the parameter set in the parameterization of a new element was an important problem. Because, there was no previous parameterization work available in the literature to make use of it. But today, many different semiempirical methods with the parameters of many elements are available. So, before assigning parameters to some random 34

PARAMETERIZATION OF SEMIEMPIRICAL METHODS Chapter 3

values and starting to optimize them, it can be very useful to perform a literature search for parameters of an element whether its parameters are already available for another semiempirical method or not. Since many parameters are common in different types of the semiempirical methods, using available parameters from another method as starting parameters may significantly help saving time and get rid of the false or spurious minima problem. In the absence of parameters for the element in hand, taking of parameters that belong to an other element in the same group of the periodic table may also be helpful for a starting guess.

PARAMETERIZATION OF SEMIEMPIRICAL METHODS Chapter 3

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4 RESULTS OF AM1* PARAMETERIZATIONS

4.1 Parameterization Data

For the parameterizations, we have used experimental heats of formation and also used a small series of model compounds whose heats of formation we have derived from DFT or ab initio calculations. As in previous AM1* parameterizations [69, 87], we checked that experimental values for heats of formation were reasonable using DFT calculations. The target values used for all of the parameterizations and their sources are defined in the tables of the Supplementary Material presented in our recently published articles relating to each element [66, 67, 68, 70].

DFT calculations used the Gaussian 03 suite of programs [113] with the LANL2DZ basis set and standard effective core potentials [114, 115, 116, 117] augmented by a set of polarization functions [118] (designated LANL2DZ+pol) and the B3LYP hybrid functional [119, 120, 121]. In some cases, coupled cluster calculations with single and double excitations and a perturbational corrections for triples (CCSD(T)) [122, 123, 124, 125] with the 6-311+G(d) basis set [126, 127, 128, 129, 130, 131] were used to check values for which DFT may be unreliable. For example, in the parameterization of bromine and iodine, we paid special attention to the heats of formation of titanium and zirconium halides, some of which appear to be significantly in error. The data and reactions used to derive the recommended heats of formation for chlorides, bromides and iodides of these two elements are defined in detail in the Supplementary Material [67], as are the other parameterization data and their sources.

− Another very important correction was applied to VCl 2 using DFT and heat of reaction − during the parameterization of vanadium element. The heat of formation for VCl 2 was changed significantly from the NIST value (-284.2 ± 5.0 kcal mol −1, claimed to be taken from [132]). Examination of the original literature revealed that the calculations are based on work on VCl 2 [133]. In our work, the following heat of reaction (gas phase) is reported. ° Using the standard heatsVCl of formation→ V + 2Cl of vanadium ∆H = 239.5(123.20 kcal kcal mol mol −1) and chlorine (28.992 −1 ° −1 kcal mol ) atoms [110], we obtain (VCl 2) = -58.3 kcal mol . This value is not included ∆H 37

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

in the NIST WebBook. The two different values given for the electron affinity of VCl 2 (-0.3 ° − −1 and 1.2 eV) [133] give (VCl 2 ) = -51.4 or -86.0 kcal mol . The NIST value of -284.2 ± 5.0 kcal mol −1 is close to∆H the sum of the heat of reaction given above and the electron affinity of 1.2 eV (-267.2 kcal mol −1), so that this may be the source of the error.

− −1 We have derived a heat of formation for VCl 2 of -58.8 kcal mol using DFT calculations (see Supporting Information [68]) which is also close to the PM5 [62] and PM6 [72] heats of −1 − formation (-52.1 and -94.5 kcal mol , respectively) for VCl 2 . We have used this value for − the parameterization. Neither VCl 2 nor VCl 2 were used for the parameterization of PM6 [72].

Experimental parameterization data were generally taken largely from the NIST Webbook [109], but also from the OpenMopac collection [134]. As in the case of copper and zinc parameterization [66], additional sources like MNDO/d [34, 135] and AM1-Zn [37] parameterization datasets, and also for heats of reaction CRC Handbook [136] and Hildebrand [137] were used. All the other experimental and theoretical sources are given in the Supplementary Material of the relating element parameterization articles [66, 67, 68, 70].

In addition to the energetic data, geometries, dipole moments and ionization potentials taken from the above sources, crystal structures from the Cambridge Structural Database (CSD) [107] were used in the parameterizations to ensure that not only the energetic and electronic properties for the “prototype” compounds, but also the structures of large transition metal compounds are well produced.

4.2 Parameterization of Vanadium and Chromium

4.2.1 Results

The optimized AM1* parameters for vanadium and chromium [68] are shown in Table 4.1. Geometries were optimized with the new AM1* parameterization using VAMP 10.0 [138], while the PM5 calculations used LinMOPAC2.0 [62] and those with PM6 used MOPAC2007 [139]. The three programs give essentially identical results for the Hamiltonians that are available in all three.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.1: AM1* parameters for the elements V and Cr. Parameter V Cr

Uss [eV] -32.5007313 -21.5000000 Upp [eV] -22.8176012 -15.0000000 Udd [eV] -34.6990829 -56.0000000 -1 ζs [bohr ] 2.3438708 1.5551176 -1 ζp [bohr ] 1.8676559 17.0408948 -1 ζd [bohr ] 1.5941826 2.1098056 βs [eV] -1.1782158 -8.6646957 βp [eV] -1.3164040 -34.3489849 βd [eV] -2.9814499 -15.0408921 gss [eV] 6.6351662 8.1213983 gpp [eV] 14.5104896 15.1012780 gsp [eV] 9.6218429 14.1688433 gp2 [eV] 5.9416348 14.6285467 hsp [eV] 3.3478389 3.1759218 -1 zsn [bohr ] 1.6228539 12.5465123 -1 zpn [bohr ] 0.7296035 0.6411768 -1 zdn [bohr ] 1.0967084 1.4560578 ρ(core) [bohr -1] 1.9933766 1.3878582 -1 ∆H° f(atom) [kcal mol ] 122.9 95.0 0 F sd [eV] 6.7975092 4.0400000 2 G sd [eV] 1.6923888 5.5000000 ααα(ij) H 3.6013897 2.8199706 C 3.7725836 3.7290093 N 2.4888949 3.3339752 O 2.6735090 3.5657676 F 3.0683228 5.0646274 Al 3.2984193 1.3373658 Si 3.3162937 0.8315555 P 3.8585547 2.2001523 S 4.0661894 1.1565308 Cl 3.3918803 4.2139509 Ti 1.7021094 2.3540000 V 5.2583117 1.9587210 Cr 1.9587210 1.8584457 Cu 3.7398185 2.3450000 Zn 3.6692571 2.4225000 Br 3.4607221 2.4900000 Zr 2.9324325 1.9546000 Mo 1.3354356 1.9985000 I 3.6466767 2.0965000 δδδ(ij) H -10.0286441 -4.6277736 C 52.7142817 24.8021840 N 4.5648766 8.7064523 O 6.6835854 9.7960490 F 12.1347506 98.3067342 Al 43.9618494 1.0379731 Si 47.3637663 0.1916771 P 121.0494602 2.9142566 S 105.6181605 0.2808183 Cl 40.9704281 92.6763694 Ti 0.6073749 4.5000000

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

V 38.9295618 3.0959306 Cr 3.0959306 1.7368306 Cu 107.0552941 3.6560000 Zn 83.5135611 3.0320000 Br 44.6144240 3.0600000 Zr 5.1029965 4.1854000 Mo 0.9513533 3.2166000 I 138.6470845 1.4262000

4.2.1.1 Vanadium

4.2.1.1.1 Heats of Formation of Vanadium Compounds

The calculated heats of formation for our training set of vanadium compounds are shown in Table 4.2. We have compared our results with Stewart’s recently published PM6 method [72] and also unpublished PM5 method implemented in LinMopac [62].

Statistically, AM1* reproduces heats of formation for the training set of vanadium compounds better than PM6 and far better than PM5. As before, however, we note that this comparison is not strictly valid as it is based on the current parameterization data, which sometimes differ from those used for PM5 and PM6. The mean unsigned error (MUE) for the AM1* parameterization dataset is 22.6 kcal mol −1, compared with 25.3 and 59.0 kcal mol −1 for PM6 and PM5, respectively. The parameterization data set for PM5 has not been published, but clearly does not cover the range of compounds used for AM1*. AM1* tends to overestimate heats of formation of vanadium-containing compounds by only 2.2 kcal mol −1 while PM6 and PM5 tend to give more positive systematic errors with MSEs of 6.0 and 12.9 kcal mol −1, respectively.

−1 The largest positive errors for AM1* are found for the molecules VCl 2 (88.9 kcal mol ), VCl −1 − −1 −1 −1 (73.5 kcal mol ), VCl 3 (71.9 kcal mol ), VCl 3 (60.9 kcal mol ), VCl 4 (60.4 kcal mol ), and −1 − V2C22 N4H20 O8 (CEKHUV) (50.9 kcal mol ). The largest negative errors are found for V 2Cl 9 −1 2+ −1 −1 (-131.0 kcal mol ), V(NH 3)6 (-104.7 kcal mol ), and V(CN) 5 (-72.2 kcal mol ). Generally, large errors in AM1* come from chlorinated compounds and also from the compounds that contain original AM1 elements. As before, we attribute this to a weakness in the AM1* parameterization for the chlorine and also general weakness of the original AM1 parameterization. In addition, as we have faced in our previous AM1* parameterizations, oxygen-containing compounds give systematic errors. Errors for some oxygenated 40

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

−1 2+ 3+ compounds are found as -52.4, -34.6, -22.1 and -23.4 kcal mol for V(H 2O) 6 , V(H 2O) 6 , − − VO 3 and VO 2 , respectively. These results are analogous to those obtained for other elements and we attribute the performance limits to the fact that AM1* uses the unchanged AM1 parameterization for the elements H, C, N, O and F, which limits the possible accuracy of the parameterization. However, this does not explain the large errors for VC 4H8S5 (CUSPOV) −1 − −1 −1 −1 (-68.4 kcal mol ), VBr 4O (-41.5 kcal mol ), VI (39.5 kcal mol ), HVZr (-33.6 kcal mol ), −1 + −1 V2Br 4 (-36.6 kcal mol ) and VBr 4 (24.4 kcal mol ). With the exception the hydrogen in − HVZr, the carbon and the hydrogen in VC 4H8S5 and the oxygen in VBr 4O , these compounds contain only “pure” AM1* elements. This is likely to be a consequence of our sequential parameterization strategy, in contrast to the simultaneous parameterization used for PM6 [72], aggravated by using the original AM1 parameters for H, C, N, O and F. Nevertheless, on aggregate AM1* performs comparably to or better than the other available methods for the heats of formation of vanadium compounds.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.2: Calculated AM1*, PM6 and PM5 heats of formation and errors compared with our target values for the vanadium-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The coded-names within parentheses indicate the CSD-names of the compounds. Target AM1* PM6 PM5

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error V– 110.8 113.7 2.9 135.6 24.8 183.0 72.2 V 122.9 122.9 0.0 122.9 0.0 116.0 -6.9 V+ 277.4 256.8 -20.6 244.3 -33.1 306.0 28.6

V2 187.4 176.9 -10.5 188.5 1.1 295.2 107.8 VH 125.9 114.8 -11.1 86.0 -39.9 133.5 7.6

VH 2 72.4 107.0 34.6 93.0 20.6 159.3 86.9 – V(CO) 3 -62.2 -82.7 -20.5 -62.6 -0.4 -38.2 24.0 – V(CO) 4 -129.0 -141.6 -12.6 -111.7 17.3 -62.9 66.2 – V(CO) 5 -186.6 -184.7 1.9 -204.7 -18.2 -140.9 45.6 – V(CO) 6 -265.3 -234.3 31.0 -262.3 3.0 -183.9 81.4 VC 10 H10 48.6 35.2 -13.4 49.6 1.0 33.8 -14.8 VC 12 H12 25.6 30.1 4.5 42.2 16.6 29.5 3.9 VC 14 H22 (COGXOL) 28.7 9.9 -18.8 13.6 -15.1 16.1 -12.6 VC 4O10 (AOXOVA) -409.0 -409.9 -0.9 -430.1 -21.1 -487.1 -78.1 VC 4H2O10 (AOXVAN10) -541.4 -541.9 -0.5 -529.3 12.1 -619.2 -77.8 VC 4H4O10 (DABKEW) -498.7 -549.5 -50.8 -534.2 -35.5 -641.1 -142.4 VC 6H6O10 (AJUJEU) -551.0 -561.7 -10.7 -569.5 -18.5 -657.1 -106.1 VC 6H15 O4 (Vanadium(V) tri-ethoxide oxide) -242.5 -260.4 -17.9 -273.4 -30.9 -235.6 6.9 VC 10 H14 O5 (Vanadium(V)diacetylacetonate oxide) -293.0 -256.7 36.3 -267.4 25.6 -301.6 -8.6 VC 11 H12 O (BEYRIG) 1.5 16.0 14.5 -7.0 -8.5 14.1 12.6 2– VC 12 H8O5 (BOBWOE) -244.4 -220.4 24.0 -215.0 29.4 -263.0 -18.6 + VC 12 H10 O2 (CCPZRB) 88.2 99.6 11.4 102.1 13.9 125.8 37.6 + VC 14 H14 O4 (BOBHIJ) -20.4 1.2 21.6 -44.1 -23.7 -0.4 20.0 2– VC 18 H12 O6 (BOBWEU) -275.3 -247.3 28.0 -254.4 20.9 -318.3 -43.0 VN 125.0 113.1 -11.9 133.5 8.5 128.4 3.4 2+ V(NH 3)6 238.8 134.2 -104.7 255.5 16.7 60.9 -177.9 V(CN) 5 270.2 198.0 -72.2 236.0 -34.2 285.3 15.1 VC 10 N2H12 O8 (Vanadium(III) EDTA) -401.6 -396.4 5.3 -444.1 -42.5 -555.0 -153.4 2+ VC 12 N6H18 (BEQQIX) 370.1 368.8 -1.3 357.3 -12.8 180.7 -189.4

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

VC 14 N3H13 O5 (CAGSAE) -206.6 -202.1 4.5 -219.3 -12.7 -310.8 -104.2 – VC 18 N2H12 O4 (BALLIJ) -190.2 -146.0 44.2 -162.8 27.4 -224.5 -34.3 VC 30 N6H24 (DPYRDV) 132.2 167.1 34.9 118.6 -13.6 -49.7 -181.9 V2C22 N4H20 O8 (CEKHUV) -352.9 -302.0 50.9 -311.2 41.7 -467.1 -114.2 VO 30.5 16.9 -13.7 24.3 -6.2 49.8 19.3 VO – 4.7 21.9 17.2 33.8 29.1 60.3 55.6

VO 2 -55.6 -68.5 -12.9 -41.0 14.6 18.2 73.8 – VO 2 -101.8 -125.2 -23.4 -69.1 32.7 -21.0 80.8 – VO 3 -167.5 -189.6 -22.1 -137.7 29.8 -59.2 108.3 3+ V(H 2O) 6 (COLNUM) 378.2 343.6 -34.6 341.1 -37.1 301.4 -76.8 2+ V(H 2O) 6 30.9 -21.5 -52.4 24.3 -6.6 -61.4 -92.3 VF -19.8 4.5 24.3 14.0 33.8 32.3 52.1 – VF 2 -168.0 -150.9 17.1 -91.8 76.2 -88.9 79.1 VF 3 -201.0 -235.4 -34.4 -192.8 8.2 -126.8 74.2 – VF 3 -247.0 -250.0 -3.0 -196.4 50.6 -188.9 58.1 – VF 4 -380.9 -343.9 37.0 -288.2 92.7 -263.8 117.1 VF 5 -348.7 -325.6 23.1 -351.7 -3.0 -245.3 103.4 – VF 5 -446.0 -451.2 -5.2 -376.7 69.3 -320.8 125.2 VOF – -113.0 -127.3 -14.3 -86.5 26.5 -59.4 53.6 – VOF 2 -221.0 -222.4 -1.4 -198.5 22.5 -166.1 54.9 VAlH 2 99.1 103.8 4.7 54.6 -44.5 107.4 8.3 HVAlH 2 109.6 114.1 4.6 56.5 -53.0 142.0 32.5 VSiH 3 89.0 105.8 16.8 152.9 63.9 131.2 42.1 HVSiH 3 89.2 87.1 -2.1 137.1 47.9 153.2 64.0 VPH 2 66.2 78.4 12.2 71.5 5.4 58.4 -7.8 HVPH 2 65.7 64.4 -1.3 44.9 -20.8 121.8 56.1 VP 95.0 105.7 10.7 117.4 22.4 124.9 30.0 VS + 218.0 237.0 19.0 255.0 37.0 338.4 120.3 VSH 42.7 63.2 20.5 80.0 37.3 92.3 49.6 HVSH 42.9 52.0 9.1 52.6 9.7 116.8 73.8

VC 4H8S5 (CUSPOV) -28.8 -97.2 -68.4 -17.1 11.7 23.8 52.6 VC 4H8S4O (CAVWAX) -110.6 -150.0 -39.4 -114.9 -4.3 -31.5 79.1 VC 9H15 S6O4 (BIRYOO10) -209.8 -166.8 43.0 -216.4 -6.6 -110.5 99.3 VC 10 H11 SO 3 (CUDNIY) -109.0 -101.2 7.8 -115.4 -6.4 -145.9 -36.9 VC 12 H18 N2O2S (BAWBUW) -125.3 -97.3 28.0 -113.6 11.7 -51.6 73.7

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

VCl 13.1 86.6 73.5 51.6 38.5 41.6 28.5 VOCl – -74.0 -55.3 18.7 -67.5 6.5 -57.4 16.6

V(C 5H5)2Cl (DCPVCL) 4.3 0.6 -3.7 11.4 7.1 -7.2 -11.5 VCl 2 -58.3 30.6 88.9 -28.5 29.8 -28.9 29.4 – VCl 2 -58.8 -47.7 11.2 -52.1 6.7 -94.5 -35.7 VCl 3 -72.8 -12.0 60.9 -59.3 13.5 -82.3 -9.5 – VCl 3 -136.0 -64.1 71.9 -105.9 30.1 -167.2 -31.2 VC 20 N2H24 Cl 3O (AFUGAJ) -98.0 -111.9 -13.9 -127.8 -29.8 -186.3 -88.3 VCl 4 -126.0 -65.6 60.4 -114.1 11.9 -130.3 -4.3 VCl 5 -131.2 -131.2 0.0 -147.3 -16.1 -147.7 -16.5 V2Cl 6 -170.2 -163.4 6.8 -160.7 9.5 -279.5 -109.3 – V2Cl 9 (DOTPAD) -350.1 -481.1 -131.0 -345.1 5.0 -470.3 -120.2 – VOCl 2 -141.0 -123.2 17.8 -137.3 3.7 -142.1 -1.1 HVTi 153.0 152.9 -0.1 180.1 27.1 341.5 188.5 VCr 141.7 176.5 34.8 277.3 135.6 132.1 -9.6 VCu 147.5 150.9 3.4 172.7 25.2 146.0 -1.4 HVCu 112.1 111.5 -0.6 143.9 31.9 191.2 79.1 VZn 125.3 124.3 -1.0 12.8 -112.5 135.6 10.4 HVZn 97.0 101.9 4.9 -30.7 -127.7 138.9 41.9

VBr 3 -43.5 -33.5 10.0 -28.9 14.6 -3.0 40.5 VBr 4 -80.5 -75.7 4.8 -74.2 6.3 -19.6 60.9 + VBr 4 91.5 115.9 24.4 106.1 14.6 201.4 109.9 – VBr 4O -211.6 -253.1 -41.5 -213.2 -1.6 -172.9 38.7 V2Br 4 -27.3 -63.9 -36.6 -44.2 -16.9 -78.2 -50.9 HVZr 173.6 140.1 -33.6 118.3 -55.3 201.1 27.5 VMo 190.5 190.5 0.0 206.5 16.0 313.0 122.5 HVMo 205.6 206.0 0.4 206.8 1.2 354.4 148.8 VI 76.0 115.5 39.5 76.7 0.7 89.1 13.1

VI 3 6.2 5.1 -1.1 36.8 30.6 -2.9 -9.1 VI 4 -29.3 -27.4 1.9 -37.2 -7.9 -35.6 -6.3 VI 5 -8.2 -8.2 0.0 -3.2 5.0 -15.3 -7.1 AM1* PM6 PM5 N=95 Most positive error 88.9 135.6 188.5 Most negative error -131.0 -127.7 -189.4

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

MSE 2.2 6.0 12.9 MUE 22.6 25.3 59.0 RMSD 33.2 35.7 75.7

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.2.1.1.2 Ionization Potentials and Dipole Moments of Vanadium Compounds

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments are shown in Table 4.3.

Table 4.3: Calculated AM1*, PM6 and PM5 Koopmans’ theorem ionization potentials and dipole moments for vanadium-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 PM5 Compound Target Error Error Error Koopmans' Theorem Ionization Potentials for Vanadium Compounds (eV)

VCp 2 6.81 7.59 0.78 7.72 0.91 7.74 0.93 VN 8.00 7.35 -0.65 7.11 -0.89 7.27 -0.73 VO 7.24 7.61 0.37 7.03 -0.21 8.06 0.82

VO 2 12.70 8.97 -3.73 8.18 -4.52 9.03 -3.67 V(CO) 6 7.52 7.43 -0.09 7.20 -0.32 7.59 0.07 VOF 3 13.88 12.28 -1.60 11.17 -2.71 12.48 -1.40 VS 8.40 7.83 -0.57 7.63 -0.77 8.19 -0.21

VClO 2 7.70 10.54 2.84 10.50 2.80 10.23 2.53 VOCl 3 11.84 11.04 -0.80 11.00 -0.84 11.23 -0.61 VBrO 2 7.40 10.52 3.12 10.04 2.64 10.13 2.73 VIO 2 6.80 8.91 2.11 9.22 2.42 9.57 2.77 VI 3 6.36 6.59 0.23 4.98 -1.38 4.59 -1.77 AM1* PM6 PM5 N=12 MSE 0.17 -0.24 0.12 MUE 1.41 1.70 1.52 Dipole Moments for Vanadium Compounds (Debye) VN 6.28 6.89 0.61 3.24 -3.04 2.90 -3.38 VO 3.10 4.28 1.18 5.07 1.97 3.76 0.66 VF 4.00 1.11 -2.89 3.67 -0.33 3.75 -0.26

VO 2F 3.51 2.11 -1.40 4.19 0.68 5.41 1.90 VOF 3 0.25 1.83 1.59 1.84 1.59 0.47 0.22 VCl 4.82 4.86 0.04 3.59 -1.23 5.85 1.03

VClO 2 3.38 3.74 0.36 3.46 0.08 5.00 1.62 VOCl 3 0.57 1.30 0.73 1.82 1.25 0.22 -0.35 VBr 5.02 5.89 0.87 3.43 -1.59 7.12 2.10

VBrO 2 3.29 2.68 -0.61 2.54 -0.76 5.17 1.88 VIO 2 3.32 3.86 0.54 0.24 -3.08 4.04 0.72 AM1* PM6 PM5 N=11 MSE 0.09 -0.41 0.56 MUE 0.98 1.42 1.28

For the ionization potentials, AM1* performs marginally better than both PM6 and PM5. The MUE for the AM1* is found 1.41 eV, compared with 1.52 and 1.70 eV for PM5 and PM6,

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

respectively. AM1* and PM5 overestimate ionization potentials of the test set of vanadium compounds by 0.17 eV and 0.12 eV, respectively, and PM6 underestimates them by -0.24 eV.

All the serious large AM1* errors are found for the oxygen-containing compounds VO 2 (-3.73 eV), VBrO 2 (3.12 eV), VClO2 (2.84 eV), VIO 2 (2.11 eV) and VOF 3 (-1.60 eV). These errors may be an indirect result of using the original AM1 parameters for oxygen, although the fact that the three methods agree well argues against this interpretation.

AM1* shows almost no systematic error for the dipole moments of vanadium compounds. Its MSE is 0.09 Debye, whereas PM6 gives a negative MSE (-0.41 Debye) and PM5 a positive one (0.56 Debye). The mean unsigned error for AM1* is 0.98 Debye, compared with 1.28 and 1.42 Debye for PM5 and PM6, respectively. Particularly large errors, more than 1.0 Debye, for AM1* are found for the fluorine- and/or oxygen-containing compounds VF (-2.89 Debye),

VOF 3 (1.59 Debye), VO 2F (-1.40 Debye) and VO (1.18 Debye). These large errors, once again, may be a consequence of using original AM1 parameters for oxygen and fluorine.

4.2.1.1.3 Geometries of Vanadium Compounds

The geometrical parameters used to parameterize AM1* for vanadium and a comparison of the AM1*, PM6 and PM5 results are shown in Table 4.4.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.4: Calculated AM1*, PM6 and PM5 bond lengths and angles for vanadium-containing compounds. The coded-names within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 PM5 Compound Variable Target Error Error Error VH V-H 1.72 1.58 -0.14 1.09 -0.63 1.82 0.10

VH 2 V-H 1.78 1.59 -0.19 1.30 -0.48 1.85 0.08 VH 3 V-H 1.67 1.59 -0.09 1.21 -0.46 1.89 0.22 H-V-H 120.0 120.0 0.0 122.0 2.0 119.5 -0.5

VC 10 H10 (Bicyclopentadienyl vanadium) V-C 2.28 2.26 -0.02 2.35 0.07 2.41 0.13 VC 10 H10 (CPNDYV) V-C 2.24 2.25 0.01 2.36 0.12 2.40 0.16 VC 12 H12 (Dibenzene vanadium) V-C 2.21 2.24 0.03 2.45 0.24 2.40 0.19 VC 12 H12 (CPLHLV01) V-C(Cp) 2.25 2.26 0.00 2.36 0.11 2.38 0.13 V-C(C6) 2.18 2.25 0.07 2.36 0.18 2.40 0.22

VC 14 H22 (COGXOL) V-C1 2.20 2.17 -0.03 2.31 0.11 2.40 0.20 V-C2 2.24 2.30 0.06 2.47 0.23 2.42 0.18 C-V-C 162.0 143.6 -18.4 177.0 15.1 145.5 -16.5 V-C3 2.24 2.30 0.06 2.37 0.13 2.49 0.25 VN V#N 1.61 1.66 0.05 1.50 -0.12 1.69 0.08

V(CN) 5 V-C 1.97 2.06 0.09 2.05 0.08 2.02 0.05 2+ V(NH 3)6 V-N 2.27 2.04 -0.23 2.27 0.00 2.16 -0.11 2+ VC 12 N6H18 (BEQQIX) V-N 2.11 2.00 -0.11 2.08 -0.03 2.01 -0.10 N-C 1.12 1.17 0.05 1.16 0.04 1.16 0.04 C-C 1.45 1.44 -0.01 1.43 -0.02 1.43 -0.02

VC 30 N6H24 (DPYRDV) V-N 2.10 2.09 -0.01 2.15 0.05 2.07 -0.03 N-V-N 79.8 82.2 2.4 79.8 0.0 80.8 1.0 VO V-O 1.59 1.70 0.11 1.55 -0.04 1.58 -0.01 VO – V-O 1.64 1.75 0.11 1.61 -0.02 1.74 0.10

VO 2 V-O 1.59 1.71 0.12 1.57 -0.02 1.62 0.03 O-V-O 110.0 131.6 21.6 115.5 5.5 102.2 -7.8 – VO 2 V-O 1.64 1.73 0.08 1.63 -0.01 1.66 0.02 – VO 3 V-O 1.64 1.74 0.10 1.63 -0.02 1.67 0.03 VO(H 2O) 5 V=O 1.59 1.71 0.12 1.54 -0.05 1.56 -0.03 V-O(eq) 2.02 2.09 0.07 2.20 0.18 2.08 0.06 V-O(ax) 2.22 2.11 -0.11 2.42 0.20 2.22 0.00

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

3+ VH 12 O6 (COLNUM) V-O 1.99 2.08 0.09 2.19 0.20 2.01 0.02 2+ V(H 2O) 6 V-O 2.16 2.09 -0.07 2.22 0.06 2.12 -0.04 VCH 5O3 (Methylvanadium(V)oxidehydroxide) V-C 2.03 2.08 0.05 2.10 0.07 2.14 0.11 V=O 1.59 1.74 0.15 1.58 -0.01 1.59 0.00 V-O 1.79 1.88 0.09 1.74 -0.05 1.76 -0.03 – V(CO) 3 V-C 1.94 2.00 0.07 1.93 -0.01 2.15 0.21 C-V-C 120.0 121.3 1.3 124.4 4.4 119.2 -0.8 – V(CO) 4 V-C 1.99 2.00 0.00 2.06 0.07 2.08 0.09 C-V-C 90.0 90.0 0.0 90.0 0.0 90.0 0.0 – V(CO) 5 V-C 1.96 1.99 0.04 1.94 -0.02 2.06 0.10 V-C 1.94 1.97 0.03 1.90 -0.04 2.13 0.19 C-V-C 120.0 120.1 0.1 120.1 0.1 130.4 10.4 C-V-C 180.0 179.9 -0.1 179.9 -0.1 159.0 -21.0

VC 11 H12 O (BEYRIG) V-O 1.96 1.99 0.03 1.67 -0.29 1.85 -0.11 V-C(Cp) 2.26 2.29 0.03 2.43 0.17 2.38 0.12 V-C(O) 2.09 2.68 0.59 2.97 0.88 2.92 0.83

VC 32 N4H34 O (CAKMAC10) V=O 1.58 1.74 0.16 1.57 -0.01 1.59 0.01 V-N 2.03 2.00 -0.03 2.03 0.00 2.05 0.02 O-V-N 106.0 104.3 -1.7 104.5 -1.5 101.4 -4.6 + VC 12 H10 O2 (CCPZRB) V-C 1.95 2.05 0.10 2.06 0.11 2.06 0.11 C-O 1.15 1.17 0.02 1.14 -0.01 1.14 -0.01 V-C(Cp) 2.24 2.23 -0.01 2.32 0.08 2.31 0.07 + VC 14 H14 O4 (BOBHIJ) V-C(O) 1.93 2.05 0.12 2.06 0.13 2.06 0.13 C-O 1.18 1.18 0.00 1.15 -0.03 1.15 -0.03 – VC 18 N2H12 O4 (BALLIJ) V=O 1.64 1.75 0.11 1.61 -0.03 1.63 -0.01 V-O 1.97 2.11 0.14 2.13 0.16 2.10 0.13 V-N 2.31 2.19 -0.12 2.41 0.10 2.16 -0.15 O=V-O 95.7 94.5 -1.2 98.6 2.9 93.9 -1.8 O=V-N 163.0 166.9 3.9 161.8 -1.2 168.2 5.2

VC 10 H14 O5 (ACACVO) V=O 1.56 1.73 0.17 1.59 0.03 1.58 0.01 V-O 1.97 1.95 -0.02 2.03 0.06 2.05 0.08 O-V-O 104.5 92.3 -12.2 105.9 1.3 85.9 -18.6 2– VC 12 H8O5 (BOBWOE) V-O 1.96 2.02 0.06 2.09 0.13 2.03 0.07 V=O 1.61 1.74 0.13 1.59 -0.02 1.60 -0.01

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

O-V-O 83.0 85.9 2.9 76.9 -6.2 85.8 2.8 O-V=O 104.0 110.7 6.7 109.2 5.2 107.3 3.3

VC 15 NH 19 O5 (CUCWUS) V=O 1.57 1.73 0.16 1.58 0.01 1.58 0.01 V-O 2.01 2.03 0.02 1.86 -0.15 1.90 -0.11 V-N 2.48 2.11 -0.37 2.44 -0.04 2.09 -0.39 O=V-O 98.2 96.9 -1.3 104.6 6.3 92.3 -5.9

VC 14 N3H13 O5 (CAGSAE) V=O 1.59 1.73 0.14 1.56 -0.03 1.58 -0.01 V-O(C) 1.99 1.99 0.00 1.90 -0.09 2.09 0.10 V-N 2.33 2.16 -0.17 2.56 0.23 2.22 -0.11 V-N' 2.11 2.06 -0.05 2.12 0.01 2.05 -0.06 O-V-O 101.1 96.1 -5.0 101.6 0.5 99.6 -1.5

V(CO) 6 V-C 2.01 2.02 0.01 2.00 -0.01 2.02 0.01 – V(CO) 6 V-C 1.93 1.98 0.05 1.95 0.02 1.95 0.02 C-O 1.14 1.19 0.05 1.16 0.02 1.18 0.04 C-V-C 180.0 180.0 0.0 140.5 -39.5 179.8 -0.2 C-V-C 90.0 90.0 0.0 87.2 -2.8 90.00 0.00 2– VC 18 H12 O6 (BOBWEU) V-O 1.92 2.00 0.08 1.93 0.01 2.10 0.18 O-V-O 80.5 84.8 4.3 77.5 -3.0 79.1 -1.4

VC 10 N2H12 O8 (Vanadium(III) EDTA) V-N 2.19 2.08 -0.11 2.26 0.07 2.07 -0.12 V-O 2.03 2.03 0.00 2.00 -0.03 1.99 -0.04 N-V-N 87.3 88.0 0.8 84.8 -2.5 86.7 -0.5 3– VC 4O10 (AOXOVA) V=O 1.65 1.74 0.09 1.62 -0.03 1.63 -0.02 V-O 1.99 1.98 -0.01 1.91 -0.08 2.17 0.18 O=V=O 103.8 121.6 17.8 111.7 7.8 106.4 2.6 O-V=O 95.3 101.3 6.0 108.2 12.9 85.6 -9.7 – VC 4H4O10 (DABKEW) V-O(H2) 1.97 2.11 0.14 3.44 1.47 2.17 0.20 V-O(C2O3) 2.00 2.00 0.00 2.00 0.00 1.97 -0.03 O-V-O 90.2 85.5 -4.7 104.4 14.3 83.6 -6.6 2– VC 6H6O10 (AJUJEU) V-O 2.00 2.03 0.03 2.05 0.05 2.05 0.05 O-V-O 87.2 91.0 3.8 92.3 5.1 95.8 8.6 V=O 1.59 1.75 0.16 1.60 0.01 1.16 -0.43 VF V-F 1.76 1.84 0.08 1.66 -0.10 1.76 0.00 – C6H5VF V-C 2.18 2.07 -0.12 2.06 -0.13 2.22 0.04 V-F 1.93 1.83 -0.10 1.82 -0.11 2.01 0.08

VO 2F V-F 1.77 1.81 0.04 1.73 -0.04 1.79 0.01

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

V=O 1.61 1.73 0.12 1.58 -0.03 1.62 0.01 – VF 2 V-F 1.89 1.81 -0.08 1.89 0.00 1.92 0.03 VF 3 V-F 1.75 1.81 0.06 1.70 -0.05 1.75 0.00 F-V-F 120.0 106.2 -13.8 120.0 0.0 107.1 -12.9 – VF 3 V-F 1.84 1.85 0.00 1.86 0.02 1.85 0.01 VOF 3 V=O 1.57 1.73 0.16 1.56 -0.01 1.59 0.02 V-F 1.73 1.82 0.09 1.74 0.01 1.74 0.01 O=V-F 107.5 112.5 5.0 109.6 2.1 105.1 -2.4 – VF 4 V-F 1.83 1.86 0.03 1.83 0.01 1.86 0.03 VF 5 V-F(ax) 1.73 1.84 0.11 1.74 0.01 1.75 0.02 V-F(eq) 1.71 1.83 0.12 1.74 0.03 1.73 0.02 – VF 5 V-F 1.76 1.85 0.09 1.79 0.03 1.77 0.01 V-F 1.83 1.87 0.05 1.85 0.02 1.89 0.06

VF 6 V-F 1.81 1.86 0.05 1.80 -0.01 1.80 -0.01 VAlH 2 V-Al 2.67 2.36 -0.31 2.05 -0.61 2.43 -0.24 VSiH 3 V-Si 2.62 2.34 -0.28 2.56 -0.05 2.59 -0.03 VP V#P 2.14 2.18 0.04 2.34 0.20 1.89 -0.25

VPH 2 V-P 2.46 2.21 -0.25 2.46 0.01 2.15 -0.31 VC 12 P2H24 (DACFUI) V-P 2.46 2.31 -0.15 2.46 0.00 1.94 -0.52 P-V-P 81.1 81.1 0.0 82.8 1.7 88.1 7.0 V-C(H3) 2.22 2.00 -0.22 2.16 -0.06 2.43 0.21 V-C(C4) 2.30 2.28 -0.02 2.35 0.05 2.52 0.22 VS + V-S 2.03 2.20 0.17 1.99 -0.04 2.38 0.35 VSH V-S 2.32 2.35 0.03 2.09 -0.23 2.46 0.14

HVSH 2 V-S 2.35 2.30 -0.04 2.25 -0.10 2.45 0.10 VC 12 N2H18 SO 2 (BAWBUW) V-S 2.07 2.20 0.13 2.13 0.06 2.21 0.14 V-O 1.95 2.04 0.09 1.73 -0.22 2.00 0.05 S-V-O 109.6 113.6 4.0 105.6 -4.0 111.2 1.6 V-N 2.03 2.00 -0.03 2.17 0.14 1.95 -0.08

VC 10 H11 SO 3 (CUDNIY) V-S 2.47 2.18 -0.29 2.28 -0.19 2.75 0.28 V-C(O) 1.88 1.99 0.11 2.00 0.12 2.00 0.12 V-C(Cp) 2.23 2.23 0.00 2.34 0.11 2.39 0.16

VC 20 N4H16 SO 5 (ASAVAR) V-O 1.58 1.74 0.16 1.58 0.00 1.59 0.01 V-O' 1.96 1.86 -0.10 1.70 -0.26 1.76 -0.20 O-V-O' 105.0 98.5 -6.5 105.8 0.7 98.7 -6.3

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

V-N 2.10 2.09 -0.01 2.06 -0.04 1.98 -0.12

V(PH 2)(NH 2)(SH) V-P 2.45 2.30 -0.15 2.46 0.01 1.80 -0.65 V-N 1.85 1.81 -0.04 1.78 -0.07 1.73 -0.12 V-S 2.28 2.29 0.01 2.22 -0.06 2.43 0.15 2– VC 4H8S4O (CAVWAX) V=O 1.63 1.76 0.13 1.58 -0.05 1.58 -0.05 V-S 2.38 2.44 0.06 2.42 0.04 2.71 0.33 O=V-S 104.0 107.7 3.7 102.8 -1.2 101.8 -2.2

VC 4H8S5 (CUSPOV) V-S 2.35 2.31 -0.04 2.29 -0.06 2.45 0.10 S-V-S 85.8 89.8 4.0 88.3 2.4 95.1 9.3 V=S 2.10 2.28 0.18 2.36 0.26 2.99 0.89

VC 9H15 S6O4 (BIRYOO10) V-S 2.47 2.47 0.00 2.43 -0.04 2.54 0.07 S-V-S 69.1 72.0 2.9 73.4 4.3 70.8 1.7 V-S 2.62 2.53 -0.09 2.60 -0.02 2.82 0.20 V=O 1.58 1.74 0.16 1.54 -0.04 1.55 -0.03

V(C 5H5)2Cl (DCPVCL) V-Cl 2.39 2.30 -0.09 2.23 -0.16 2.32 -0.07 V-C 2.27 2.27 0.00 2.39 0.12 2.40 0.13

VClO 2 V-Cl 2.19 2.20 0.01 2.18 -0.01 2.20 0.01 V=O 1.60 1.72 0.12 1.56 -0.04 1.60 0.00

VC 11 P2H23 Cl 2 (CECKIE) V-Cl 2.40 2.29 -0.11 2.57 0.17 2.31 -0.09 Cl-V-Cl 126.1 151.8 25.7 160.6 34.6 149.4 23.3 V-P 2.51 2.25 -0.26 2.50 -0.01 2.00 -0.51 V-C 2.31 2.31 0.00 2.37 0.06 2.48 0.17

VC 12 P4H32 Cl 2 (DAJDOH) V-Cl 2.44 2.22 -0.22 2.67 0.23 2.38 -0.06 V-P 2.50 2.19 -0.31 2.48 -0.02 2.03 -0.47 Cl-V-P 88.2 88.8 0.6 89.3 1.1 98.6 10.4 – VCl 2 V-Cl 2.35 2.21 -0.14 2.39 0.04 2.38 0.03 VCl 3 V-Cl 2.15 2.23 0.08 2.12 -0.03 2.16 0.01 – VCl 3 V-Cl 2.29 2.30 0.01 2.35 0.06 2.30 0.01 VCl 3O V-O 1.57 1.71 0.14 1.55 -0.02 1.57 0.00 V-Cl 2.14 2.21 0.07 2.16 0.02 2.15 0.01 O-V-Cl 111.3 117.6 6.3 108.2 -3.1 105.3 -6.0

VC 20 N2H24 Cl 3O (AFUGAJ) V-Cl 2.32 2.27 -0.05 2.31 -0.01 2.28 -0.04 Cl-V-Cl 170.9 166.3 -4.5 164.0 -6.8 119.9 -51.0 V-O 2.12 2.18 0.06 2.23 0.11 2.16 0.04 V-N 2.13 1.97 -0.16 2.11 -0.02 2.04 -0.09

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

VCl 4 V-Cl 2.14 2.22 0.08 2.16 0.02 2.13 -0.01 – VCl 4O V-O 1.56 1.72 0.16 1.55 -0.01 1.57 0.01 V-Cl 2.26 2.25 -0.01 2.32 0.06 2.26 0.00 O-V-Cl 103.3 107.2 3.9 104.9 1.6 103.0 -0.3

VCl 5 V-Cl(eq) 2.19 2.20 0.01 2.17 -0.02 2.13 -0.06 V-Cl(ax) 2.26 2.21 -0.05 2.24 -0.02 2.18 -0.09 – VCl 6 V-Cl 2.33 2.23 -0.10 2.29 -0.04 2.22 -0.11 V2 V-V 1.77 1.57 -0.20 1.70 -0.07 1.70 -0.07 V2C16 H16 (CAMXAP) V-C(C5) 2.23 2.24 0.01 2.30 0.07 2.43 0.20 V-C(C4) 2.26 2.23 -0.03 2.35 0.09 2.40 0.14

V2C12 H20 O8 (BIWDIU) V=O 1.59 1.73 0.14 1.59 0.00 1.59 0.00 V-O(C5) 1.97 2.05 0.08 1.85 -0.12 2.10 0.13 O-V-O 108.1 105.1 -3.0 109.0 0.9 80.5 -27.6 V-O(C) 1.95 2.02 0.07 2.07 0.12 1.99 0.04

V2C22 N4H20 O8 (CEKHUV) V-O(br) 2.20 2.19 -0.01 1.99 -0.21 2.25 0.05 O-V-O 73.4 79.7 6.3 60.2 -13.2 76.1 2.7 V-N 2.13 2.07 -0.06 2.16 0.03 2.02 -0.11 V-O(t) 1.62 1.74 0.12 1.62 0.00 1.63 0.00

V2C18 H10 O8F12 (CPVFAC) V-V 3.71 3.52 -0.19 4.65 0.94 2.87 -0.84 V-O 2.31 2.14 -0.17 6.62 4.31 2.03 -0.28 O-V-V 70.8 68.6 -2.2 36.4 -34.4 74.7 3.9 V-C 2.39 2.35 -0.04 2.44 0.05 2.73 0.34

V2Cl 4 V-Cl(t) 2.17 2.23 0.06 2.08 -0.09 2.16 -0.01 V-Cl(b) 2.34 2.24 -0.10 2.46 0.12 2.20 -0.14 Cl-V-Cl 98.1 94.0 -4.1 74.6 -23.5 115.9 17.8 – V2Cl 9 (DOTPAD) V-Cl(t) 2.19 2.20 0.01 2.25 0.06 2.26 0.07 Cl-V-Cl 96.6 101.1 4.5 102.2 5.6 90.3 -6.3 V-Cl(br) 2.46 2.46 0.00 2.52 0.06 2.49 0.03 HVTi V-Ti 1.73 1.73 0.01 2.66 0.93 11.82 10.09 VCr V-Cr 2.65 2.59 -0.06 3.12 0.47 2.65 0.00 VCu V-Cu 2.40 2.48 0.09 2.65 0.25 2.32 -0.08 HVCu V-Cu 2.48 2.46 -0.02 2.72 0.24 2.31 -0.17 VZn V-Zn 2.67 2.64 -0.03 2.02 -0.65 2.35 -0.32 HVZn V-Zn 2.72 2.65 -0.07 2.04 -0.68 2.37 -0.35 VBr V-Br 2.39 2.39 0.00 2.25 -0.14 2.50 0.11

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

VBrO 2 V-Br 2.33 2.28 -0.05 2.30 -0.04 2.46 0.13 V=O 1.61 1.67 0.06 1.57 -0.05 1.60 -0.01

VBr 3 V-Br 2.33 2.29 -0.04 2.27 -0.06 2.42 0.09 VBr 4 V-Br 2.31 2.28 -0.03 2.29 -0.02 2.39 0.09 + VBr 4 V-Br 2.23 2.24 0.01 2.22 -0.02 2.31 0.08 – VBr 4O V-Br 2.48 2.34 -0.14 2.48 0.00 2.51 0.04 – VBr 6 V-Br 2.50 2.31 -0.19 2.47 -0.03 2.47 -0.03 HVZr V-Zr 2.06 1.94 -0.12 2.39 0.33 3.11 1.05 VMo V-Mo 1.91 1.76 -0.15 2.21 0.30 3.46 1.55 HVMo V-Mo 1.87 1.96 0.09 2.18 0.31 3.72 1.85 VI V-I 2.59 2.51 -0.08 2.58 -0.01 2.21 -0.38

VIO 2 V-I 2.55 2.64 0.09 2.56 0.01 2.37 -0.18 V=O 1.60 1.67 0.07 1.56 -0.04 1.60 0.00

VI 3 V-I 2.54 2.58 0.04 2.54 0.00 2.34 -0.20 VI 4 V-I 2.52 2.58 0.06 2.69 0.17 2.33 -0.19 VI 5 V-I 2.59 2.47 -0.12 2.63 0.04 2.77 0.18 AM1* PM6 PM5 N=178 MSE bond length 0.00 0.05 0.09 MUE bond length 0.09 0.14 0.20 N=42 MSE bond angle 1.4 -0.1 -2.4 MUE bond angle 5.2 6.7 7.7

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* performs slightly better than both PM6 and PM5 for bond angles and significantly better for bond lengths. The AM1* MUE for bond lengths is 0.09 Å, compared with 0.14 Å and 0.20 Å for PM6 and PM5, respectively. PM6 and PM5 overestimate bond lengths to vanadium systematically, with MSEs of 0.05 Å and 0.09 Å, respectively. AM1* shows no systematic error for bond lengths to vanadium. AM1* tends to overestimate the bond angles by 1.4°, whereas PM5 underestimates them by -2.4°. PM6 with an MSE of -0.1° shows no significant systematic error. AM1* performs slightly better for the bond angles to vanadium with a mean unsigned error of 5.2°, compared with 6.7° and 7.7° for PM6 and PM5, respectively. These differences are, however, hardly significant.

4.2.1.2 Chromium

4.2.1.2.1 Heats of Formation of Chromium Compounds

The calculated heats of formation for our training set of chromium compounds are shown in Table 4.5.

Table 4.5 shows that, for this set of compounds AM1* gives the best results for the heats of formation of chromium compounds. Its MUE (25.1 kcal mol −1) is significantly lower than those for PM6 and PM5, 38.4 and 55.9 kcal mol −1, respectively. PM6 and PM5 generally predict heats of formation to be too negative with mean signed errors of -23.5 and -43.2 kcal mol −1, respectively, whereas AM1* tends to overestimate them by around nine kcal mol −1. − -1 The largest positive errors for AM1* are found for the compounds HCrO 3 (135.1 kcal mol ), − −1 2− −1 CrF (120.6 kcal mol ), Cr 2(CO) 10 (112 kcal mol ), Cr 2C24 N4H24 O4 (tetrakis(mu-(6- −1 3− −1 methyl-2(1H)-pyridinato)dichromium) (93.7 kcal mol ), CrF 6 (84 kcal mol ), −1 3− −1 Cr(CO) 4(piperidine) 2 (75.7 kcal mol ), Cr(C 2O4)3 (AMOXCR) (72.7 kcal mol ) and − −1 − CrC 4H4O10 (KOXACR) (70.6 kcal mol ). In addition, the chlorinated compounds CrCl , − −1 CrCl 2, CrCl 2 , CrOCl and CrCl 4 give positive errors of more than 40 kcal mol . The large − −1 3+ −1 negative errors are found for Cr(CO) 4 (-69 kcal mol ), Cr (-65.8 kcal mol ), Cr 2PH (-59.8 −1 −1 −1 −1 kcal mol ), HCrAlH 2 (-52.3 kcal mol ), CrTi (-51.5 kcal mol ), HCrPH 2 (-47.6 kcal mol ) and CrZn (-41.5 kcal mol −1).

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.5: Calculated AM1*, PM6 and PM5 heats of formation and errors compared with our target values for the chromium-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The coded-names within parentheses indicate the CSD-names of the compounds.

Target AM1* PM6 PM5

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error Cr – 79.4 76.0 -3.4 127.0 47.5 143.7 64.3 Cr 95.0 95.0 0.0 94.3 -0.7 95.0 0.0 Cr + 251.0 251.8 0.8 236.0 -15.0 261.5 10.5 Cr 2+ 631.0 658.6 27.6 613.0 -18.0 658.0 27.0 Cr 3+ 1345.0 1279.2 -65.8 1202.8 -142.2 1284.5 -60.5

Cr 2 148.0 147.4 -0.6 123.2 -24.8 184.6 36.6 – Cr 2 144.8 144.7 -0.1 185.7 40.9 144.7 -0.1 CrH 99.9 96.9 -3.0 30.4 -69.5 20.4 -79.4

CrH 2 109.2 109.2 0.0 -48.6 -157.8 -28.3 -137.5 Cr(Cp) 2 59.6 90.2 30.6 83.3 23.7 41.5 -18.1 Cr(C 6H6)2 56.0 31.4 -24.6 73.3 17.3 57.7 1.7 CrN 120.7 108.4 -12.3 130.2 9.5 -14.6 -135.3 2+ Cr(NH 3)6 279.1 279.0 -0.1 302.2 23.1 48.4 -230.7 3+ CrN 6C12 H30 (SUKFEJ) 597.6 618.4 20.8 538.3 -59.3 521.1 -76.5 CrO 45.0 43.7 -1.3 40.6 -4.4 19.5 -25.5 CrO – 23.9 16.7 -7.2 30.5 6.6 -5.5 -29.4

CrO 2 -18.0 -33.0 -15.0 -60.3 -42.3 -42.7 -24.7 – CrO 2 -70.0 -54.7 15.3 -67.6 2.4 -122.6 -52.6 CrO 3 -70.0 -115.7 -45.7 -59.0 11.0 -77.9 -7.9 – CrO 3 -158.4 -140.1 18.3 -146.0 12.4 -200.6 -42.2 2– CrO 4 -186.0 -185.7 0.3 -175.7 10.3 -227.4 -41.4 – HCrO 3 -270.5 -135.4 135.1 -192.4 78.1 -253.2 17.3 2+ Cr(H 2O) 6 58.1 34.8 -23.3 29.0 -29.1 -55.7 -113.8 Cr(CO) 3 -44.0 -38.0 6.0 -36.7 7.3 -10.4 33.6 Cr(CO) 4 -102.0 -75.5 26.6 -92.1 9.9 -36.2 65.8 – Cr(CO) 4 -66.1 -135.1 -69.0 -117.6 -51.5 -144.9 -78.7 – CrC 4H4O10 (KOXACR) -545.7 -475.2 70.6 -569.2 -23.5 -656.8 -111.1

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Cr(CO) 5 -154.0 -158.1 -4.1 -162.4 -8.4 -140.4 13.6 Cr(CO) 6 -218.0 -194.4 23.6 -216.6 1.4 -212.8 5.2 3– Cr(C 2O4)3 (AMOXCR) -547.4 -474.8 72.7 -589.7 -42.3 -679.0 -131.6 Cr(CO) 3(C 6H6) -83.7 -82.7 1.0 -75.4 8.3 -84.6 -0.9 Cr(CO) 3C7H8 -91.5 -76.8 14.7 -70.4 21.1 -81.5 10.0 Cr(CO) 3(C 6H5CH 3) -90.6 -90.6 0.0 -87.9 2.7 -92.0 -1.4 Cr(CO) 3(C 6H5-CHO) -114.0 -114.4 -0.3 -106.9 7.1 -111.9 2.1 Cr(CO) 3(Ph-O-Me) -117.0 -120.8 -3.8 -121.2 -4.2 -119.9 -2.9 Cr(CO) 4(C 7H8) -73.4 -85.0 -11.6 -99.0 -25.6 -117.6 -44.2 CrC 12 H12 O3 (1,3,5-Trimethylbenzene chromium tricarbonyl) -111.4 -89.2 22.2 -112.2 -0.8 -128.0 -16.6

Cr(CO) 3C10 H8 -61.7 -65.0 -3.3 -65.2 -3.5 -63.4 -1.7 CrC 15 H18 O3 (Hexamethylbenzene chromium tricarbonyl) -134.2 -116.9 17.3 -133.6 0.6 -118.6 15.6

CrC 16 H36 O4 (Cr(O-t-butyl) 4) -309.6 -288.4 21.2 -300.8 8.8 -324.3 -14.7 Cr 2C8H12 O8 (Chromium diacetate dimer) -476.5 -439.1 37.4 -484.9 -8.4 -459.1 17.4 2– Cr 2(CO) 10 -423.9 -311.9 112.0 -392.7 31.2 -449.0 -25.1 Cr(NO) 4 -32.6 -32.4 0.2 -22.2 10.4 -212.8 -180.2 CrC 10 NH 5O5 (Cr(CO) 5(Py)) -150.4 -128.6 21.8 -166.1 -15.7 -158.7 -8.3 CrC 10 NH 10 O5 (Cr(CO) 5(Piperidine) -200.0 -153.3 46.7 -192.6 7.4 -196.6 3.4 Cr(CO) 3(C 6H5-NMe 2) -80.4 -73.5 6.9 -79.4 1.0 -75.4 5.0 CrC 14 N2H10 O4 (Cr(CO) 4(Py) 2) -92.7 -50.8 41.9 -97.8 -5.1 -94.8 -2.1 CrC 14 N2H20 O4 (Cr(CO) 4(Piperidine) 2) -189.0 -113.3 75.7 -166.9 22.1 -184.9 4.1 (Cp) 2Cr 2(NO) 4 -29.0 39.0 68.0 -17.4 11.6 -223.1 -194.1 Cr 2C24 N4H24 O4 (Tetrakis(mu-(6-methyl-2(1H)- pyridinato) dichromium)) -189.1 -95.4 93.7 -208.8 -19.7 -258.6 -69.5 CrF 9.7 -8.8 -18.5 -13.9 -23.6 -33.8 -43.5 CrF – -52.3 68.3 120.6 28.3 80.6 -10.2 42.1

CrF 2 -79.0 -64.2 14.8 -105.6 -26.6 -131.4 -52.4 – CrF 2 -152.2 -118.1 34.1 -117.9 34.3 -157.2 -5.0 CrF 3 -157.3 -220.1 -62.8 -235.1 -77.8 -243.8 -86.5 – CrF 3 -255.9 -234.0 21.9 -239.2 16.7 -269.5 -13.6 – CrF 4 -343.4 -349.7 -6.3 -367.0 -23.6 -366.4 -23.0 – CrF 5 -417.2 -417.5 -0.3 -453.6 -36.4 -439.6 -22.4 3– CrF 6 -249.8 -165.8 84.0 -233.7 16.1 -285.4 -35.6 CrOF 15.5 36.1 20.6 -77.8 -93.3 -93.5 -109.0

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CrOF – -88.0 -73.7 14.3 -115.4 -27.4 -140.2 -52.2

CrO 2F -131.8 -147.4 -15.6 -148.9 -17.1 -103.5 28.3 – CrO 2F -173.0 -156.4 16.6 -210.1 -37.1 -235.5 -62.5 CrOF 2 -148.9 -178.8 -29.9 -202.6 -53.7 -195.4 -46.5 – CrOF 2 -196.0 -195.6 0.4 -248.5 -52.5 -257.0 -61.0 CrO 2F2 -219.6 -242.1 -22.5 -244.6 -25.0 -236.0 -16.4 2– CrF 5H2O (YASHAB) -421.0 -398.7 22.3 -419.1 1.9 -461.7 -40.7 3– Cr 2F9 (OCOLIB) -601.3 -598.7 2.6 -594.0 7.3 -599.4 1.9 + CrC 2N2H12 O2F2 (BUTDAV) -142.2 -143.3 -1.1 -164.9 -22.7 -243.1 -100.9 CrCl 42.6 50.5 7.9 16.4 -26.2 -9.5 -52.1 CrCl – -35.0 36.3 71.3 46.7 81.7 17.4 52.4

CrCl 2 -5.6 44.4 50.0 -25.6 -20.0 -68.7 -63.1 – CrCl 2 -74.0 -27.5 46.5 -49.1 24.9 -89.8 -15.8 CrOCl -59.2 -13.6 45.6 -33.8 25.4 -52.8 6.4 CrOCl – -55.0 -49.6 5.4 -71.7 -16.7 -99.9 -44.9

CrO 2Cl -92.4 -101.4 -9.0 -95.7 -3.3 -91.3 1.1 – CrO 2Cl -127.0 -148.0 -21.0 -171.3 -44.3 -198.2 -71.2 CrOCl 2 -79.6 -70.5 9.1 -91.6 -12.0 -100.9 -21.3 – CrOCl 2 -131.0 -133.8 -2.8 -156.0 -25.0 -168.3 -37.3 CrCl 2O2 -127.0 -125.1 1.9 -148.2 -21.2 -130.4 -3.4 CrCl 3 -33.6 -37.2 -3.7 -66.4 -32.8 -92.6 -59.0 CrCl 4 -110.7 -68.0 42.7 -95.7 15.0 -104.7 6.0 Cr(CO) 4ClC 2H3 (CATYOL) -134.9 -120.1 14.8 -132.6 2.3 -115.5 19.4 CrC 10 H15 Cl 2O (AFEHIC) -126.0 -128.7 -2.7 -126.2 -0.2 -118.1 7.9 CrC 4N3H13 Cl 3 (AMZCCR) -106.2 -100.0 6.2 -110.2 -4.0 -221.4 -115.2 CrAlH 2 216.6 216.9 0.3 101.1 -115.5 57.6 -159.0 HCrAlH 2 264.3 212.0 -52.3 -54.7 -319.0 32.3 -232.0 CrSiH 3 204.9 208.3 3.4 187.9 -17.0 38.4 -166.5 HCrSiH 3 199.6 193.3 -6.3 149.9 -49.7 -76.8 -276.4 Cr 2PH 195.0 135.2 -59.8 105.8 -89.2 152.0 -43.0 HCrPH 2 158.5 110.9 -47.6 54.8 -103.7 -15.8 -174.3 Cr(PF 3)6 -1430.9 -1389.5 41.4 -1431.7 -0.8 -1435.9 -5.0 CrS 116.6 113.7 -2.8 53.8 -62.7 109.8 -6.8 CrSH 149.9 150.8 0.9 71.7 -78.2 127.0 -22.9 HCrSH 159.3 159.3 0.0 -185.2 -344.5 84.7 -74.6

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

2– CrS 4C4H8 (CUWLIP) -1.2 60.0 61.2 -0.3 0.9 71.5 72.7 CrBr 147.7 112.8 -34.9 97.4 -50.3 115.9 -31.8

CrBr 2 148.4 148.5 0.1 71.1 -77.3 69.8 -78.6 CrTi 253.3 201.8 -51.5 232.4 -20.9 348.9 95.6 CrNi 105.4 89.9 -15.6 149.7 44.3 -94.1 -199.5 CrCu 232.3 222.8 -9.5 190.3 -42.0 -33.4 -265.7 CrZn 249.4 207.9 -41.5 79.6 -169.8 193.7 -55.7 CrZr 248.8 222.7 -26.1 213.5 -35.3 136.3 -112.5 CrMo 271.6 265.6 -6.0 138.7 -132.9 234.3 -37.3 CrI 135.6 135.6 0.0 89.4 -46.2 87.6 -48.0 AM1* PM6 PM5 N=105 Most positive error 135.1 81.7 95.6 Most negative error -69.0 -344.5 -276.4 MSE 9.0 -23.5 -43.2 MUE 25.1 38.4 55.9 RMSD 37.9 65.9 82.7

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Additionally, all three methods give very large negative errors for chromium tetra-, penta- and hexa-cations (not shown in Table 4.5 and not included in the statistics). AM1* errors are found to be -345.8 kcal mol -1 (-462.8 and -549 kcal mol −1 for PM6 and PM5, respectively) for Cr 4+ , -875.2 kcal mol −1 (-1027.8 and -1098.1 kcal mol −1 for PM6 and PM5, respectively) for Cr 5+ and -1673.9 kcal mol −1 (-1871.6 and -1910.3 kcal mol −1 for PM6 and PM5, respectively) for Cr 6+ . Experimental heats of formation of these cations are given in Table S1 of the Supplementary Material [68]. Once again, very large errors are given by the compounds that contain the original AM1 elements, as expected. The large errors for the compounds containing “pure” AM1* elements are likely to be a consequence of our sequential parameterization strategy.

4.2.1.2.2 Ionization Potentials and Dipole Moments of Chromium Compounds

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for the compounds containing chromium are shown in Table 4.6.

Table 4.6: Calculated AM1*, PM6 and PM5 Koopmans’ theorem ionization potentials and dipole moments for chromium-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 PM5 Compound Target Error Error Error Koopmans' Theorem Ionization Potentials for Chromium Compounds (eV)

CrCp 2 5.70 7.11 1.41 7.28 1.58 7.64 1.94 Cr(C 6H6)2 5.40 7.36 1.96 6.51 1.11 6.95 1.55 Cr(CO) 3(C 6H5CH 3) 6.60 8.14 1.54 7.37 0.77 8.43 1.83 Cr(CO) 3C7H8 6.90 8.23 1.33 7.17 0.27 8.57 1.67 CrC 12 H12 O3 (1,3,5-Trimethylbenzene chromium tricarbonyl) 7.20 7.19 -0.02 6.57 -0.63 7.06 -0.14 CrC 15 H18 O3 (Hexamethylbenzene chromium tricarbonyl) 6.40 7.94 1.54 7.04 0.64 8.18 1.78

Cr(CO) 3(C 6H5-NMe 2) 7.38 8.05 0.67 7.35 -0.03 8.28 0.90 Cr(CO) 3(Ph-O-Me) 7.38 8.15 0.77 7.40 0.02 8.51 1.13 CrC 10 NH 5O5 (Cr(CO) 5(Py)) 7.30 8.10 0.80 6.68 -0.62 8.42 1.12 Cr(CO) 6 8.20 8.87 0.67 8.05 -0.15 9.54 1.34 Cr 2C24 N4H24 O4 (Tetrakis(mu-(6-methyl- 2(1H)-pyridinato) dichromium)) 6.50 8.14 1.64 6.03 -0.47 8.12 1.62

Cr 2C8H12 O8 (Chromium diacetate dimer) 8.00 8.87 0.87 7.39 -0.61 8.43 0.43 CrCl 2 9.40 8.43 -0.97 8.13 -1.27 10.75 1.35 CrF 9.30 8.18 -1.12 8.04 -1.26 7.68 -1.62

CrF 2 10.60 9.05 -1.55 8.16 -2.44 9.93 -0.67 CrO 2F2 12.91 12.29 -0.62 12.07 -0.84 12.71 -0.20 CrF 3 12.50 10.14 -2.36 9.58 -2.92 11.15 -1.35 60

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CrBr 2 9.30 9.33 0.03 8.81 -0.49 10.33 1.03 AM1* PM6 PM5 N=18 MSE 0.37 -0.41 0.76 MUE 1.10 0.90 1.20 Dipole Moments for Chromium Compounds (Debye) CrF 3.71 3.15 -0.56 2.00 -1.71 4.06 0.35

CrO 2F2 0.02 1.39 1.37 1.83 1.81 2.00 1.98 CrCl 4.55 3.73 -0.82 8.92 4.37 6.78 2.23

CrCl 2O2 0.76 1.19 0.43 2.24 1.48 1.48 0.72 CrBr 4.41 4.10 -0.31 0.01 -4.40 7.21 2.80 CrI 4.37 1.08 -3.29 3.86 -0.51 4.19 -0.18 AM1* PM6 PM5 N=6 MSE -0.53 0.17 1.32 MUE 1.13 2.38 1.38

AM1* and PM5 overestimate ionization potentials by 0.37 and 0.76 eV, respectively, whereas PM6 underestimates them by -0.41 eV. The performance of all three methods is comparable. The mean unsigned errors vary in a relatively small range from 0.90 (PM6) to 1.20 eV (PM5). The AM1* MUE, 1.10 eV, lies in the middle of this range. All the large errors (more than 1.0 eV) for AM1* are given by the compounds containing AM1 elements, C, N, O, F.

AM1* performs best for dipole moments with an MUE of 1.13 Debye. PM5 is slightly worse than AM1* with an MUE of 1.38 Debye. PM6 performs least well in reproducing dipole moments for chromium compounds with an MUE of 2.38 Debye. AM1* tends to underestimate dipole moments by -0.53 Debye, whereas PM6 and PM5 overestimate them by about 0.17 and 1.32 Debye, respectively. The largest AM1* error is given by CrI (-3.29 Debye). That is not very surprising and reflects the known weakness [67] of AM1* parameterization for iodine in reproducing dipole moments.

4.2.1.2.3 Geometries of Chromium Compounds

The geometrical parameters used to parameterize AM1* for chromium and a comparison of the AM1*, PM6 and PM5 results are shown in Table 4.7.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.7: Calculated AM1*, PM6 and PM5 bond lengths and angles for chromium-containing compounds. The coded-names within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 PM5 Compound Variable Target Error Error Error

Cr 2 Cr-Cr 1.68 1.75 0.07 1.71 0.03 1.62 -0.06 – Cr 2 Cr-Cr 1.68 1.71 0.03 1.67 -0.01 1.66 -0.02 CrH Cr-H 1.67 1.67 0.00 0.97 -0.70 1.51 -0.16

CrH 2 Cr-H 1.65 1.66 0.00 0.94 -0.71 1.51 -0.15 CrCp 2 Cr-C 2.44 2.39 -0.05 2.24 -0.20 2.24 -0.20 Cr(C 6H6)2 Cr-C 2.17 2.20 0.03 2.16 -0.02 2.21 0.04 3– Cr(CH 3)6 (MCRLDX) Cr-C 2.30 2.20 -0.10 2.11 -0.19 2.02 -0.28 CrN Cr#N 1.58 1.66 0.08 1.42 -0.16 1.31 -0.28 2+ Cr(NH 3)6 Cr-N 2.21 2.10 -0.11 2.13 -0.08 4.74 2.53 3+ CrN 6C12 H30 (SUKFEJ) Cr-N 2.09 2.08 -0.01 2.09 0.00 1.96 -0.13 N-Cr-N 82.9 85.7 2.9 85.9 3.0 85.04 2.2

CrC 6N15 H18 (BGUCRM) Cr-N 2.03 1.99 -0.04 1.99 -0.04 1.83 -0.20 CrO Cr=O 1.65 1.66 0.01 1.60 -0.05 1.64 -0.01 CrO – Cr=O 1.67 1.68 0.01 1.69 0.02 1.70 0.02

CrO 2 Cr=O 1.60 1.64 0.04 1.57 -0.03 1.61 0.01 O=Cr=O 130.8 99.2 -31.6 150.6 19.8 116.3 -14.5 – CrO 2 Cr=O 1.64 1.65 0.01 1.65 0.01 1.64 0.00 CrO 3 Cr-O 1.63 1.61 -0.02 1.61 -0.02 1.61 -0.02 – CrO 3 Cr=O 1.62 1.64 0.03 1.62 0.00 1.62 0.01 O=Cr=O 120.0 101.7 -18.3 120.0 0.0 120.0 0.0 – HCrO 3 Cr-H 1.59 1.67 0.08 1.03 -0.56 1.51 -0.08 Cr=O 1.60 1.63 0.03 1.64 0.04 1.62 0.02 H-Cr=O 103.3 112.0 8.6 92.6 -10.7 104.4 1.1 O=Cr=O 114.9 106.9 -8.0 119.8 4.9 114.0 -0.8 2– CrO 4 Cr-O 1.66 1.67 0.01 1.67 0.01 1.62 -0.04 3+ Cr(H 2O) 6 (TAPBUH) Cr-O 1.96 1.96 0.00 2.06 0.10 1.91 -0.05 2+ Cr(H 2O) 6 Cr-O 2.11 2.00 -0.11 2.14 0.03 1.97 -0.14 2– Cr 2O7 Cr-O 1.75 1.78 0.03 1.81 0.06 1.62 -0.13 O-Cr-O 109.5 114.4 4.9 108.3 -1.2 115.8 6.3 2– Cr 3O10 Cr-O 1.83 1.84 0.01 1.88 0.05 1.85 0.02

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Cr-O 1.74 1.72 -0.02 1.74 0.00 1.62 -0.12

Cr(CH 3)2O2 Cr-C 1.98 2.01 0.03 1.99 0.01 1.93 -0.05 Cr=O 1.59 1.60 0.01 1.58 -0.01 1.58 -0.01 O=Cr-C 107.9 107.0 -0.9 104.5 -3.4 108.5 0.6

Cr(CO) 4 Cr-C 1.91 1.95 0.04 1.89 -0.03 1.94 0.03 C-Cr-C 90.0 90.0 0.0 90.0 0.0 82.2 -7.8 – CrC 4H4O10 (KOXACR) Cr-O(-C) 1.92 1.89 -0.03 1.98 0.06 1.96 0.04 O-Cr-O 83.4 87.6 4.2 81.5 -1.9 91.4 8.0

Cr-O(H 2) 2.29 2.02 -0.28 2.22 -0.07 1.96 -0.33

Cr(CO) 5 Cr-C(1) 1.84 1.86 0.02 1.84 -0.01 1.89 0.05 Cr-C(2) 1.92 1.95 0.04 1.91 0.00 1.92 0.00 C-Cr-C 90.0 90.0 0.0 90.0 0.0 89.6 -0.4

Cr(CO) 6 Cr-C 1.91 1.95 0.04 1.90 -0.01 1.91 0.00 C-Cr-C 90.0 90.0 0.0 90.0 0.0 90.0 0.0 3– Cr(C 2O4)3 (AMOXCR) Cr-O 2.01 1.91 -0.10 2.03 0.02 1.96 -0.05 O-Cr-O 89.7 90.1 0.4 88.6 -1.1 89.5 -0.2

Cr(C 5H5)(CO) 3 Cr-C(C=O) 1.86 1.90 0.04 1.88 0.02 1.89 0.03 C-O 1.15 1.18 0.03 1.16 0.01 1.15 0.00

Cr-C(C 4H4) 2.23 2.22 -0.01 2.26 0.03 2.21 -0.02 Cr(CO) 3(C 6H6) Cr-Bz 1.69 1.89 0.20 1.75 0.06 2.24 0.55 C-Cr-C 90.0 90.2 0.2 91.9 1.9 92.5 2.5

Cr(CO) 3C7H8 Cr-C 1.85 1.90 0.04 1.87 0.02 1.89 0.04 + CrC 10 H18 O6 (BAPWIZ) Cr-O 1.94 1.87 -0.07 1.93 -0.01 1.93 -0.01 + CrC 14 H14 O6 (ATOLAW) Cr-O(=C) 1.96 1.85 -0.11 1.99 0.03 1.91 -0.05 Cr-O(-C) 1.97 1.78 -0.19 1.94 -0.03 1.95 -0.02 O-Cr-O 92.3 112.2 19.9 90.5 -1.8 89.4 -2.9 Cr-O(H2) 2.00 2.14 0.14 2.11 0.11 1.95 -0.05

CrC 15 H21 O6 (ACACCR) Cr-O 1.95 1.91 -0.04 2.00 0.05 1.95 0.00 O-Cr-O 91.7 92.1 0.4 93.3 1.6 88.5 -3.2 2– Cr 2(CO) 10 Cr-Cr 3.22 2.94 -0.28 3.05 -0.17 2.91 -0.31 Cr 2C12 H20 O12 (ACETCR) Cr-O 2.02 1.89 -0.14 2.04 0.02 1.92 -0.10 Cr-O' 2.31 1.89 -0.42 2.59 0.28 2.09 -0.22

Cr(NO) 4 Cr-N 1.75 1.76 0.01 1.69 -0.06 1.64 -0.11 N-O 1.18 1.15 -0.03 1.17 -0.01 1.13 -0.05 – CrC 10 N2H12 O8 (Chromium(III) EDTA) Cr-N 2.12 2.17 0.05 2.04 -0.08 1.91 -0.21

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

N-Cr-N 86.5 83.1 -3.3 87.9 1.4 92.4 5.9 Cr-O 1.94 1.91 -0.03 2.00 0.06 1.96 0.02

Cr 2(Cp) 2(NO) 3(NH 2) Cr-Cr 2.65 2.59 -0.06 2.44 -0.21 3.24 0.59 Cr-N 1.65 1.79 0.14 1.63 -0.02 1.42 -0.23 N-O 1.20 1.16 -0.04 1.19 -0.01 1.18 -0.02 Cr-N 1.94 1.94 0.00 1.85 -0.09 1.34 -0.60 N-O 1.12 1.15 0.03 1.20 0.08 1.23 0.11

(Cp) 2Cr 2(NO) 4 Cr-N(br) 1.90 1.90 0.00 1.96 0.06 1.41 -0.49 Cr-N(ter) 1.71 1.74 0.03 1.94 0.23 1.41 -0.30 Cr-C 2.25 2.26 0.01 2.27 0.02 2.30 0.05 CrF Cr-F 1.77 1.76 -0.01 1.53 -0.24 1.65 -0.12 2– CrF 6 Cr-F 1.72 1.75 0.03 1.75 0.03 1.80 0.08 3- Cr 2F9 (OCOLIB) Cr-Cr 2.77 2.80 0.03 2.66 -0.11 2.86 0.09 Cr-F(t) 1.85 1.82 -0.03 1.82 -0.03 1.72 -0.13 Cr-F(br)-Cr 121.9 124.1 2.2 125.3 3.4 121.9 0.0

CrO 2F2 Cr-O 1.57 1.60 0.03 1.58 0.01 1.61 0.04 Cr-F 1.72 1.76 0.04 1.60 -0.12 1.56 -0.16 O-Cr-O 107.8 99.8 -8.1 106.3 -1.5 107.5 -0.3 F-Cr-F 111.9 126.7 14.8 123.0 11.1 112.1 0.2 2– CrF 5H2O (YASHAB) Cr-F 1.91 1.86 -0.05 1.81 -0.10 1.77 -0.14 Cr-O 1.99 3.86 1.87 4.24 2.25 2.36 0.37

CrF 4N2C2H8 (DIYFEW) Cr-F 1.89 1.77 -0.13 1.82 -0.07 1.70 -0.20 F-Cr-N 92.1 84.3 -7.8 89.4 -2.7 91.5 -0.6 + CrC 2N2H12 O2F2 (BUTDAV) Cr-F 1.88 1.77 -0.11 1.70 -0.18 1.73 -0.15 Cr-O 2.00 2.04 0.04 2.21 0.21 2.04 0.04 Cr-N 2.04 2.01 -0.03 2.06 0.02 1.82 -0.22 CrCl Cr-Cl 2.17 2.18 0.01 1.97 -0.20 2.27 0.10

CrCl 2 Cr-Cl 2.19 2.24 0.05 1.95 -0.24 2.23 0.04 2– CrCl 4 (BAHVIP) Cr-Cl 2.43 2.37 -0.06 2.39 -0.04 2.14 -0.29 Cl-Cr-Cl 105.2 80.9 -24.3 90.5 -14.7 109.5 4.3 3– Cr 2Cl 9 (ZEBRON) Cr-Cr 3.15 2.49 -0.66 3.33 0.18 3.52 0.37 Cr-Cl(br) 2.31 2.22 -0.09 2.31 0.00 2.50 0.19 Cr-Cl(t) 2.29 2.27 -0.02 2.31 0.02 2.15 -0.14

CrCl 2O2 Cr-Cl 2.13 2.17 0.04 1.94 -0.19 2.13 0.00 Cr=O 1.58 1.59 0.01 1.59 0.01 1.59 0.01

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Cr(CO) 4ClC 2H3 (CATYOL) Cr-Cl 2.44 2.40 -0.04 2.35 -0.09 2.26 -0.18 Cr-C(O) 1.93 1.95 0.02 1.93 0.00 1.95 0.02 C-Cr-Cl 86.3 109.2 22.9 83.2 -3.1 91.4 5.1

Cr-C(H 3) 1.71 1.81 0.10 1.72 0.01 1.94 0.23 CrC 10 H15 Cl 2O (AFEHIC) Cr-Cl 2.25 2.16 -0.09 2.05 -0.20 2.21 -0.04 Cl-Cr-Cl 96.5 86.3 -10.1 94.7 -1.8 95.5 -1.0 Cr-O 1.59 1.59 0.00 1.56 -0.03 1.58 -0.01 Cr-C 2.24 2.22 -0.02 2.27 0.03 2.29 0.05

CrC 4N3H13 Cl 3 (AMZCCR) Cr-Cl 2.33 2.20 -0.13 2.23 -0.10 2.32 -0.02 Cr-N 2.08 2.11 0.03 2.12 0.04 1.87 -0.21

CrAlH 2 CrAl 2.49 2.49 0.00 2.11 -0.38 1.76 -0.74 HCrAlH 2 CrAl 2.63 2.54 -0.09 2.11 -0.52 1.90 -0.73 CrSiH 3 Cr-Si 2.44 2.46 0.02 2.85 0.41 1.93 -0.51 HCrSiH 3 Cr-Si 2.45 2.45 0.00 2.74 0.29 1.74 -0.71 HCrPH 2 Cr-P 2.35 2.24 -0.11 2.20 -0.15 2.47 0.12 CrS Cr=S 2.11 2.09 -0.02 1.80 -0.31 2.43 0.32 CrSH Cr-S 2.22 2.28 0.06 1.73 -0.49 2.42 0.21 HCrSH Cr-S 2.20 2.20 0.00 1.09 -1.11 2.38 0.18

CrC 12 P4H34 S2 (JIYDOK) Cr-S 2.39 2.33 -0.06 1.93 -0.46 3.02 0.63 Cr-P 2.36 2.17 -0.19 2.41 0.05 2.48 0.12 S-Cr-P 89.4 99.7 10.3 90.7 1.3 97.6 8.2 2– CrS 4C4H8 (CUWLIP) Cr-S 2.39 2.28 -0.11 2.28 -0.11 2.69 0.30 S-Cr-S 91.7 96.3 4.6 91.6 -0.1 95.9 4.2 CrTi Cr-Ti 1.62 1.84 0.22 2.51 0.89 12.59 10.97 CrNi Cr-Ni 2.13 2.17 0.04 2.67 0.54 1.39 -0.74 CrCu Cr-Cu 2.35 2.55 0.20 3.10 0.75 1.51 -0.84 CrZn Cr-Zn 2.37 2.60 0.23 1.91 -0.46 1.84 -0.54 CrBr Cr-Br 2.43 2.25 -0.18 2.42 -0.01 2.41 -0.02

CrBr 2 Cr-Br 2.43 2.27 -0.16 2.06 -0.37 2.30 -0.13 CrZr Cr-Zr 1.98 2.16 0.18 2.31 0.33 2.21 0.23 CrMo Cr-Mo 1.77 1.85 0.08 1.60 -0.17 2.00 0.23 CrI Cr-I 2.57 2.20 -0.37 2.49 -0.08 2.28 -0.30

CrI 2 Cr-I 2.41 2.41 0.00 2.45 0.04 2.24 -0.16

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* PM6 PM5 N=110 MSE bond length 0.00 -0.02 0.06 MUE bond length 0.09 0.16 0.29 N=25 MSE bond angle -0.6 0.2 0.7 MUE bond angle 8.4 3.7 3.2

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

The mean unsigned errors for calculated bond lengths to chromium are found 0.09 Å for AM1*, 0.16 Å and 0.29 Å for PM6 and PM5, respectively. AM1* shows no systematic error. PM6 underestimates bond lengths to chromium by -0.02 Å, whereas PM5 systematically overestimates them by 0.06 Å.

None of the three methods shows significant systematic error in bond angles to chromium with the mean signed errors of -0.6° (AM1*), 0.2° (PM6) and 0.7° (PM5). Surprisingly, AM1* performs significantly (MUE of 8.4°) and PM6 slightly (MUE = 3.7°) worse for bond angles than PM5 (MUE of 3.2°).

4.2.2 Conclusions and Outlook

The current AM1* parameterization for vanadium and chromium, for which the parameterization data have been extended and made more reliable by including results from DFT calculations, is of the standard expected for a modern NDDO-based method with d- orbitals. Parameters for vanadium and chromium provide important additional elements for catalytic chemistry and biochemistry applications [140, 141, 142]. AM1* gives good results for both energetic and electronic properties of the training set of molecules. AM1* also performs very well for the structural properties with one exception, relatively large errors for the bond angles of chromium compounds comparing with the other two available methods.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.3 Parameterization of Manganese and Iron

4.3.1 Results

Table 4.8 shows the optimized AM1* parameters for manganese and iron [143]. Geometries were optimized with the new AM1* parameterization using VAMP 10.0 [138], while the PM5 calculations used LinMOPAC2.0 [62]. Since PM5 was not parameterized for manganese, it’s only used for iron compounds. And those with PM6 used MOPAC2009 [144].

Table 4.8: AM1* parameters for the elements Mn and Fe. Parameter Mn Fe

Uss [eV] -33.2275445 -99.0000000 Upp [eV] -27.2535784 -38.2000000 Udd [eV] -69.8244104 -83.1000000 -1 ζs [bohr ] 1.9646322 2.8351398 -1 ζp [bohr ] 18.8965365 37.1808614 -1 ζd [bohr ] 1.2348158 2.2895425 βs [eV] -8.1782339 -20.4335137 βp [eV] -21.7780791 -66.1689990 βd [eV] -6.2336234 -26.5282533 gss [eV] 5.0059282 8.4047951 gpp [eV] 13.6386827 10.4447975 gsp [eV] 12.3772691 7.6833614 gp2 [eV] 96.0815576 13.9440172 hsp [eV] 4.5810741 1.6747978 -1 zsn [bohr ] 26.0703955 75.1015032 -1 zpn [bohr ] 1.9830213 0.7086051 -1 zdn [bohr ] 1.9132012 1.4519328 ρ(core) [bohr -1] 1.2307875 1.0769040 -1 ∆H° f(atom) [kcal mol ] 67.701 99.3 0 F sd [eV] 3.3270203 14.1017174 2 G sd [eV] 1.8796412 13.4789419 ααα(ij) H 4.1317380 3.6162132 C 2.8147514 4.0432263 N 1.8883089 3.8755726 O 3.0560315 4.9080254 F 2.5828364 5.3397259 Al 3.5620838 2.0238999 Si 4.2623991 2.6259521 P 2.4072008 2.9339288 S 2.7156160 2.7835642 Cl 2.5923979 2.4937637 Ti 2.3993667 1.4496317 V 3.8190630 1.9484452 Cr 2.7010078 2.0835714 Mn 3.1647134 2.4029678 Fe 2.4029678 3.3225842 Co 2.2792673 2.6623880 68

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Ni 4.5772694 4.4251916 Cu 2.2179615 4.1806484 Zn 4.5907029 4.4519730 Br 3.6890036 2.8134065 Zr 2.6907788 1.7761525 Mo 3.0996586 1.9309316 I 4.1561815 3.5275630 Au 3.0829513 2.8842586 δδδ(ij) H -12.2571050 -10.2036220 C 3.8500280 41.7471647 N 0.6216587 18.5709816 O 6.1303519 98.7945881 F 1.8592303 98.4859864 Al 32.1147597 4.4417867 Si 79.1063414 7.6467930 P 2.9611118 21.4786698 S 3.7385117 8.4757133 Cl 2.4354976 3.7093945 Ti 1.5477850 1.1499629 V 127.1273363 5.0747072 Cr 7.1369564 3.3205625 Mn 5.9226904 4.7319791 Fe 4.7319791 20.2552175 Co 2.1958330 8.1077071 Ni 265.4707317 178.9982694 Cu 1.8893296 96.7779734 Zn 87.3866849 52.0532649 Br 25.1186833 4.3023002 Zr 3.2445347 2.7554220 Mo 14.0341168 3.2515086 I 53.7439446 43.5771427 Au 10.1393842 7.0870550

4.3.1.1 Manganese

4.3.1.1.1 Heats of Formation of Manganese Compounds

The calculated heats of formation for our training set of manganese compounds are shown in Table 4.9. We have compared our results with Stewart’s published PM6 method [72].

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.9: Calculated AM1* and PM6 heats of formation and errors compared with our target values for the manganese-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The codenames within parentheses indicate the CSD-names of the compounds.

Target AM1* PM6

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error Mn 67.7 67.7 0.0 67.7 0.0 Mn – 90.2 151.8 61.6 97.9 7.7 Mn + 239.1 334.9 95.8 224.8 -14.3 Mn 2+ 599.8 760.9 161.1 566.7 -33.1 Mn 3+ 1376.0 1208.7 -167.3 1053.2 -322.8

Mn 2 184.3 203.7 19.4 128.2 -56.1 MnH 57.3 115.4 58.1 114.2 56.9 MnH – 41.2 96.7 55.5 124.2 83.0

MnH 2 114.1 117.0 2.9 114.6 0.5 Mn(C 5H5)2 66.2 100.8 34.6 95.4 29.2 MnN 123.1 121.1 -2.0 99.2 -23.9 2+ Mn(NH 3)6 269.5 275.4 5.9 229.9 -39.6 – MnO 2 -62.1 -3.0 59.1 -35.3 26.8 – MnO 3 -127.1 -97.5 29.6 -127.7 -0.6 – MnO 4 -158.4 -149.7 8.7 -168.8 -10.4 2+ Mn(H 2O) 6 65.7 9.6 -56.1 50.6 -15.1 – Mn(CO) 3 -54.8 -58.6 -3.8 -113.0 -58.1 – Mn(CO) 4 -122.3 -131.1 -8.7 -157.7 -35.3 Mn(CO) 5 -178.0 -152.9 25.1 -174.4 3.6 Mn(CO) 5H -176.8 -180.2 -3.4 -170.4 6.4 + Mn(CO) 6 -49.7 -67.8 -18.1 -78.8 -29.1 Mn(CO) 5CH 3 -179.5 -196.5 -17.0 -179.5 0.0 Mn(CO) 5C6H5 -140.8 -169.9 -29.1 -151.3 -10.5 Mn(CO) 5(C 6H5CH 2) -151.9 -173.7 -21.8 -154.6 -2.7 Mn(CO) 5COCH 3 -215.3 -228.5 -13.2 -230.3 -15.0 Mn(CO) 5(C 6H5CO) -173.2 -195.1 -21.9 -192.3 -19.1 MnC 15 H21 O6 (Mn(acac) 3) -285.2 -280.0 5.2 -267.2 18.0 – MnC 6H8O10 (KAMMND) -543.1 -576.9 -33.8 -537.4 5.7 MnC 9H12 O (BUTMNC) 11.9 -53.6 -65.5 22.8 10.9 MnC 8H5O3 (cyclopentadienyl manganese tricarbonyl) -115.2 -65.3 49.9 -81.5 33.7

MnC 9H7O3 (HEXMNC) -95.5 -89.4 6.1 -83.9 11.6 Mn 2(CO) 9 -314.5 -310.0 4.5 -323.3 -8.8 Mn 2(CO) 10 -385.9 -378.7 7.2 -336.8 49.1 Mn(NO) 8.5 47.9 39.4 98.1 89.6

Mn(CO)(NO) 3 -60.6 -52.9 7.7 -23.0 37.6 – MnC 10 N2H12 O8 (EDTMNK01) -388.3 -407.0 -18.7 -413.1 -24.8 MnF 2 -126.2 -50.4 75.8 -76.8 49.4 – MnF 2 -226.0 -146.5 79.5 -106.1 119.9 MnF 3 -188.0 -173.3 14.7 -139.0 49.0 – MnF 3 -272.2 -158.5 113.7 -164.8 107.4 MnF 4 -231.0 -280.9 -49.9 -170.0 61.0 – MnF 4 -343.6 -308.5 35.1 -250.3 93.3 – MnF 5 -373.0 -433.3 -60.3 -300.3 72.7 – Mn 2F5 -448.3 -440.7 7.6 -257.2 191.1

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

– Mn 2F7 -600.0 -630.6 -30.6 -392.6 207.4 MnOF 2 -125.8 -120.5 5.3 -114.7 11.1 Mn(H 2O) 4F2 trans -333.2 -366.8 -33.6 -315.4 17.8 MnC 7HO 5F2 (CDFVMN) -252.2 -273.1 -20.9 -314.4 -62.2 Mn(CO) 5CF 3 -330.5 -355.7 -25.2 -363.7 -33.2 Mn(CO) 5COCF 3 -359.7 -378.5 -18.8 -381.9 -22.2 MnC 7O7F3 (FACMNA) -437.0 -437.3 -0.3 -431.9 5.1 MnAl 116.5 115.6 -0.9 77.3 -39.2 – MnF 3AlF 4 -704.0 -734.6 -30.6 -220.0 484.0 MnSi 153.2 127.8 -25.4 -275.3 -428.5 MnSiH 93.9 108.2 14.3 -30.9 -124.8

MnSiH 2 85.2 91.6 6.4 131.5 46.3 MnP 81.9 81.9 0.0 110.0 28.1 MnPH 67.6 77.4 9.8 82.1 14.5

MnC 9H11 SO 2 (VALXAI) -76.7 -109.1 -32.4 -54.7 22.0 MnC 7H5SO 4 (CPCSMN) -125.0 -56.8 68.2 -119.5 5.5 – MnC 7N2H12 S4 (COWHOL) -19.9 -161.8 -141.9 -37.2 -17.3 MnC 7H10 S2ClO 3 (GEQLUJ) -179.2 -198.5 -19.3 -161.0 18.2 MnCl 11.3 69.7 58.4 40.9 29.6

Mn(CO) 5Cl (ZOSWEJ) -219.5 -240.6 -21.1 -220.0 -0.5 MnCl 2 -63.0 13.5 76.5 -31.2 31.8 Mn(H 2O) 4Cl 2 trans -263.1 -384.6 -121.5 -275.3 -12.2 Mn 2Cl 4 -168.2 -163.0 5.2 -30.9 137.3 MnCl 2O -136.0 -46.5 89.5 -67.7 68.3 MnTi 148.8 141.8 -7.1 106.2 -42.6

MnV 2 228.3 228.3 0.0 196.1 -32.2 MnCr 184.4 184.4 0.0 173.3 -11.1 MnCo 158.9 158.8 -0.1 93.3 -65.6 MnNi 80.9 80.9 0.0 168.3 87.4 MnCu 158.2 158.2 0.0 133.6 -24.6 MnZn 89.3 90.4 1.1 -34.3 -123.6

MnOBr 2 -37.0 2.5 39.5 -22.2 14.8 Mn(H 2O) 4Br 2 trans -244.3 -305.5 -61.2 -240.4 3.9 Mn(CO) 5Br -210.9 -208.5 2.4 -214.7 -3.8 2– MnBr 4 (PYDMNB) -174.7 -174.4 0.3 -75.9 98.8 MnZr 173.7 80.5 -93.2 190.4 16.7 MnMo 191.5 191.5 0.0 222.7 31.2 MnI 65.8 84.9 19.1 59.1 -6.7

MnOI 2 -7.0 37.1 44.1 6.0 13.0 Mn(H 2O) 4I2 trans -213.7 -267.0 -53.3 -209.7 4.0 Mn(CO) 5I (VUCFAA) -199.4 -193.5 5.9 -204.2 -4.8 MnC 13 N2H8O3I (YOMHEN) -83.2 -68.7 14.5 -80.7 2.5

AM1* PM6 N=86 Most positive error 161.1 484.0 Most negative error -167.3 -428.5 MSE 2.3 9.8 MUE 32.3 51.0 RMSD 49.7 95.5

Results for the PM6 parameterization set ( N=44 ) AM1* PM6 MSE -7.5 0.1 MUE 31.1 15.8 RMSD 43.7 20.9 71

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* reproduces the heats of formation for the training set of manganese compounds used in parameterization better than PM6. However, we note that this comparison is not strictly valid as it is based on the current parameterization data. As it can be seen from Table 4.9, AM1* parameterization data set contains 86 compounds and 44 of them are taken from original PM6 parameterization data set. These data absolutely demonstrate the influence of the extent of the training data. AM1* performs significantly better for its extended training set, whereas PM6 performs better for the subset for which it was trained. This situation is unavoidable and is a direct consequence of the relative paucity of data for parameterizing semiempirical MO techniques for transition metals. Both AM1* and PM6 tend to give positive systematic errors to manganese-containing compounds. For AM1* with the mean signed error (MSE) of 2.3 kcal mol −1 this tendency is less pronounced than PM6 (MSE of 9.8 kcal mol −1). The mean unsigned error (MUE) for the AM1* parameterization dataset is 32.3 kcal mol −1, compared with 51.0 kcal mol −1 for PM6. PM6 especially produces large errors for the compounds that were not included in its original training set. The largest errors for AM1* are mainly found for Mn3+ , Mn 2+ and Mn + (-167.3, 161.1 and 95.8 kcal mol −1, respectively). Since the ionization potential of manganese is an important determinant of the reactivity of manganese centers, these errors are important. However, we could not detect serious systematic trends caused by these errors. Molecules that give the − −1 −1 largest positive errors for AM1* are MnF 3 (113.7 kcal mol ), MnCl 2O (89.5 kcal mol ), − −1 −1 −1 MnF 2 (79.5 kcal mol ), MnCl 2 (76.5 kcal mol ), MnF 2 (75.8 kcal mol ), MnC 7H5SO 4 −1 − −1 (Mn(Cp)(CO) 2(SO 2), CPCSMN) (68.2 kcal mol ), MnO 2 (59.1 kcal mol ), MnH (58.1 kcal −1 − −1 − mol ) and MnH (55.5 kcal mol ). The largest negative errors are found for MnC 7N2H12 S4 − −1 (Mn(C 3N2H4)(C 2H4S2)2 , COWHOL) (-141.9 kcal mol ), trans-Mn(H 2O) 4Cl 2 (-121.5 kcal −1 −1 −1 mol ), MnZr (-93.2 kcal mol ), MnC 9H12 O (Mn(CO)(C 4H6)2, BUTMNC) (-65.5 kcal mol ), −1 − −1 trans-Mn(H 2O) 4Br 2 (-61.2 kcal mol ) and MnF 5 (-60.3 kcal mol ). AM1* uses the unchanged AM1 parameterization for the elements H, C, N, O and F, which limits the possible accuracy of the parameterization. The large errors with the compounds containing these elements are not surprising as we have pointed out in our previous parameterizations [66, 67, 68, 70]. As found for other metals, the large errors in pure AM1* element-containing compounds are likely to be a consequence of our sequential parameterization strategy, in contrast to the simultaneous parameterization used for PM6 [72].

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.3.1.1.2 Ionization Potentials and Dipole Moments of Manganese Compounds

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for AM1* and PM6 are given Table 4.10.

Table 4.10: Calculated AM1* and PM6 Koopmans’ theorem ionization potentials and dipole moments for manganese-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 Compound Target Error Error Koopmans' Theorem Ionization Potentials for Manganese Compounds (eV) MnH 7.80 9.39 1.59 5.82 -1.98 MnO 8.70 10.58 1.88 7.66 -1.04

Mn(CO) 5 8.10 9.18 1.08 7.44 -0.66 Mn(CO) 5H 8.85 8.71 -0.14 8.44 -0.41 MnF 2 11.40 8.34 -3.06 8.56 -2.84 MnF 3 12.60 8.60 -4.00 8.15 -4.45 MnF 4 13.50 9.62 -3.88 6.91 -6.59 MnCl 2 11.03 9.67 -1.36 8.11 -2.92 Mn(CO) 5Br 8.83 8.52 -0.31 8.74 -0.09 MnBr 2 10.30 9.70 -0.60 8.78 -1.52 Mn(CO) 5I 8.40 8.71 0.31 8.65 0.25 N=11 AM1* PM6 MSE -0.77 -2.02 MUE 1.66 2.07 Dipole Moments for Manganese Compounds (Debye) MnH 0.50 0.75 0.25 0.99 0.49 MnN 3.07 4.38 1.31 3.98 0.91 MnNO 5.89 4.46 -1.43 4.45 -1.44 MnO 4.72 4.57 -0.15 3.74 -0.98 MnOH 0.40 1.64 1.24 3.13 2.73 MnF 2.27 0.67 -1.60 4.23 1.96

MnOF 2 0.53 4.56 4.03 0.61 0.08 MnAl 1.67 1.60 -0.07 0.19 -1.48 MnSi 3.27 2.85 -0.42 4.03 0.76 MnSiH 3.15 2.75 -0.40 4.03 0.88

MnSiH 2 3.22 2.54 -0.68 3.96 0.74 MnP 2.54 2.88 0.34 2.70 0.16 MnPH 4.34 3.12 -1.22 2.97 -1.37 MnS 4.22 3.91 -0.31 1.56 -2.66 MnCl 2.36 0.81 -1.55 3.59 1.23 MnBr 4.29 3.10 -1.19 7.72 3.43

MnOBr 2 0.51 2.12 1.61 0.56 0.05 MnI 4.25 1.68 -2.57 2.13 -2.12

MnOI 2 0.94 4.30 3.36 0.30 -0.64 N=19 AM1* PM6 MSE 0.03 0.14 MUE 1.25 1.27

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* with an MUE of 1.66 eV performs better than PM6 (MUE of 2.07 eV) for Koopman’s theorem ionization potentials. Both AM1* and PM6 tend to underestimate ionization potentials to manganese-containing compounds. However, this tendency is more serious for PM6 with an MSE of -2.02 eV whereas AM1* gives an MSE of -0.77 eV.

Large AM1* errors are found for MnF 2 (-3.06 eV), MnF 3 (-4.00 eV) and MnF 4 (-3.88 eV). This may be an indirect result of using the original AM1 parameters for fluorine. But, however, PM6 also produces very large errors for MnF 2 (-2.84 eV), MnF 3 (-4.45 eV) and

MnF 4 (-6.59 eV). Since, both methods produce these large errors in the same direction, this may be a result of possible erroneous reference values presented in NIST [109].

AM1* with an MSE of 0.03 Debye shows no considerable tendency to systematic errors for dipole moments of manganese compounds whereas PM6 shows positive systematic error with 0.14 Debye (MSE). AM1* and PM6 perform comparable, with the MUEs of 1.25 and 1.27

Debye for AM1* and PM6, respectively. The largest AM1* errors are found for MnOF 2 (4.03

Debye), MnOI 2 (3.36 Debye) and MnI (-2.57 Debye). The large error for MnOF 2 can be an indirect result of using original AM1 parameters for oxygen and fluorine. However, the large errors with iodine containing compounds are not surprising and result from the known weakness [66, 67] of AM1* parameterization for iodine in reproducing dipole moments.

4.3.1.1.3 Geometries of Manganese Compounds

Table 4.11 shows a comparison of AM1* and PM6 results in reproducing the geometries of the manganese-containing compounds.

Table 4.11: Calculated AM1* and PM6 bond lengths and angles for manganese-containing compounds. The codenames within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 Compound Variable Target Error Error

Mn 2 Mn-Mn 2.29 2.40 0.11 2.89 0.60 MnH Mn-H 1.74 1.91 0.18 1.68 -0.05 MnH – Mn-H 1.77 1.83 0.06 1.66 -0.11

Mn(C 5H5)2 Mn-C 2.42 2.79 0.37 2.37 -0.05 – MnO 2 Mn-O 1.62 1.86 0.24 1.63 0.02 – MnO 3 Mn-O 1.59 1.85 0.26 1.62 0.03 – MnO 4 Mn-O 1.64 1.86 0.22 1.63 -0.01 74

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

2+ Mn(H 2O) 6 Mn-O 2.14 2.21 0.07 2.15 0.01 Mn-O 2.19 2.23 0.04 2.17 -0.02 Mn-O 2.20 2.27 0.07 2.17 -0.03

Mn(CH 3)O 3 Mn=O 1.59 1.84 0.25 1.60 0.01 Mn-C 1.99 1.91 -0.08 1.93 -0.06 – Mn(CO) 3 Mn-C 1.82 1.97 0.16 1.82 0.01 Mn(CO) 5 Mn-C 1.82 1.89 0.07 1.85 0.03 Mn-C 1.86 1.90 0.04 1.89 0.03

Mn(CO) 5H Mn-C 1.86 1.93 0.07 1.84 -0.02 Mn-C 1.85 1.92 0.07 1.86 0.01 H-Mn-C 85.5 90.7 5.2 83.5 -2.0

Mn(CO) 5CH 3 Mn-C 1.83 1.90 0.07 1.85 0.02 Mn-C 1.85 1.94 0.09 1.85 0.00 Mn-C 2.19 1.99 -0.21 2.08 -0.12 + Mn(CO) 6 Mn-C 1.91 1.95 0.04 1.89 -0.02 Mn(CO) 5C6H5 Mn-C 1.83 1.90 0.07 1.85 0.02 Mn-C 1.85 1.94 0.09 1.86 0.01 Mn-C 2.15 1.99 -0.16 1.99 -0.16

Mn(CO) 5(C 6H5CH 2) Mn-C 1.82 1.90 0.08 1.85 0.03 Mn-C 1.85 1.94 0.09 1.85 0.00 Mn-C 2.26 2.02 -0.24 2.09 -0.17

Mn(CO) 5COCH 3 Mn-C 1.84 1.91 0.07 1.85 0.01 Mn-C 1.85 1.93 0.08 1.88 0.03 Mn-C 2.17 2.02 -0.15 1.97 -0.20

Mn(CO) 5(C 6H5CO) Mn-C 1.84 1.90 0.07 1.86 0.02 Mn-C 1.85 1.93 0.08 1.87 0.02 Mn-C 2.18 2.03 -0.15 1.97 -0.20 – MnC 6H8O10 (KAMMND) Mn-O 1.90 2.07 0.17 1.93 0.03 Mn-O 2.30 2.28 -0.02 2.44 0.14 O-Mn-O 91.7 74.1 -17.6 88.3 -3.4

MnC 9H12 O (BUTMNC) Mn-C 1.81 1.92 0.11 1.81 0.00 Mn-C 2.15 1.98 -0.17 2.11 -0.04

Mn(CO) 3Cp (CPMNCO) Mn-C(ring) 2.14 2.21 0.07 2.16 0.02 Mn-C(O) 1.79 1.93 0.14 1.81 0.02 C-Mn-C 91.4 101.0 9.6 92.6 1.2

MnC 9H7O3 (HEXMNC) Mn-C 2.15 2.12 -0.03 2.17 0.02 Mn-C 1.78 1.92 0.14 1.82 0.04

Mn 2C8H12 O8 (Mn 2(Ac) 4) Mn-Mn 3.31 2.43 -0.88 3.28 -0.03 Mn 2(CO) 10 Mn-Mn 2.89 2.36 -0.53 2.70 -0.19 Mn 2(CO) 10 C2 (JIPVOT) Mn-C 1.86 1.93 0.07 1.84 -0.02 Mn-C 1.83 1.90 0.07 1.83 0.00 C-Mn-C 85.9 87.6 1.7 85.4 -0.5 MnN Mn#N 1.59 1.52 -0.07 1.57 -0.02 MnNO Mn-N 1.73 1.76 0.03 1.74 0.01 2+ Mn(NH 3)6 Mn-N 2.16 2.21 0.05 2.15 -0.01 Mn(CO)(NO) 3 Mn-N 1.70 1.67 -0.03 1.64 -0.06 Mn-C 1.87 1.94 0.06 1.93 0.06 C-Mn-N 106.0 92.9 -13.1 107.7 1.8 – MnC 10 N2H12 O8 (EDTMNK01) Mn-O 2.02 2.15 0.13 1.95 -0.07 Mn-O 1.89 2.16 0.27 1.98 0.09 Mn-N 2.24 2.11 -0.13 2.10 -0.14 O-Mn-O 88.3 89.7 1.4 84.2 -4.1 N-Mn-O 77.5 82.2 4.7 83.7 6.2

MnC 12 N2H12 O6 (XOYHAU) Mn-O 2.15 2.19 0.04 2.33 0.18 Mn-N 2.26 1.81 -0.45 1.84 -0.42 75

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

O-Mn-O 85.4 66.7 -18.7 62.5 -22.9 MnC 12 N2H16 O4 (Mn phenanthroline tetrahydrate) Mn-O 2.16 2.33 0.17 3.45 1.29 MnF Mn-F 1.82 2.14 0.32 1.87 0.05

MnF 2 Mn-F 1.79 1.84 0.05 1.78 -0.01 – MnF 2 Mn-F 1.86 1.88 0.03 1.83 -0.03 MnOF 2 Mn-O 1.55 1.89 0.34 1.57 0.02 Mn-F 1.72 1.79 0.06 1.73 0.01 O-Mn-F 121.3 102.0 -19.3 124.1 2.8

Mn(H 2O) 4F2 trans Mn-F 1.98 1.87 -0.11 1.78 -0.20 Mn-O 2.13 2.35 0.22 2.34 0.21

MnC 7HO 5F2 (CDFVMN) Mn-C 1.72 1.90 0.18 1.85 0.13 Mn-C 1.77 1.94 0.17 1.86 0.09 Mn-C 1.94 2.03 0.09 1.97 0.03 C-Mn-C 93.8 87.6 -6.2 93.3 -0.5

MnF 3 Mn-F 1.79 1.79 0.00 1.76 -0.03 F-Mn-F 120.0 141.7 21.7 136.1 16.1

MnC 7O7F3 (FACMNA) Mn-C 1.81 1.89 0.08 1.82 0.01 Mn-O 2.03 2.29 0.26 2.05 0.02

Mn 2(CO) 8(CF 2)2 (DOFPET) Mn-Mn 2.66 2.42 -0.24 2.73 0.07 Mn-C(F 2) 2.02 2.10 0.08 1.98 -0.04 Mn-C(O) 1.88 1.96 0.08 1.87 -0.01 C-Mn-Mn 49.4 54.8 5.4 46.4 -3.0 MnAl Mn-Al 2.34 2.34 0.00 2.05 -0.28

Mn(AlH 2)2 Mn-Al 2.41 2.42 0.00 2.15 -0.26 MnSi Mn-Si 2.34 2.25 -0.10 2.45 0.11 MnSiH Mn-Si 2.34 2.34 0.00 2.51 0.17

MnSiH 2 Mn-Si 2.38 2.44 0.06 2.60 0.22 MnSi 2C9H15 O5 (KIRYUF) Mn-Si 2.34 2.39 0.05 2.34 0.00 Mn-O 2.95 2.99 0.04 2.99 0.04 Si-Mn-Si 71.2 81.5 10.3 68.8 -2.4 MnP Mn-P 1.97 2.06 0.09 2.15 0.18 MnPH Mn-P 2.22 2.21 -0.02 2.23 0.01 MnS Mn-S 1.99 2.14 0.15 2.01 0.02

MnS 2 Mn-S 2.20 2.00 -0.20 2.02 -0.18 MnC 9H11 SO 2 (VALXAI) Mn-S 2.27 2.25 -0.02 2.18 -0.09 Mn-C(O) 1.77 2.01 0.24 1.79 0.02

Mn-C(C 4) 2.12 2.10 -0.02 2.19 0.07 MnC 7H5SO 4 (CPCSMN) Mn-S 2.04 2.38 0.34 2.10 0.06 Mn-C 1.79 1.99 0.20 1.82 0.03 Mn-C' 2.10 2.10 0.00 2.18 0.08 S-Mn-C 91.0 80.8 -10.1 92.6 1.6 – MnC 7N2H12 S4 (COWHOL) Mn-S 2.32 2.33 0.01 2.28 -0.04 S-Mn-S 157.5 144.9 -12.6 156.2 -1.3

MnC 7H10 S2ClO 3 (GEQLUJ) Mn-S 2.39 2.35 -0.04 2.26 -0.13 Mn-C 1.80 1.92 0.12 1.79 -0.01 Mn-Cl 2.38 2.17 -0.21 2.31 -0.07 S-Mn-Cl 92.2 87.7 -4.5 88.6 -3.6

MnC 4N2H8S2O6 (WIFSEJ) Mn-S 2.61 2.26 -0.35 2.21 -0.40 Mn-O 2.20 2.23 0.03 2.13 -0.07 O-Mn-S 87.3 111.8 24.5 80.6 -6.7 MnCl Mn-Cl 2.12 2.31 0.19 2.13 0.01

Mn(CO) 5Cl (ZOSWEJ) Mn-Cl 2.37 2.13 -0.24 2.23 -0.14 Mn-C 1.81 1.91 0.10 1.83 0.02 Mn-C 1.89 1.94 0.05 1.86 -0.03

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Mn(H 2O) 4Cl 2 trans Mn-Cl 2.36 2.21 -0.15 1.98 -0.38 Mn-O 2.10 2.33 0.23 2.21 0.11 Mn-O 2.50 2.41 -0.09 3.70 1.20 Mn-O 2.52 2.59 0.07 3.79 1.27

Mn 2Cl 4 Mn-Mn 2.29 2.38 0.09 2.49 0.20 Mn-Cl 2.13 2.10 -0.03 1.96 -0.18

MnCl 2O Mn-O 1.55 1.89 0.34 1.57 0.02 Mn-Cl 2.10 2.08 -0.02 1.87 -0.23 O-Mn-Cl 121.5 86.3 -35.1 119.1 -2.3

MnC 12 N4H12 Cl 2O (MUPYUR) Mn-Cl 2.47 2.12 -0.35 2.15 -0.32 Mn-N(py) 2.26 1.81 -0.45 1.92 -0.34 Mn-N' 2.34 1.94 -0.40 1.94 -0.40 N-Mn-N' 95.2 96.2 1.0 94.7 -0.5 MnTi Mn-Ti 2.25 2.25 0.00 3.62 1.37

MnV 2 Mn-V 2.28 2.21 -0.07 4.90 2.62 MnCr Mn-Cr 2.35 2.35 0.00 5.90 3.55 MnCo Mn-Co 2.44 2.27 -0.18 3.39 0.95 MnNi Mn-Ni 2.50 2.41 -0.08 6.02 3.52 MnCu Mn-Cu 2.50 2.50 0.00 7.67 5.17 MnZn Mn-Zn 2.62 2.62 0.00 2.29 -0.33 MnBr Mn-Br 2.25 2.41 0.16 2.56 0.31

MnBr 2 Mn-Br 2.34 2.33 -0.01 2.23 -0.11 MnOBr 2 Mn-Br 2.24 2.29 0.05 2.31 0.07 Mn-O 1.55 1.88 0.33 1.56 0.01 O-Mn-Br 120.7 104.2 -16.5 125.5 4.8

Mn(H 2O) 4Br 2 trans Mn-Br 2.50 2.40 -0.10 2.45 -0.05 Mn-O 2.10 2.23 0.13 2.08 -0.02

Mn(CO) 5Br Mn-Br 2.56 2.39 -0.17 2.49 -0.07 Mn-C 1.82 1.90 0.09 1.82 0.01 Mn-C' 1.88 1.94 0.07 1.86 -0.01 2– MnBr 4 (PYDMNB) Mn-Br 2.50 2.43 -0.07 2.44 -0.06 MnAlC 6Br 3O5 (CMNCXA10) Mn-Al 3.53 3.63 0.10 3.45 -0.08 Mn-C 1.95 1.97 0.02 1.92 -0.03 Mn-C' 1.87 1.93 0.06 1.87 0.00 Br-Al-Mn 140.2 117.0 -23.2 126.9 -13.3 MnZr Mn-Zr 2.43 2.43 0.00 3.02 0.59 MnMo Mn-Mo 2.27 2.27 0.00 4.71 2.44 MnI Mn-I 2.46 2.49 0.04 2.29 -0.17

MnOI 2 Mn-I 2.45 2.33 -0.12 2.44 -0.01 Mn-O 1.55 1.89 0.34 1.55 0.00 O-Mn-I 120.1 112.7 -7.4 116.1 -4.0

Mn(H 2O) 4I2 trans Mn-I 2.73 2.44 -0.29 2.52 -0.21 Mn-O 2.08 2.27 0.19 2.24 0.16

Mn(CO) 5I (VUCFAA) Mn-I 2.69 2.39 -0.30 2.62 -0.07 Mn-C 1.84 1.91 0.07 1.82 -0.02

MnC 13 N2H8O3I (YOMHEN) Mn-I 2.72 2.36 -0.36 2.70 -0.02 Mn-N 2.05 1.98 -0.07 1.92 -0.13 Mn-C 1.77 1.93 0.16 1.84 0.07 I-Mn-N 87.7 87.1 -0.6 83.3 -4.4

Mn 2(CO) 8I2 (SIZYUV) Mn-Mn 3.98 3.98 0.00 3.96 -0.02 Mn-I 2.70 2.51 -0.19 2.66 -0.04 Mn-C 1.88 1.93 0.05 1.85 -0.03 I-Mn-Mn 42.6 37.8 -4.8 43.6 1.0 MnI(SH) Mn-I 2.41 2.36 -0.05 2.41 0.00 Mn-S 2.10 2.27 0.17 2.05 -0.05 77

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

I-Mn-S 115.6 146.2 30.6 101.6 -14.0

MnI(F)(PH 2)(SH) Mn-I 2.50 2.39 -0.12 2.46 -0.04 Mn-F 1.75 1.79 0.04 1.73 -0.02 Mn-P 2.27 2.25 -0.02 2.28 0.01 Mn-S 2.16 2.22 0.06 2.16 0.00 AM1* PM6 N=151 MSE bond length 0.02 0.14 MUE bond length 0.13 0.24 N=25 MSE bond angle -3.0 -2.1 MUE bond angle 12.2 5.0

Both AM1* and PM6 overestimate bond lengths to manganese-containing compounds systematically by 0.02 and 0.14 Å, respectively. AM1*, with an MUE of 0.13 Å performs better than PM6 (MUE of 0.24 Å) for bond lengths. Here we note that, PM6 reproduces bond lengths to be very long for the manganese-transition metal diatomic compounds. Parameterization dataset of PM6 clearly does not cover these model compounds which seriously affects statistics. For the bond angles, PM6 with an MUE of 5.0° performs quite well, compared with AM1* (MUE = 12.2°). AM1* and PM6 reproduce bond angles for manganese-containing compounds that are on average 3.0° and 2.1° to be too small.

4.3.1.2 Iron

4.3.1.2.1 Heats of Formation of Iron Compounds

The results obtained for heats of formation of iron-containing compounds are shown in Table 4.12. We have compared our results with Stewart’s published PM6 method [72] and also unpublished PM5 method implemented in LinMopac [62].

AM1* reproduces the heats of formation of the training set of iron compounds used in parameterization better than both PM6 and PM5. Once again, one must consider that this comparison is not strictly valid as it is based on the current parameterization data, which sometimes differ from those used in PM6 and PM5. As it can be seen from Table 4.12, AM1* parameterization data set contains 98 compounds and 55 of them are taken from original PM6 parameterization data set. Since PM5 is unpublished, we don’t know if these data cover original PM5 parameterization dataset or not. These data demonstrate the influence of the extent of the training data. AM1* with the mean unsigned error of 26.5 kcal mol −1 performs

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

significantly better for its extended training set than PM6 and PM5 (MUEs of 31.6 and 34.5 kcal mol −1, respectively), whereas PM6 performs better with the MUE of 17.8 kcal mol −1 than AM1* and PM5 (MUEs of 32.4 and 33.8 kcal mol −1, respectively) for the subset for which it was trained. As before, we note that, this situation is unavoidable and is a direct consequence of the relative paucity of data for parameterizing semiempirical MO techniques for transition metals.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.12: Calculated AM1*, PM6 and PM5 heats of formation and errors compared with our target values for the iron-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The codenames within parentheses indicate the CSD-names of the compounds. Target AM1* PM6 PM5

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error Fe 99.3 99.3 0.0 99.3 0.0 99.3 0.0 Fe + 281.6 251.5 -30.1 262.3 -19.3 282.2 0.6 Fe – 92.0 160.3 68.3 201.3 109.3 140.7 48.7 Fe 2+ 654.6 697.5 42.9 637.4 -17.2 647.3 -7.3 Fe 3+ 1361.0 1361.6 0.6 1358.0 -3.0 1349.7 -11.3

Fe 2 180.0 164.3 -15.7 210.5 30.5 207.5 27.5 FeH 113.9 90.4 -23.5 145.9 32.0 123.7 9.8 FeH – 91.1 100.4 9.3 193.0 101.9 102.2 11.1

FeCH 3 71.0 51.7 -19.3 109.6 38.6 79.9 8.9 FeC 5H5 88.0 82.5 -5.5 110.7 22.7 142.6 54.6 Fe(C 5H5)2 57.9 67.2 9.3 49.3 -8.6 102.3 44.3 + Fe(C 5H5)2 210.2 250.4 40.2 252.0 41.8 294.3 84.1 FeO 60.0 32.8 -27.2 69.2 9.2 61.0 1.0 FeO + 265.0 289.8 24.8 246.0 -19.0 259.3 -5.7 FeO – 31.0 81.7 50.7 94.1 63.1 44.0 13.0 – FeO 2 -30.0 -26.9 3.1 48.0 78.0 -18.8 11.2 FeOH 32.0 13.5 -18.5 28.5 -3.5 37.6 5.6

Fe(OH) 2 -79.0 -83.3 -4.3 -56.5 22.5 -50.4 28.6 Fe(H 2O) 4(OH) 2 -294.0 -327.1 -33.1 -334.5 -40.5 -294.5 -0.5 Fe(H 2O) 5(OH) -162.2 -222.7 -60.5 -194.9 -32.7 -183.3 -21.1 2+ Fe(H 2O) 6 64.8 -4.3 -69.1 90.8 26.0 39.4 -25.4 3+ Fe(H 2O) 6 492.6 466.0 -26.7 455.0 -37.6 415.8 -76.8 Fe(CO) 4H2 -131.0 -129.8 1.2 -82.7 48.3 -130.9 0.1 Fe(CO) 63.9 26.1 -37.8 59.1 -4.8 60.4 -3.5 Fe(CO) – 34.8 2.0 -32.8 94.1 59.3 42.4 7.6

Fe(CO) 2 0.2 6.7 6.5 -3.4 -3.6 1.9 1.7 – Fe(CO) 2 -27.3 -76.6 -49.3 15.9 43.2 -43.8 -16.5 Fe(CO) 3 -55.8 -57.3 -1.5 -32.0 23.8 -41.0 14.8 – Fe(CO) 3 -99.2 -124.1 -24.9 -50.2 49.0 -103.6 -4.4

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Fe(CO) 4 -105.1 -148.7 -43.6 -127.5 -22.4 -108.0 -2.9 – Fe(CO) 4 -160.9 -205.1 -44.2 -139.2 21.7 -173.0 -12.1 2– Fe(CO) 4 -115.1 -125.9 -10.8 -114.6 0.5 -127.3 -12.2 Fe(CO) 5 -174.0 -181.1 -7.2 -188.4 -14.4 -138.1 35.8 3– FeC 6O12 (Fe(III)(Ox) 3) -506.7 -554.5 -47.8 -510.4 -3.7 -618.7 -112.0 FeC 6H3O12 (H 3Fe(III)(Ox) 3) -516.8 -481.2 35.6 -501.4 15.4 -505.4 11.4 Fe(CO) 4C2H4 -129.2 -142.1 -12.9 -133.4 -4.2 -128.5 0.7 FeC 8H2O6 (FCPENO) -173.8 -211.7 -37.9 -170.4 3.4 -210.0 -36.2 FeC 10 H14 O4 (bis(acetylacetonate)iron) -198.0 -97.2 100.8 -178.2 19.8 -150.6 47.4 – FeC 15 H21 O6 (Fe(II)(Acac)3 anion) -340.2 -331.6 8.6 -317.9 22.3 -340.3 -0.1 Fe 2(CO) 9 -319.2 -322.7 -3.5 -378.8 -59.6 -324.1 -4.9 2+ Fe(NH 3)6 266.4 258.1 -8.3 284.2 17.8 247.0 -19.4 3– Fe(CN) 6 374.3 156.5 -217.8 337.0 -37.3 126.8 -247.5 4– Fe(CN) 6 484.5 361.2 -123.3 494.5 10.0 318.1 -166.4 2+ FeC 6N6H24 (Fe(II)en) 3) 283.9 290.6 6.7 286.9 3.0 283.8 -0.1 2+ FeC 36 N6H24 (Ferrous tris(ortho phenantholine) 451.2 535.5 84.3 428.1 -23.1 489.1 37.9

FeC 8NH 5O2 (ACODUR) -12.1 -12.0 0.1 -9.2 2.9 -5.1 7.0 + FeC 9NH 8O2 (CPACFE) 113.2 147.1 33.9 96.1 -17.1 145.4 32.2 Fe(CO) 2(NO) 2 -75.0 -72.8 2.2 -62.3 12.7 -2.9 72.1 FeC 16 N5H11 O4 -53.9 8.2 62.1 -54.8 -0.9 -31.2 22.7 FeC 7NH 5O5 (CNOFEA) -89.2 -57.0 32.2 -94.6 -5.4 -65.6 23.6 – FeC 10 N2H12 O8 (Iron(III)EDTA) -405.6 -377.8 27.9 -404.1 1.5 -425.7 -20.1 FeN 174.3 139.8 -34.5 113.5 -60.8 159.5 -14.8 FeN + 348.8 340.5 -8.3 294.5 -54.3 326.5 -22.3 FeN – 123.7 147.8 24.1 162.4 38.7 135.0 11.3 FeF 11.4 44.6 33.2 22.1 10.7 9.9 -1.5 + Fe(H 2O) 5F -184.7 -252.6 -67.9 -214.0 -29.3 -212.6 -27.9 FeF 2 -93.1 -97.1 -4.0 -80.7 12.4 -95.8 -2.7 FeF 3 -196.2 -159.3 36.9 -162.1 34.1 -185.6 10.6 3– FeF 6 -175.3 -175.3 0.0 -177.2 -1.9 -323.5 -148.2 FeAl 157.8 161.1 3.3 181.0 23.2 181.6 23.8

Fe(AlH 2)2 216.8 214.8 -2.0 299.6 82.8 169.9 -46.9 FeSiH 133.7 121.6 -12.1 190.5 56.8 162.1 28.4

FeSiH 2 125.6 122.9 -2.7 184.7 59.1 146.7 21.1

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Fe(SiH 3)2 126.7 133.4 6.7 234.7 108.0 136.0 9.3 FeP 156.9 157.0 0.1 29.8 -127.1 174.0 17.1 FePH 104.6 104.4 -0.2 56.8 -47.8 126.3 21.7 FeS 88.6 55.0 -33.6 137.0 48.4 101.1 12.5

FeC 9H10 SO 2 (CEYTFE) -59.3 -42.6 16.7 -39.5 19.8 -36.1 23.2 FeC 12 H14 S4O2 (CIBGAV10) -73.1 -73.1 0.0 -88.8 -15.7 -64.0 9.1 FeCl 60.0 51.4 -8.6 52.5 -7.5 50.7 -9.3

FeCl 2 -33.7 33.7 67.4 12.6 46.3 -24.0 9.7 FeCl 3 -60.5 -5.7 54.8 -37.9 22.6 -59.8 0.7 2– FeCl 4 (GOXLUA) -105.2 -106.9 -1.7 -100.8 4.4 -187.2 -82.0 3– FeCl 6 -56.5 -109.4 -52.9 -54.3 2.2 -177.8 -121.3 + Fe(H 2O) 5Cl -148.4 -208.0 -59.6 -146.3 2.1 -175.4 -27.0 FeC 6N2H18 Cl 3 (FINJIV) -91.7 -74.4 17.3 -104.0 -12.3 -126.7 -35.0 FeTi 179.7 179.8 0.1 140.2 -39.5 153.7 -26.0 FeV 146.0 146.0 0.0 250.8 104.8 171.9 25.9 FeCr 215.2 215.2 0.0 216.4 1.2 -20.1 -235.3 FeCo 158.4 158.4 0.0 133.9 -24.5 -11.3 -169.7 FeNi 93.6 93.6 0.0 199.4 105.8 178.5 84.9 FeCu 140.7 140.7 0.0 180.0 39.3 83.8 -56.9 FeZn 119.7 129.6 9.9 113.1 -6.6 180.9 61.2 FeBr 44.7 51.9 7.2 83.7 39.0 58.6 13.9

FeBr 2 -9.9 -16.5 -6.6 55.9 65.8 62.3 72.2 Fe 2Br 4 -60.5 -60.5 0.0 -23.5 37.0 -35.2 25.3 FeC 6H5BrO 3 (ALCFEA) -110.8 -122.7 -11.9 -119.6 -8.8 -132.4 -21.6 + Fe(H 2O) 5Br -137.9 -211.7 -73.8 -141.7 -3.8 -165.0 -27.1 Fe(H 2O) 4Br 2 -248.8 -239.4 9.5 -293.3 -44.5 -281.1 -32.3 FeZr 206.1 180.3 -25.8 311.3 105.2 314.0 107.9 FeMo 251.3 251.2 -0.1 242.5 -8.8 317.4 66.1

Fe(CO) 3(C 3H5)I -82.1 -86.7 -4.6 -81.0 1.1 -67.1 15.0 FeC 6H5IO 3 (ALCOFE10) -97.1 -79.1 18.0 -100.2 -3.1 -108.1 -11.0 Fe(CO) 4I2 -151.9 -127.6 24.3 -140.5 11.4 -166.4 -14.5 Fe 2I4 2.0 74.1 72.1 16.5 14.5 18.8 16.8 FeI 2 21.0 77.7 56.7 125.4 104.4 47.3 26.3 FeI 52.9 91.2 38.3 107.2 54.3 78.3 25.4 FeMn 126.6 126.7 0.1 161.6 35.0 - -

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* PM6 PM5 N=98 Most positive error 100.8 109.3 107.9 Most negative error -217.8 -127.1 -247.5 MSE -3.1 13.7 -5.5 MUE 26.5 31.6 34.5 RMSD 41.4 43.6 57.4

Results for the PM6 parameterization set ( N=55 )

MSE -6.3 1.6 -13.5 MUE 32.4 17.8 33.8 RMSD 48.9 23.5 57.6

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* and PM5 underestimate heats of formation to iron compounds by only -3.1 and -5.5 kcal mol −1, respectively. On the other hand, PM6 systematically predicts the heats of formation of iron compounds to be too positive with a mean signed error of 13.7 kcal mol −1.

The largest positive errors for AM1* are found for the compounds FeC 10 H14 O4 −1 2+ (bis(acetylacetonate)iron) (100.8 kcal mol ), FeC 36 N6H24 (ferrous tris(ortho phenantholine)) −1 −1 − −1 −1 (84.3 kcal mol ), Fe 2I4 (72.1 kcal mol ), Fe (68.3 kcal mol ) and FeCl 2 (67.4 kcal mol ). 3− −1 4− The largest negative errors for AM1* are found for Fe(CN) 6 (-217.8 kcal mol ), Fe(CN) 6 −1 + −1 2+ −1 (-123.3 kcal mol ), Fe(H 2O) 5Br (-73.8 kcal mol ), Fe(H 2O) 6 (-69.1 kcal mol ) and + −1 Fe(H 2O) 5F (-67.9 kcal mol ). The large negative errors with oxygen-containing compounds are not surprising as we have pointed out in our previous parameterizations [68, 70]. Generally large errors in AM1* for iron are given by the compounds that contain original AM1 elements or AM1 elements with chlorine, bromine and also from iodine-containing compounds. We attribute this to a weakness in the AM1* parameterization for the halogens and also general weakness of the original AM1 parameterization.

4.3.1.2.2 Ionization Potentials and Dipole Moments of Iron Compounds

A comparison of the calculated and experimental ionization potentials and dipole moments of iron-containing compounds for AM1*, PM6 and PM5 are shown in Table 4.13.

Table 4.13: Calculated AM1*, PM6 and PM5 Koopmans’ theorem ionization potentials and dipole moments for iron-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 PM5 Compound Target Error Error Error Koopmans' Theorem Ionization Potentials for Manganese Compounds (eV)

Fe(CO) 4H2 9.65 9.36 -0.29 9.70 0.05 9.72 0.07 Fe(CO) 2 6.68 8.01 1.33 8.07 1.39 8.51 1.83 Fe(CO) 4 8.48 9.90 1.42 9.02 0.54 9.78 1.30 Fe(CO) 5 8.60 9.76 1.16 9.23 0.63 9.21 0.61 FeBr 2 9.70 10.05 0.35 9.23 -0.47 11.02 1.32 Fe 2Br 4 12.60 11.04 -1.56 7.11 -5.49 10.53 -2.07 Fe(CO) 4H2 9.65 9.46 -0.19 9.70 0.05 9.72 0.07 FeCl 2 10.10 11.21 1.11 8.38 -1.72 11.09 0.99 AM1* PM6 PM5 N=8 MSE 0.42 -0.63 0.52 MUE 0.93 1.29 1.03 Dipole Moments for Manganese Compounds (Debye) FeO 7.50 6.62 -0.88 4.44 -3.06 4.95 -2.55

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

FeCH 3 0.90 0.67 -0.23 0.48 -0.42 1.58 0.68 Fe(CO) 4C2H4 1.50 2.02 0.52 3.25 1.75 1.16 -0.34 FeO 2 (3B1) 2.00 0.91 -1.09 3.33 1.33 0.74 -1.26 FeO 2 (5B2) 3.40 5.06 1.66 2.10 -1.30 4.94 1.54 Fe(CO) 3C4H6 2.10 0.36 -1.74 4.41 2.31 1.73 -0.37 FeC 6NH 3O4 (Fe(CO) 4 acetonitrile) 5.00 7.67 2.67 5.13 0.13 6.61 1.61 FeF 4.19 3.82 -0.37 5.00 0.81 4.53 0.34

FeO 2F2 1.60 3.04 1.44 2.00 0.40 2.34 0.74 FeC 10 PH 15 O4 (Fe(CO) 4(PEt 3) 5.20 5.93 0.73 1.56 -3.64 5.10 -0.10 FeCl 4.51 5.98 1.47 1.06 -3.45 4.59 0.08

FeCl 2O2 0.22 0.42 0.20 2.70 2.48 1.65 1.43 FeBr 4.18 4.41 0.23 1.12 -3.06 6.17 1.99 FeI 4.20 3.97 -0.23 5.05 0.85 5.24 1.04 AM1* PM6 PM5 N=14 MSE 0.31 -0.35 0.34 MUE 0.96 1.79 1.01

AM1* and PM5 overestimate Koopmans’ theorem ionization potentials of iron-containing compounds with MSEs of 0.42 and 0.52 eV, respectively for the dataset used whereas PM6 underestimates by -0.63 eV. AM1* with an MUE of 0.93 eV performs better than both PM5 (MUE = 1.03 eV) and PM6 (1.29 eV) for ionization potentials of iron compounds. The large errors for AM1* are mainly found for iron-carbonyl compounds which is once again an indirect result of using original AM1 parameters for carbon and oxygen.

Both AM1* and PM5 tend to give positive systematic errors to dipole moments of iron- containing compounds with MSEs of 0.31 and 0.34 Debye, respectively, whereas PM6 underestimates by -0.35 Debye. AM1* with an MUE of 0.96 Debye performs slightly better than PM5 (MUE = 1.01 Debye) and far better PM6 (1.79 Debye) for dipole moments of iron- containing compounds. The large errors for AM1* are mainly obtained from the compounds containing hydrogen, carbon, oxygen and nitrogen. This is not an extraordinary situation while AM1* uses original AM1 parameters for these elements.

4.3.1.2.3 Geometries of Iron Compounds

The geometrical variables used to parameterize AM1* for iron and a comparison of the AM1*, PM6 and PM5 results are shown in Table 4.14.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* shows no systematic error trend to iron compounds for bond lengths whereas both PM5 and PM6 overestimate by 0.08 Å and 0.12 Å, respectively. AM1* with a mean unsigned error of 0.09 Å performs better than PM5 (MUE = 0.15 Å) and far better than PM6 (MUE = 0.27 Å) for bond lengths. Here once again we note that, the large PM6 errors for bond lengths resulted from iron-transition metal diatomic model compounds and these compounds are not covered by PM6 parameterization dataset. All three available methods produce negative systematic errors for bond angles of iron- containing compounds. While AM1* underestimates by -1.3°, PM5 and PM6 also underestimate by -1.7° and -2.6°, respectively. The performance of AM1* for bond angles to iron-containing compounds is comparable to PM5 and better than PM6. The MUEs for AM1* and PM5 are 5.8° and 4.0°, respectively, and for PM6 10.4°. Here the performance of relatively old method PM5 is surprisingly comparable or better than more modern methods.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.14: Calculated AM1*, PM6 and PM5 bond lengths and angles for iron-containing compounds. The codenames within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 PM5 Compound Variable Target Error Error Error

Fe 2 Fe-Fe 2.19 2.02 -0.17 2.35 0.17 1.83 -0.36 FeH Fe-H 1.63 1.63 0.00 1.08 -0.55 1.70 0.07 FeH – Fe-H 1.69 1.69 0.00 1.98 0.29 1.70 0.01 FeH + Fe-H 1.60 1.53 -0.07 1.16 -0.44 1.58 -0.02

FeCH 3 Fe-C 1.97 1.90 -0.07 2.12 0.15 1.94 -0.03 FeC 5H5 Fe-C 2.17 2.05 -0.13 2.06 -0.11 2.03 -0.14 Fe(C 5H5)2 Fe-C 2.06 2.12 0.06 2.06 0.00 2.22 0.16 + Fe(III)Cp 2 Fe-C 2.06 1.99 -0.07 2.05 -0.01 2.08 0.02 FeO Fe-O 1.62 1.76 0.14 1.66 0.04 1.63 0.00 FeO – Fe-O 1.69 1.74 0.05 1.79 0.10 1.73 0.04 FeO + Fe-O 1.56 1.75 0.19 1.65 0.09 1.65 0.09 – FeO 2 Fe-O 1.71 1.77 0.06 1.71 0.00 1.72 0.01 FeOH Fe-O 1.83 1.83 0.00 1.61 -0.22 1.77 -0.06

Fe(OH) 2 Fe-O 1.78 1.85 0.08 1.81 0.03 1.79 0.02 Fe(H 2O) 4(OH) 2 Fe-O 2.02 1.93 -0.09 1.66 -0.36 1.94 -0.08 Fe-O 2.08 2.13 0.05 3.17 1.09 2.32 0.24

Fe(H 2O) 5(OH) Fe-O 1.95 1.85 -0.10 1.83 -0.12 1.92 -0.03 Fe-O 2.05 2.05 0.00 2.17 0.12 2.10 0.05 2+ Fe(H 2O) 6 Fe-O 2.07 1.99 -0.08 2.01 -0.06 2.15 0.08 Fe-O 2.15 2.08 -0.07 2.53 0.38 2.22 0.07 3+ Fe(H 2O) 6 Fe-O 2.06 2.01 -0.05 2.05 -0.01 2.08 0.02 FeCH 5O2 (methyl iron(III)dihydroxide) Fe-O 1.75 1.83 0.08 1.75 0.00 1.71 -0.04 Fe-C 1.93 1.92 -0.01 1.64 -0.29 1.93 0.00 Fe(CO) Fe-C 1.72 1.80 0.08 1.63 -0.09 1.76 0.04 Fe(CO) – Fe-C 1.79 1.85 0.06 1.80 0.01 1.19 -0.60

Fe(CO) 2 Fe-C 1.84 1.88 0.04 1.76 -0.08 1.84 0.00 – Fe(CO) 2 Fe-C 1.79 1.85 0.06 1.75 -0.04 1.82 0.03 Fe(CO) 3 Fe-C 1.67 1.82 0.15 1.67 -0.01 1.82 0.14 – Fe(CO) 3 Fe-C 1.82 1.88 0.06 1.40 -0.42 1.92 0.09 Fe(CO) 4 Fe-C 1.78 1.89 0.11 1.71 -0.07 1.84 0.05

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Fe-C 1.82 1.89 0.08 1.80 -0.02 1.84 0.02 – Fe(CO) 4 Fe-C 1.78 1.88 0.10 1.66 -0.13 1.84 0.06 2– Fe(CO) 4 Fe-C 1.75 1.84 0.09 1.46 -0.29 1.78 0.03 Fe(CO) 4H2 Fe-C 1.81 1.89 0.09 1.81 0.00 1.84 0.03 Fe-H 1.56 1.58 0.02 1.36 -0.20 1.62 0.06 H-Fe-C 89.9 89.9 0.0 56.9 -33.0 90.0 0.1

Fe(CO) 5 Fe-C(eq) 1.81 1.92 0.11 1.77 -0.04 1.82 0.01 Fe-C(ax) 1.81 1.92 0.11 1.83 0.02 1.85 0.04

Fe(CO) 4C2H4 Fe-C 1.81 1.89 0.08 1.75 -0.06 1.84 0.03 Fe-C 2.13 1.98 -0.15 2.33 0.20 2.00 -0.13 3– FeC 6O12 (Fe(III)(Ox) 3) Fe-O 1.97 1.97 0.00 1.99 0.02 2.04 0.07 O-Fe-O 83.2 80.8 -2.4 99.8 16.6 82.1 -1.1

FeC 6H3O12 (H 3Fe(III)(Ox) 3) Fe-O 1.92 1.93 0.01 1.89 -0.03 2.02 0.10 Fe-O 2.03 2.02 -0.01 1.98 -0.05 2.22 0.19

FeC 7H4O3 (cyclobutadiene iron tricarbonyl) Fe-C(C=O) 1.79 1.92 0.13 1.74 -0.05 1.78 -0.01 Fe-C(C 4H4) 2.06 2.00 -0.06 2.08 0.02 2.34 0.28 C-Fe-C 99.3 83.0 -16.3 88.5 -10.8 97.6 -1.7

FeC 8H2O6 (FCPENO) Fe-C 1.81 1.90 0.09 1.82 0.01 1.86 0.05 Fe-C 2.02 1.95 -0.07 1.83 -0.19 2.02 0.00

FeC 9H12 O (BUDFEC01) Fe-C(O) 1.77 2.05 0.28 1.67 -0.10 1.82 0.05 Fe-C 2.06 2.05 -0.01 2.08 0.02 2.13 0.07 C-Fe-C 125.6 117.9 -7.7 109.5 -16.2 118.4 -7.2

FeC 9H12 O (FeCO(1,3-C4H6)2) Fe-C 2.11 2.00 -0.11 2.20 0.09 2.07 -0.04 C-Fe-C 88.8 83.3 -5.5 79.2 -9.5 82.9 -5.9

Fe 2(CO) 9 Fe-C 1.83 1.94 0.11 1.80 -0.03 1.85 0.02 Fe-C 1.98 1.96 -0.02 2.02 0.04 2.03 0.05 Fe-C#O 180.0 175.2 -4.8 177.0 -3.0 179.9 -0.1 Fe-C#O 140.7 138.9 -1.8 141.8 1.1 139.1 -1.7

FeC 10 H14 O4 (Fe(II)(Acac) 2) Fe-O 1.90 1.91 0.01 1.92 0.02 1.94 0.04 O-Fe-O 93.9 90.9 -3.0 73.4 -20.6 92.4 -1.5 – FeC 15 H21 O6 (Fe(II)(Acac) 3) Fe-O 1.97 1.98 0.01 2.03 0.06 2.02 0.05 O-Fe-O 95.1 90.2 -4.9 91.3 -3.7 94.7 -0.4 FeN Fe-N 1.56 1.72 0.16 1.33 -0.23 1.62 0.06 FeN + Fe-N 1.58 1.66 0.08 1.36 -0.22 1.54 -0.04 FeN – Fe-N 1.58 1.80 0.22 1.36 -0.22 1.71 0.13

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

2+ Fe(NH 3)6 Fe-N 2.10 2.07 -0.03 2.04 -0.06 2.19 0.09 Fe(CN) 4– Fe-C 1.99 1.98 -0.01 1.98 -0.01 1.95 -0.04 C-Fe-C 180.0 179.9 -0.1 179.9 -0.1 180.0 0.0

Fe(CO) 2(NO) 2 Fe-C 1.82 1.97 0.15 1.78 -0.04 1.88 0.05 Fe-N 1.68 1.79 0.11 1.66 -0.02 1.69 0.01 C-Fe-C 98.7 83.8 -14.9 90.5 -8.2 86.8 -11.9 N-Fe-N 109.0 146.7 37.8 92.5 -16.5 118.7 9.7 2+ FeC 6N6H24 (Fe(II)en) 3) Fe-N 2.13 2.00 -0.14 2.13 0.00 2.19 0.06 FeC 7NH 5O5 (CNOFEA) Fe-C 1.79 1.89 0.10 1.93 0.14 1.82 0.03 Fe-C 2.09 2.06 -0.03 2.07 -0.02 2.27 0.18 Fe-O 1.97 1.97 0.00 1.84 -0.13 2.06 0.09

FeC 8NH 5O2 (ACODUR) Fe-C 1.91 1.90 -0.01 1.92 0.01 1.96 0.05 Fe-C 1.78 1.90 0.12 1.76 -0.02 1.81 0.03 Fe-C 2.19 2.11 -0.08 2.07 -0.12 2.23 0.04 C-Fe-C 89.2 83.0 -6.2 74.2 -15.0 89.2 0.0 + FeC 9NH 8O2 (CPACFE) Fe-N 1.91 1.95 0.04 1.83 -0.08 2.04 0.13 Fe-C 1.77 1.91 0.14 1.78 0.01 1.84 0.07 FeC 10 N4H10 O6 (Diaqua-bis(pyrazinecarboxylato)- iron) Fe-O 2.11 1.93 -0.18 1.99 -0.12 2.08 -0.03 Fe-N 2.12 1.95 -0.17 1.92 -0.20 2.08 -0.04

Fe-OH 2 2.14 2.14 0.00 2.07 -0.07 2.09 -0.05 O-Fe-N 78.1 83.4 5.3 76.5 -1.6 79.7 1.6 – FeC 10 N2H12 O8 (Iron(III)EDTA) Fe-N 2.03 2.21 0.18 2.19 0.16 2.32 0.29 FeC 16 N5H11 O4 Fe-O 2.12 2.60 0.48 2.08 -0.04 2.26 0.14 Fe-O 1.92 1.87 -0.05 1.95 0.03 2.01 0.09 Fe-N 1.89 1.83 -0.06 1.88 -0.01 2.02 0.13 O-Fe-O 81.4 78.8 -2.6 73.4 -8.0 77.9 -3.5

FeC 17 N2H16 (Toluene-(2,2'-bipyridine)-iron) Fe-N 1.90 1.84 -0.06 1.86 -0.04 1.90 0.00 Fe-C 2.11 2.07 -0.04 2.07 -0.04 2.28 0.17 N-Fe-N 81.9 86.3 4.4 76.5 -5.4 82.7 0.8 N-Fe-C 122.8 114.7 -8.1 107.3 -15.5 128.2 5.4

FeC 20 H12 N4 (iron porphyrin) Fe-N 1.97 1.93 -0.04 1.92 -0.05 2.02 0.05 + FeC 36 N6H24 (ferrous tris(ortophenantholine) Fe-N 2.05 1.97 -0.08 1.95 -0.10 2.14 0.09 FeF Fe-F 1.76 1.80 0.04 1.75 -0.01 1.77 0.01 + Fe(II)(H 2O) 5F Fe-F 1.89 1.70 -0.19 1.82 -0.07 1.90 0.01

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Fe-O 2.05 2.04 -0.01 2.15 0.10 2.10 0.05

FeF 2 Fe-F 1.77 1.71 -0.06 1.76 -0.01 1.79 0.02 FeO 2F2 (iron(VI)difluoride dioxide) Fe-F 1.74 1.71 -0.03 1.74 0.00 1.81 0.07 Fe=O 1.58 1.85 0.27 1.55 -0.03 1.66 0.08

FeF 3 Fe-F 1.78 1.75 -0.03 1.73 -0.05 1.77 -0.01 3– FeF 6 Fe-F 2.06 1.85 -0.21 1.94 -0.12 2.02 -0.04 FeAl Fe-Al 2.30 2.27 -0.03 2.65 0.35 2.28 -0.03

Fe(AlH 2)2 Fe-Al 2.47 2.39 -0.08 3.06 0.59 2.69 0.22 FeSiH Fe-Si 2.30 2.30 0.00 3.96 1.66 2.48 0.18

FeSiH 2 Fe-Si 2.26 2.31 0.05 4.24 1.98 2.48 0.22 Fe(SiH 3)2 Fe-Si 2.52 2.52 0.00 4.47 1.95 2.52 0.00 FeP Fe-P 2.23 2.20 -0.03 1.85 -0.38 2.30 0.06 FePH Fe-P 2.20 2.30 0.10 2.05 -0.15 2.35 0.15

FeC 12 P4H34 S2 (JIYFAY) Fe-S 2.35 2.33 -0.02 2.10 -0.25 2.33 -0.02 Fe-P 2.23 2.64 0.41 2.26 0.03 2.49 0.26 P-Fe-S 89.4 90.8 1.4 83.1 -6.4 70.5 -18.9 FeS Fe-S 2.04 2.10 0.06 1.99 -0.05 2.06 0.02

Fe(SH) 2 Fe-S 2.25 2.26 0.02 1.82 -0.43 2.26 0.01 FeC 9H10 SO 2 (CEYTFE) Fe-S 2.30 2.32 0.02 2.00 -0.30 2.34 0.04 Fe-C(O) 1.75 1.89 0.14 1.74 -0.01 1.80 0.05

Fe-C(C 4) 2.12 2.12 0.00 2.04 -0.08 2.25 0.13 C-Fe-S 90.7 85.0 -5.7 102.3 11.6 91.9 1.2 FeC 16 N2H18 S2O2 (dicarbonyl ethylenediamine bis(phenylthiolato)iron) Fe-S 2.33 2.37 0.04 2.26 -0.07 2.38 0.05 Fe-S 2.34 2.37 0.03 2.13 -0.21 2.39 0.04 Fe-N 2.04 1.96 -0.08 2.15 0.11 2.15 0.11 Fe-N 2.03 1.97 -0.06 1.95 -0.08 2.15 0.12 Fe-C 1.76 1.88 0.12 1.73 -0.03 1.79 0.03 N-Fe-S 86.8 88.2 1.4 80.1 -6.7 82.0 -4.8 C-Fe-S 93.2 84.9 -8.3 96.1 2.9 98.0 4.8 FeC 9N3H18 S3O3 (tris(N,N- dimethylthiocarbamato)iron(III)) Fe-S 2.43 2.44 0.01 2.49 0.06 2.52 0.09 Fe-O 2.09 1.99 -0.10 1.88 -0.21 2.07 -0.02 S-Fe-O 68.9 70.5 1.6 72.1 3.2 66.9 -2.0 S-Fe-S 103.1 96.0 -7.1 98.0 -5.1 101.5 -1.6

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Fe 4S4 Fe-S 2.27 2.27 0.00 2.28 0.01 2.37 0.10 FeC 12 H14 S4O2 (CIBGAV10) Fe-S 2.31 2.35 0.04 2.23 -0.08 2.36 0.05 Fe-C 1.80 1.89 0.09 1.73 -0.07 1.81 0.01 S-Fe-S 85.2 85.7 0.4 108.8 23.6 87.8 2.6 C-Fe-S 90.1 89.4 -0.7 83.1 -7.0 90.7 0.6 FeC 14 N6H16 S6 (diisothiocyanato-bisthiazoline iron(II)) Fe-N 2.19 2.09 -0.10 1.87 -0.32 2.06 -0.13 Fe-N(CS) 2.08 1.87 -0.21 1.84 -0.24 1.98 -0.10 N-Fe-N 73.9 81.3 7.4 101.9 28.0 78.1 4.2 SCN-Fe-NCS 97.4 94.3 -3.1 99.8 2.4 89.0 -8.4 FeCl Fe-Cl 2.13 2.23 0.10 1.55 -0.58 2.16 0.02 + Fe(II)(H 2O) 5Cl Fe-Cl 2.29 2.17 -0.12 2.45 0.16 2.29 0.00 Fe-O 2.06 2.06 0.00 2.07 0.01 2.10 0.04

FeCl 2 Fe-Cl 2.16 2.17 0.01 1.94 -0.22 2.15 -0.01 FeCl 3 Fe-Cl 2.16 2.17 0.02 2.18 0.03 2.17 0.02 FeC 6N2H18 Cl 3 (FINJIV) Fe-Cl 2.23 2.35 0.12 2.34 0.11 2.25 0.02 Fe-N 2.27 1.93 -0.34 1.96 -0.31 2.28 0.01 Cl-Fe-Cl 121.0 120.1 -0.9 119.4 -1.6 119.8 -1.3 – FeCl 4 Fe-Cl 2.19 2.22 0.03 2.11 -0.08 2.18 -0.01 2– FeCl 4 (GOXLUA) Fe-Cl 2.34 2.33 -0.01 2.35 0.01 2.36 0.02 3– FeCl 6 Fe-Cl 2.53 2.54 0.01 2.51 -0.02 2.41 -0.12 FeTi Fe-Ti 2.54 2.54 0.00 3.67 1.13 - - FeV Fe-V 2.31 2.31 0.00 3.50 1.19 2.04 -0.27 FeCr Fe-Cr 2.27 2.06 -0.21 3.65 1.38 1.60 -0.67 FeMn Fe-Mn 2.40 2.40 0.00 5.21 2.81 - - FeCo Fe-Co 2.31 2.30 -0.01 4.68 2.38 1.70 -0.61 FeNi Fe-Ni 2.33 2.21 -0.12 4.69 2.36 2.05 -0.29 FeCu Fe-Cu 2.31 2.31 0.00 7.36 5.05 2.05 -0.26 FeZn Fe-Zn 2.53 2.37 -0.16 2.98 0.45 2.63 0.10 FeBr Fe-Br 2.23 2.16 -0.07 2.17 -0.06 2.31 0.08

FeBr 2 Fe-Br 2.31 2.13 -0.18 2.13 -0.18 2.31 0.00 FeC 6H5BrO 3 (ALCFEA) Fe-Br 2.50 2.20 -0.30 2.46 -0.04 2.43 -0.07 Fe-C(C 2) 2.13 2.03 -0.10 2.14 0.01 2.13 0.00 Fe-C(O) 1.79 1.91 0.12 1.83 0.04 1.85 0.06 C-Fe-Br 88.6 87.6 -1.0 108.9 20.3 84.9 -3.7

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

+ Fe(H 2O) 5Br Fe-Br 2.42 2.14 -0.28 2.47 0.05 2.38 -0.04 Fe-O 2.06 2.10 0.04 2.07 0.01 2.24 0.18

Fe(H 2O) 4Br 2 Fe-O 2.07 1.99 -0.08 2.15 0.08 2.09 0.02 Fe-Br 2.50 2.20 -0.30 2.71 0.21 2.48 -0.02 FeC 4H8BrO 7 (Diaquabromo(oxydiacetato- O,O',O")-iron(III)) Fe-Br 2.37 2.17 -0.20 2.38 0.01 2.36 -0.02 Fe-O 2.00 2.07 0.07 1.85 -0.15 1.98 -0.02 Br-Fe-O 105.6 94.5 -11.1 98.6 -7.0 111.5 5.9

FeBr 2O2 Fe-Br 2.27 2.15 -0.12 2.56 0.29 2.38 0.11 Fe=O 1.58 1.74 0.16 1.55 -0.03 1.52 -0.06 Br-Br-Fe 110.6 110.0 -0.6 129.6 19.0 98.1 -12.5 FeZr Fe-Zr 2.59 2.59 0.00 2.84 0.25 3.04 0.46 FeMo Fe-Mo 2.21 2.14 -0.07 3.29 1.08 11.58 9.37 FeI Fe-I 2.44 2.46 0.02 2.70 0.26 2.38 -0.06

Fe(CO) 3(C 3H5)I Fe-I 2.75 2.61 -0.14 2.80 0.05 2.48 -0.27 Fe-C(O) 1.80 1.96 0.16 1.73 -0.07 1.84 0.04 C-Fe-I 81.6 81.7 0.1 75.3 -6.3 76.2 -5.4

Fe(CO) 3(C 3H5)I (ALCOFE10) Fe-I 2.75 2.59 -0.16 2.80 0.05 2.59 -0.16 Fe-C 1.80 1.95 0.15 1.73 -0.07 1.83 0.03 C-Fe-I 81.6 96.5 14.9 75.3 -6.3 81.8 0.2

FeI 2 Fe-I 2.50 2.49 -0.01 2.55 0.05 2.43 -0.07 AM1* PM6 PM5 N=153 MSE bond length 0.00 0.12 0.08 MUE bond length 0.09 0.27 0.15 N=33 MSE bond angle -1.3 -2.6 -1.7 MUE bond angle 5.8 10.4 4.0

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.3.2 Conclusions and Outlook

In this work, we have presented our new AM1* parameters for manganese and iron providing important additional elements for the chemistry of organometallic and biological catalysts and for biochemical systems especially in the active sites of the enzymes [145, 146]. We have extended the range of the parameterization dataset that would otherwise not be available and made it more reliable checking experimental data by including results from DFT calculations. We aim to produce a parameter set that is more robust and generally applicable than the ones trained only using experimental data. For our extended training set used, AM1* parameterizations for manganese and iron give very good energetic and electronic results and also perform very well for the structural properties. Even though PM6 does not have core-core parameters for transition metal-transition metal interactions and from this point misses its general applicability property, as modern techniques, both AM1* and PM6 extend the range of applicability of NDDO-based MNDO-like techniques and provide good starting points for reaction-specific local parameterizations and comparison calculations.

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.4 Parameterization of Cobalt and Nickel

4.4.1 Results

The optimized AM1* parameters for cobalt and nickel [70] are shown in Table 4.15. Geometries were optimized with the new AM1* parameterization using VAMP 10.0 [138], while the PM5 calculations used LinMOPAC2.0 [62] and those with PM6 used MOPAC2007 [139]. The three programs give essentially identical results for the Hamiltonians that are available in all three.

Table 4.15: AM1* parameters for the elements Co and Ni. Parameter Co Ni

Uss [eV] -147.9969721 -47.9262400 Upp [eV] -75.4376929 -33.5123050 Udd [eV] -85.9948020 -92.9262050 -1 ζs [bohr ] 10.6559732 2.1694428 -1 ζp [bohr ] 31.1355546 2.0212614 -1 ζd [bohr ] 1.6662813 2.9999800 βs [eV] -94.1552039 -9.7800503 βp [eV] -126.5074725 -7.8215436 βd [eV] -15.8120720 -10.1277693 gss [eV] 5.7855014 4.0808760 gpp [eV] 16.2498362 5.6217732 gsp [eV] 10.4339713 6.0176787 gp2 [eV] 66.1182470 5.5014852 hsp [eV] 2.9132649 2.1328830 -1 zsn [bohr ] 2.2158238 0.7464700 -1 zpn [bohr ] 1.4599934 0.4533270 -1 zdn [bohr ] 1.4576614 1.4613450 ρ(core) [bohr -1] 1.6385615 1.3878582 -1 ∆H° f(atom) [kcal mol ] 101.98 102.8 0 F sd [eV] 7.9584630 4.6516640 2 G sd [eV] 6.6939630 1.8805020 ααα(ij) H 3.7250884 3.9112954 C 3.3514488 3.0416771 N 3.2268224 3.3195694 O 3.9648169 2.6648814 F 4.7295078 2.8884516 Al 2.2854320 2.4006390 Si 2.5793441 3.8488001 P 1.9571093 1.9182580 S 2.4315562 1.2619302 Cl 2.5666738 3.7009365 Ti 2.5672155 2.2550000 V 1.8037355 2.8635660 Cr 1.8441671 2.5326653 Co 2.9455643 3.5988970 Ni 3.5988970 2.3078430 Cu 2.0999846 2.4949800 94

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Zn 2.5946347 2.9100500 Br 3.2938616 2.5296864 Zr 1.9076098 2.1815542 Mo 1.7152160 2.3116050 I 2.9718264 2.6608247 δδδ(ij) H -7.4149924 -14.3720184 C 8.8159639 4.8355503 N 4.5514730 8.3058789 O 12.7561475 1.8194408 F 36.8730508 2.1280313 Al 3.6287393 4.4492610 Si 3.6071357 37.3623757 P 1.9376263 1.2970389 S 1.8108567 0.1685772 Cl 2.4236274 21.3405907 Ti 3.4060864 4.7044000 V 2.4096866 11.2551742 Cr 1.5174067 3.0903718 Co 18.3120000 35.4531600 Ni 35.4531600 2.4076920 Cu 0.8291495 3.5090000 Zn 1.3844244 4.1615000 Br 12.7590650 3.2087055 Zr 1.3523255 6.9245885 Mo 1.8055727 3.7298645 I 11.9594831 2.9999300

4.4.1.1 Cobalt

4.4.1.1.1 Heats of Formation of Cobalt Compounds

The calculated heats of formation for our training set of cobalt compounds are shown in Table 4.16. We have compared our results with Stewart’s recently published PM6 method [72] and also unpublished PM5 method implemented in LinMopac [62].

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.16: Calculated AM1*, PM6 and PM5 heats of formation and errors compared with our target values for the cobalt-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The codenames within parentheses indicate the CSD-names of the compounds. Target AM1* PM6 PM5

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error Co – 86.2 83.3 -2.9 -84.2 -170.4 43.8 -42.4 Co 102.0 102.0 0.0 82.3 -19.7 91.4 -10.6 Co + 281.5 389.9 108.4 304.1 22.6 292.6 11.1

Co 2 183.5 179.5 -4.0 -72.1 -255.6 114.5 -69.0 – Co 2 137.6 146.8 9.2 -263.1 -400.7 121.1 -16.5 HCo 102.8 79.0 -23.8 50.5 -52.3 14.8 -87.9 HCo – 98.5 67.6 -30.9 -52.0 -150.5 16.9 -81.6 – C5H5Co 114.8 111.1 -3.7 10.0 -104.8 95.8 -19.0 CoC 10 H10 73.9 72.1 -1.8 52.4 -21.5 72.2 -1.7 CoCp 2 (DCYPCO) 52.0 72.2 20.2 51.2 -0.8 71.4 19.4 3+ CoC 6N6H24 (COTENC01) 587.5 587.8 0.3 557.2 -30.3 531.6 -55.9 2+ CoC 6N6H24 (QICSOK) 280.9 263.3 -17.6 284.9 4.0 228.4 -52.5 CoC 9N6H15 (FEFRUD) 58.2 85.3 27.1 68.4 10.2 -24.8 -83.0 CoO – 36.6 -38.9 -75.5 -130.2 -166.8 -81.4 -118.0 – CoO 2 -34.0 -5.0 29.1 -57.7 -23.7 -109.1 -75.1 4+ Co 2(H 2O) 4 1052.6 1009.7 -42.8 857.5 -195.1 839.0 -213.5 2+ Co(H 2O) 6 58.3 -51.7 -110.0 36.0 -22.3 -19.0 -77.3 Co(CO) 4 -134.3 -153.2 -18.9 -136.8 -2.5 -62.5 71.8 CoH(CO) 4 -136.0 -147.2 -11.2 -114.1 21.9 -152.2 -16.2 + Co(CO) 5 4.1 -39.8 -43.9 33.4 29.3 38.2 34.1 3– CoC 6O12 (Co(iii)(ox) 3) -542.2 -515.7 26.5 -532.3 9.9 -751.5 -209.3 Co 2(CO) 8 -283.0 -286.5 -3.5 -278.8 4.2 -253.6 29.4 2+ CoN 6H15 O2 (FAMYEX) 252.3 211.0 -41.3 247.2 -5.1 254.2 1.9 + CoC 6N4H16 O4 (AETXCO) -93.9 -71.5 22.4 -68.0 25.9 -153.2 -59.3 + CoC 6N4H16 O4 (OXENCO) -96.0 -77.7 18.3 -74.8 21.2 -159.3 -63.3 + CoC 6N6H18 O4 (NIXGEG) 27.9 26.3 -1.6 48.2 20.3 20.8 -7.1 CoC 9N4H19 O5 (AMGXCO01) -131.7 -92.4 39.3 -123.3 8.4 -158.5 -26.8 + CoC 6N6H20 O6 (NITNCO) -39.2 -39.7 -0.5 -21.5 17.7 -123.3 -84.1 CoOF -70.8 -85.9 -15.1 -32.6 38.2 -128.8 -58.0

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CoF 2 -85.2 -85.2 0.0 -66.1 19.1 -85.4 -0.2 CoF 3 -139.6 -180.7 -41.1 -137.1 2.5 -95.3 44.3 – CoF 4 -302.0 -297.9 4.1 -253.8 48.2 -238.7 63.3 CoAlH 2 125.9 92.4 -33.6 33.8 -92.1 49.7 -76.2 HCoAlH 2 160.3 131.7 -28.6 80.3 -80.0 10.6 -149.7 CoSiH 3 109.6 97.1 -12.5 32.2 -77.3 41.2 -68.4 CoP 131.2 131.3 0.0 79.3 -51.9 41.8 -89.5

CoPH 2 100.3 72.5 -27.8 17.0 -83.3 -127.9 -228.2 HCoPH 2 111.1 57.9 -53.2 38.6 -72.6 -68.1 -179.3 CoS 117.5 83.7 -33.8 20.8 -96.7 117.4 -0.1 CoSH 82.7 81.6 -1.1 4.7 -78.0 90.8 8.1 HCoSH 87.4 61.6 -25.8 4.9 -82.5 19.9 -67.4

CoC 10 H14 S4 (TACACO10) -11.8 -1.9 9.9 -22.1 -10.3 -5.3 6.5 CoC 9H21 S6 (MEDTCO10) -65.7 -105.0 -39.3 -65.2 0.5 -72.6 -6.9 CoC 3N3H6S6 (TDTCCO) -24.9 -25.1 -0.2 -7.1 17.8 30.9 55.8 CoCl 46.1 45.6 -0.5 51.6 5.5 35.3 -10.8 CoClO 13.8 7.9 -5.9 0.3 -13.5 -44.5 -58.3

CoCl 2 -22.4 11.4 33.8 10.1 32.5 -38.8 -16.4 CoCl 3 -39.1 -37.1 2.0 -24.5 14.6 -49.1 -10.0 Co 2Cl 4 -83.8 -81.4 2.4 -89.7 -5.9 63.5 147.3 2+ CoC 4N5H19 Cl (ADETCO) 254.0 262.4 8.4 250.2 -3.8 224.5 -29.5 + Co(NH 3)2(H 2O) 2ClF -104.6 -147.8 -43.2 -113.3 -8.7 -128.2 -23.6 CoC 2N4H8S2Cl 2 (COTUCL11) -61.2 -54.2 7.0 -99.5 -38.3 -83.5 -22.3 CoC 6N3H17 Cl 3 (AMPRCO) -159.2 -150.9 8.3 -138.4 20.8 -214.5 -55.3 CoC 4N2H12 SCl 3 (CATBAA) -128.2 -118.7 9.5 -117.8 10.4 -159.5 -31.3 CoTi 116.0 116.0 0.0 66.4 -49.6 147.4 31.4 CoV 161.5 161.5 0.0 59.3 -102.2 -72.4 -233.9 CoCr 217.7 191.2 -26.5 89.3 -128.4 -347.4 -565.1 CoNi 108.1 108.2 0.1 1.4 -106.6 -118.0 -226.1 CoCu 143.1 141.8 -1.3 36.7 -106.4 -108.7 -251.9 HCoCu 150.9 150.9 0.0 79.2 -71.6 -127.7 -278.6 CoZn 124.6 114.3 -10.3 -158.1 -282.6 89.6 -34.9 HCoZn 121.4 91.7 -29.7 -78.0 -199.4 13.5 -107.9 CoBr 86.4 72.9 -13.5 61.0 -25.4 22.4 -64.0 CoOBr 19.9 -48.7 -68.6 17.6 -2.3 -129.4 -149.3

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CoBr 2 29.0 52.6 23.6 63.2 34.2 -94.6 -123.6 CoBr 3 15.9 21.8 5.9 40.1 24.2 -149.5 -165.4 CoBr 4 19.3 -10.6 -29.9 38.9 19.6 -196.7 -216.0 2– CoBr 4 -99.0 -100.3 -1.3 -169.9 -70.9 -286.5 -187.5 C4H8N4O5CoBr (BUKPIG) -99.6 -80.2 19.4 -121.0 -21.4 -152.7 -53.1 CoZr 209.8 172.1 -37.7 -10.4 -220.3 133.7 -76.2 CoMo 285.3 285.4 0.1 75.6 -209.6 288.2 3.0 HCoMo 280.4 261.9 -18.5 83.3 -197.1 222.7 -57.7 CoI 96.2 90.1 -6.2 49.9 -46.3 38.6 -57.6 ICoO 34.0 -2.7 -36.7 25.6 -8.4 -98.2 -132.2

CoI 3 19.5 42.7 23.2 38.1 18.6 -78.0 -97.5 CoI 4 39.0 40.0 0.9 -3.9 -42.9 -102.3 -141.3 C10 H15 NS 2CoI (GECVEP) -13.3 38.7 52.0 2.5 15.8 -71.7 -58.4 – C4H4N4O4CoI 2 (FIRCOY01) -16.8 -29.3 -12.5 -15.6 1.2 -135.0 -118.2 AM1* PM6 PM5 N=78 Most positive error 108.4 48.2 147.3 Most negative error -110.0 -400.7 -565.1 MSE -7.4 -48.6 -70.8 MUE 20.5 61.9 84.3 RMSD 30.4 98.1 121.8

Results for the PM6 parameterization set ( N=42 )

MSE -2.0 2.0 -32.4 MUE 22.9 15.7 52.5 RMSD 34.3 19.3 69.5

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* reproduces the heats of formation of the training set of cobalt compounds used in parameterization better than either PM6 or PM5. The mean unsigned error (MUE) for the AM1* parameterization dataset is 20.5 kcal mol −1, compared with 61.9 and 84.3 kcal mol −1 for PM6 and PM5, respectively. PM6 produces large errors for the compounds that were not included in its original training set. The parameterization data set for PM5 has not been published, but clearly does not cover the range of compounds used for AM1*. All three methods tend to underestimate heats of formation to cobalt-containing compounds. However, this tendency is less pronounced for AM1* (mean signed error (MSE) -7.4 kcal mol −1) than PM6 and PM5 (MSEs of -48.6 and -70.8 kcal mol −1, respectively).

The largest single positive error for AM1* is found for Co + (108.4 kcal mol −1). This is potentially disturbing as the ionization potential of Co is an important determinant of the reactivity of cobalt centers. However, we cannot detect serious systematic trends caused by this error. Molecules that give the largest positive errors are C 10 H15 NS 2CoI (GECVEP) (52.0 −1 −1 −1 kcal mol ), CoC 9N4H19 O5 (AMGXCO01) (39.3 kcal mol ) and CoCl 2 (33.8 kcal mol ). The 2+ −1 − largest negative errors are found for Co(H 2O) 6 (-110.0 kcal mol ), CoO (-75.5 kcal −1 −1 −1 mol ), CoOBr (-68.6 kcal mol ) and HCoPH 2 (-53.2 kcal mol ). The large negative errors with oxygen-containing compounds are not surprising as we have pointed out in our previous parameterizations [68]. AM1* uses the unchanged AM1 parameterization for the elements H, C, N, O and F, which limits the possible accuracy of the parameterization. In this respect, the 2+ 4+ heats of formation of Co(H 2O) 6 and Co(H 2O) 4 agree remarkably well with experiment considering the large AM1* errors for Co 2+ and Co 4+ (see below). As found for other metals, the large errors in pure AM1* element-containing compounds is likely to be a consequence of our sequential parameterization strategy, in contrast to the simultaneous parameterization used for PM6 [72].

Not only AM1* gives very large errors for cobalt di-, tri-, tetra- and penta-cations (not shown in Table 4.16 and not included in the statistics), but also PM6 and PM5. AM1* errors are found to be 143.0 kcal mol -1 (-96.5 and 119.6 kcal mol −1 for PM6 and PM5, respectively) for Co 2+ , 131.8 kcal mol −1 (-545.6 and -126.7 kcal mol −1 for PM6 and PM5, respectively) for Co 3+ , -56.8 kcal mol −1 (-1356.1 and -335.6 kcal mol −1 for PM6 and PM5, respectively) for Co 4+ and -704.5 kcal mol −1 (-2758.8 and -902.8 kcal mol −1 for PM6 and PM5, respectively) for Co 5+ . Experimental heats of formation of these cations are given in Table S1 of the

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Supplementary Material [70]. Nonetheless, on aggregate AM1* performs better than the other available methods for the heats of formation of cobalt compounds.

Table 4.16, however, also shows the performance of the three methods for only the PM6 parameterization dataset [72]. These data demonstrate the influence of the extent of the training data. AM1* performs approximately equally well for its own training set and for the subset used to parameterize PM6, whereas PM6 performs significantly better for the subset for which it was trained. This situation is unavoidable and is a direct consequence of the relative paucity of data for parameterizing semiempirical MO techniques for transition metals.

4.4.1.1.2 Ionization Potentials and Dipole Moments of Cobalt Compounds

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for AM1*, PM6 and PM5 are shown in Table 4.17.

Table 4.17: Calculated AM1*, PM6 and PM5 Koopmans’ theorem ionization potentials and dipole moments for cobalt-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 PM5 Compound Target Error Error Error Koopmans' Theorem Ionization Potentials for Cobalt Compounds (eV)

CoCH 3 7.00 8.88 1.88 9.57 2.57 9.01 2.01 CoC 10 H10 5.55 7.42 1.87 7.08 1.53 7.94 2.39 Co(CO) 4 8.30 7.98 -0.32 8.97 0.67 8.04 -0.26 Co 2(CO) 8 8.30 6.76 -1.54 10.86 2.56 8.78 0.48 CoCl 8.90 8.78 -0.12 9.48 0.58 8.29 -0.61

CoCl 2 10.70 8.60 -2.10 8.27 -2.43 9.78 -0.92 CoBr 2 9.90 9.09 -0.81 10.05 0.15 9.67 -0.23 AM1* PM6 PM5 N=7 MSE -0.16 0.80 0.41 MUE 1.23 1.50 0.99 Dipole Moments for Cobalt Compounds (Debye) CoO – 1.07 1.42 0.35 3.72 2.65 3.61 2.54

Co(CO) 4 0.25 0.54 0.29 0.02 -0.23 4.35 4.10 CoH(CO) 4 0.42 1.18 0.76 0.61 0.19 0.95 0.53 Co 2(CO) 8 1.23 1.23 0.00 0.23 -1.01 0.02 -1.21 CoOF 0.16 0.57 0.41 0.34 0.18 1.26 1.10 CoClO 0.93 1.31 0.38 0.81 -0.12 1.51 0.58 CoBr 3.65 1.88 -1.77 0.77 -2.88 5.67 2.02 CoBrO 1.81 1.98 0.17 3.44 1.63 1.33 -0.48 CoI 2.32 5.08 2.76 1.58 -0.74 5.91 3.59 CoIO 2.40 2.40 0.00 3.04 0.64 0.97 -1.43

100

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* PM6 PM5 N=10 MSE 0.34 0.03 1.13 MUE 0.69 1.03 1.76

The performance of the three methods is comparable. The mean unsigned errors vary in a relatively small range from 0.99 (PM5) to 1.50 eV (PM6). The AM1* MUE, 1.23 eV, lies in the middle of this range. With an MSE of -0.16 eV, AM1* tends to underestimate ionization potentials slightly, whereas PM6 and PM5 overestimate them by 0.80 and 0.41 eV, respectively.

Large AM1* errors are found for CoCl 2 (-2.10 eV), CoCH 3 (1.88 eV), CoC 10 H10 (1.87 eV) and Co 2(CO) 8 (-1.54 eV). The large error for CoCl 2 may originate from a general weakness in the original chlorine parameterization, whereas the others may be an indirect result of using the original AM1 parameters for hydrogen, carbon and oxygen.

AM1* and PM5 show positive systematic errors for the dipole moments of cobalt compounds, whereas PM6 with 0.03 Debye (MSE) shows no tendency to systematic errors. AM1* and PM5 overestimate dipole moments by 0.34 and 1.13 Debye (MSE), respectively. AM1* performs well, with an MUE of 0.69 Debye for the dipole moments of the training set of cobalt compounds. The largest AM1* errors are found for CoI (2.76 Debye) and CoBr (-1.77 Debye). These errors may be a consequence of our sequential parameterization strategy. The MUEs for PM6 and PM5 are found to be 1.03 and 1.76 Debye, respectively.

4.4.1.1.3 Geometries of Cobalt Compounds

Table 4.18 shows a comparison of AM1*, PM6 and PM5 results in reproducing the geometries of the cobalt-containing compounds.

101

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.18: Calculated AM1*, PM6 and PM5 bond lengths and angles for cobalt-containing compounds. The codenames within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 PM5 Compound Variable Target Error Error Error

Co 2 Co-Co 2.30 2.45 0.15 2.07 -0.23 2.11 -0.19 – Co 2 Co-Co 2.63 2.56 -0.08 2.10 -0.53 2.26 -0.37 HCo Co-H 1.55 1.59 0.04 1.71 0.16 1.40 -0.15 HCo – Co-H 1.66 1.62 -0.04 2.20 0.54 1.44 -0.23 – CoC 5H5 Co-C 1.93 2.00 0.07 2.07 0.14 2.27 0.34 Co(Cp 2 (DCYPCO) Co-C 2.08 2.26 0.18 2.08 0.00 2.52 0.44 + Co(CN) 4 Co-C 1.81 2.00 0.19 1.77 -0.04 2.08 0.27 C-N 1.20 1.16 -0.04 1.16 -0.04 1.16 -0.04 3– Co(CN) 6 Co-C 1.97 1.99 0.02 1.93 -0.04 2.16 0.19 CoC 6N6H24 (Co(II)(en) 3) Co-N 2.06 2.10 0.04 2.02 -0.04 2.21 0.15 3+ CoC 6N6H24 (COTENC01) Co-N 2.00 2.00 0.00 2.01 0.01 2.21 0.21 N-Co-N 90.2 93.7 3.5 87.9 -2.3 81.4 -8.8 2+ CoC 6N6H24 (QICSOK) Co-N 2.20 2.11 -0.09 2.24 0.04 2.26 0.06 N-Co-N 78.7 83.3 4.7 85.5 6.8 80.8 2.1

CoC 9N6H15 (FEFRUD) Co-N 2.01 2.00 -0.01 2.06 0.05 2.23 0.22 N-Co-N 90.3 92.5 2.2 92.1 1.8 92.0 1.7 Co-C 1.89 2.05 0.16 1.84 -0.05 2.11 0.22 CoO – Co=O 1.65 1.72 0.06 1.78 0.12 1.53 -0.13 – CoO 2 Co=O 1.68 1.81 0.13 1.79 0.11 1.61 -0.07 2+ Co(H 2O) 4 Co-O 1.94 1.93 -0.02 1.91 -0.03 2.07 0.13 3+ Co(H 2O) 6 Co-O 2.03 1.94 -0.09 1.99 -0.04 1.99 -0.04 4+ Co 2(H 2O) 4 Co-O 2.17 1.96 -0.21 1.92 -0.25 1.95 -0.22 2+ Co(H 2O) 6 (NAZVOZ) Co-O 2.06 1.97 -0.09 1.88 -0.18 1.52 -0.54 Co-O' 2.12 2.02 -0.10 1.87 -0.25 2.23 0.11 2+ Co(H 2O) 6 Co-O 2.12 1.96 -0.16 1.99 -0.13 2.11 -0.02 Co-O' 1.96 1.95 -0.01 2.01 0.05 2.09 0.13

Co(CO) 4 Co-C 1.85 1.89 0.04 1.98 0.13 2.18 0.33 – Co(CO) 4 (FUBYOQ) Co-C 1.75 1.95 0.20 1.90 0.15 2.04 0.29 CoH(CO) 4 Co-H 1.55 1.62 0.06 1.70 0.14 1.39 -0.17 Co-C 1.81 1.90 0.09 1.83 0.02 2.02 0.21

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+ Co(CO) 5 Co-C(eq) 1.83 2.00 0.17 1.82 -0.01 2.07 0.24 Co-C(ax) 1.89 1.92 0.03 1.82 -0.07 2.92 1.03 3– CoC 6O12 (Co(iii)(ox) 3) Co-O 1.95 1.95 0.00 1.98 0.03 2.00 0.05 Co 2(CO) 8 Co-Co 2.47 3.08 0.61 2.47 0.00 3.50 1.03 Co(CO) 3NO Co-C 1.81 1.94 0.13 2.14 0.33 2.04 0.23 C-Co-C 103.2 85.9 -17.3 81.0 -22.2 93.1 -10.2 Co-N 1.67 1.74 0.07 1.60 -0.07 1.93 0.26

Co(NO 3)3 Co-O 1.89 1.84 -0.05 1.88 -0.01 2.19 0.30 O-Co-O 68.0 65.3 -2.7 71.1 3.1 176.0 108.0 O-Co-O' 93.0 98.8 5.8 98.6 5.6 86.8 -6.2 2+ CoN 6H15 O2 (FAMYEX) Co-N(O2) 1.95 1.91 -0.04 1.79 -0.16 2.09 0.14 Co-N(H3) 1.96 2.08 0.12 2.03 0.07 2.20 0.24 N-Co-N 90.0 92.9 2.9 89.0 -1.0 88.8 -1.2 + CoC 6N4H16 O4 (OXENCO) Co-N 1.98 2.04 0.06 1.98 0.00 2.30 0.32 N-Co-N 86.0 85.3 -0.7 89.7 3.6 81.2 -4.8 Co-O 1.94 1.92 -0.02 1.95 0.01 1.91 -0.03 + CoC 6N4H16 O4 (AETXCO) Co-O 1.92 1.90 -0.02 1.93 0.01 1.91 -0.01 O-Co-O 84.8 84.3 -0.5 87.8 3.0 85.9 1.1 Co-N(H2C) 1.98 2.05 0.07 1.96 -0.02 2.21 0.23 Co-N(H3) 1.95 2.04 0.09 2.00 0.05 2.27 0.32 C-N(HC2) 1.92 2.07 0.15 1.94 0.02 2.23 0.31 + CoC 6N6H18 O4 (NIXGEG) Co-N(C3) 1.96 2.11 0.15 1.96 0.00 2.20 0.24 Co-N(CH2) 1.96 2.09 0.13 2.04 0.08 2.20 0.24 N-Co-N 86.8 87.7 0.9 85.4 -1.4 90.7 3.9 Co-N(O2) 1.99 2.01 0.02 1.87 -0.12 2.13 0.14 Co-N(O2) 1.93 1.90 -0.03 1.83 -0.10 2.08 0.15

CoC 9N4H19 O5 (AMGXCO01) Co-N 1.89 1.99 0.10 1.88 -0.01 2.12 0.23 N-Co-N 82.0 82.1 0.1 82.8 0.8 74.5 -7.5 Co-C 1.98 2.04 0.06 2.01 0.03 2.15 0.17 Co-O 2.06 2.03 -0.03 2.21 0.15 2.16 0.10 – CoC 15 H21 O6 (Co(II)(Acac) 3(-) IKEYAY) Co-O 2.06 1.95 -0.11 2.12 0.06 1.97 -0.09 O-Co-O 88.0 87.0 -0.9 101.1 13.1 94.0 6.1 + CoC 6N6H20 O6 (NITNCO) Co-N 2.00 2.01 0.01 1.99 -0.01 2.23 0.23 N-Co-N 87.7 89.6 1.9 89.0 1.3 95.0 7.3 Co-O 1.90 1.87 -0.03 1.99 0.09 1.91 0.01

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CoF Co-F 1.91 1.91 0.00 1.84 -0.07 1.91 0.00 CoOF Co=O 1.59 1.63 0.04 1.57 -0.02 1.44 -0.15 Co-F 1.72 1.72 0.00 1.68 -0.04 1.53 -0.20

CoF 2 Co-F 1.72 1.76 0.04 1.70 -0.02 1.55 -0.17 CoF 3 Co-F 1.72 1.72 0.00 1.76 0.04 1.76 0.04 F-Co-F 108.5 147.4 39.0 119.8 11.3 143.1 34.7 – CoF 4 Co-F 1.79 1.81 0.02 1.75 -0.04 1.85 0.06 CoAlH 2 Co-Al 2.40 2.37 -0.03 2.28 -0.12 2.40 0.00 HCoAlH 2 Co-Al 2.53 2.57 0.04 2.29 -0.24 2.36 -0.16 CoSiH 3 Co-Si 2.33 2.33 0.00 2.50 0.17 2.30 -0.02 CoSiC 4O4F3 (FUZMAO) Co-Si 2.23 2.46 0.23 2.23 0.00 2.27 0.04 Si-F 1.50 1.71 0.21 1.56 0.06 1.59 0.09 F-Si-Co 114.8 116.6 1.8 107.5 -7.3 117.2 2.4 Co-C 1.79 1.91 0.12 1.82 0.03 2.15 0.36 C-O 1.11 1.18 0.07 1.13 0.02 1.15 0.03 CoP Co ≡P 2.16 2.28 0.11 2.04 -0.13 1.87 -0.29

CoPH 2 Co-P 2.26 2.31 0.04 2.10 -0.16 1.91 -0.36 HCoPH 2 Co-P 2.32 2.34 0.02 2.26 -0.06 1.96 -0.36 CoS Co=S 2.01 2.05 0.04 1.70 -0.31 1.96 -0.06 CoSH Co-S 2.16 1.99 -0.17 1.91 -0.25 2.45 0.29 HCoSH Co-S 2.23 2.24 0.01 2.01 -0.23 2.28 0.05

CoC 10 H14 S4 (TACACO10) Co-S 2.17 2.18 0.01 2.13 -0.04 2.51 0.34 S-Co-S 96.9 91.9 -4.9 94.8 -2.0 82.9 -14.0

CoC 9H21 S6 (MEDTCO10) Co-S 2.30 2.42 0.12 2.27 -0.03 2.68 0.38 S-Co-S 89.8 50.2 -39.6 90.7 0.9 82.4 -7.4

CoC 3N3H6S6 (TDTCCO) Co-S 2.29 2.32 0.03 2.26 -0.03 2.56 0.27 S-Co-S 76.3 74.2 -2.2 79.9 3.5 69.2 -7.1 CoCl Co-Cl 2.07 2.02 -0.05 1.96 -0.11 1.97 -0.10 CoClO Co=O 1.61 1.73 0.12 1.59 -0.02 1.56 -0.05 Co-Cl 2.07 2.34 0.27 1.82 -0.25 2.15 0.08

CoCl 2 Co-Cl 2.11 2.07 -0.04 1.98 -0.12 2.07 -0.04 CoCl 3 Co-Cl 2.13 2.12 0.00 2.10 -0.03 2.06 -0.06 2– CoCl 4 (DMDPCO) Co-Cl 2.25 2.29 0.04 2.31 0.06 2.14 -0.11 Co 2Cl 4 Co-Cl 2.12 2.09 -0.04 2.01 -0.11 2.03 -0.09 Co-Cl' 2.21 2.23 0.01 2.04 -0.17 2.18 -0.04

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CoCH 3ClOH Co-O 1.73 1.82 0.09 1.78 0.05 1.66 -0.07 Co-C 1.91 2.06 0.15 1.87 -0.04 2.08 0.17 Co-Cl 2.10 2.15 0.05 2.08 -0.02 2.23 0.13 2+ CoC 4N5H19 Cl (ADETCO) Co-Cl 2.28 2.16 -0.12 2.29 0.01 2.27 -0.01 Co-N(H3) 1.97 2.07 0.10 2.02 0.05 2.18 0.21 N-Co-Cl 87.7 87.9 0.2 83.9 -3.8 86.2 -1.5 Co-N(C2H) 1.94 2.14 0.20 1.93 -0.01 2.17 0.23 N-Co-N 94.3 90.9 -3.4 93.7 -0.6 96.8 2.5 Co-N(H2C) 1.99 2.07 0.08 1.98 -0.01 2.20 0.21 + Co(NH 3)2(H 2O) 2ClF Co-Cl 2.23 2.16 -0.07 2.30 0.07 2.30 0.06 Co-N 1.97 2.08 0.11 1.96 -0.01 2.15 0.18 Co-F 1.85 1.81 -0.04 1.84 -0.01 1.84 -0.01 Co-O 1.97 2.01 0.04 2.00 0.03 2.00 0.03

CoC 9P3H27 Cl (BUTDEZ) Co-Cl 2.22 2.32 0.10 2.38 0.16 2.36 0.14 Co-P 2.24 2.26 0.02 2.28 0.04 2.00 -0.24 Cl-Co-P 113.8 82.8 -31.0 167.6 53.8 169.9 56.1

CoC 2N4H8S2Cl 2 (COTUCL11) Co-Cl 2.26 2.15 -0.11 2.29 0.03 2.32 0.06 Co-Cl' 2.27 2.23 -0.04 2.44 0.17 2.33 0.06 Cl-Co-Cl 107.7 74.2 -33.5 105.3 -2.4 90.7 -17.1 Co-S 2.30 2.38 0.08 2.11 -0.19 2.66 0.36 Co-C 3.31 3.32 0.01 3.15 -0.16 3.41 0.10

CoC 6N3H17 Cl 3 (AMPRCO) Co-Cl 2.24 2.10 -0.14 2.30 0.06 2.31 0.07 Co-Cl' 2.31 2.18 -0.13 2.36 0.05 2.35 0.04 Cl-Co-Cl 91.2 90.8 -0.4 93.7 2.5 92.3 1.1 Co-N 1.97 2.09 0.12 1.95 -0.02 2.16 0.19

CoC 4N2H12 SCl 3 (CATBAA) Co-Cl 2.28 2.21 -0.07 2.32 0.04 2.29 0.01 Cl-Co-Cl 91.7 86.4 -5.4 98.4 6.6 98.4 6.7 Co-N 1.93 2.11 0.18 1.95 0.02 2.20 0.27 Co-S 2.22 2.47 0.25 2.02 -0.20 2.78 0.56 CoTi Co-Ti 2.35 2.35 0.00 2.50 0.15 36.49 34.14 CoV Co-V 2.34 2.36 0.02 2.56 0.22 1.62 -0.72 CoCr Co-Cr 2.35 2.35 0.00 2.79 0.44 1.29 -1.05 CoNi Co-Ni 2.38 2.38 0.00 2.49 0.10 1.28 -1.10 CoCu Co-Cu 2.29 2.33 0.04 2.59 0.29 1.69 -0.61 HCoCu Co-Cu 2.35 2.35 0.00 2.60 0.26 1.70 -0.65

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CoZn Co-Zn 2.54 2.49 -0.06 1.89 -0.65 2.55 0.00 HCoZn Co-Zn 2.49 2.49 0.00 2.03 -0.46 2.41 -0.08 CoBr Co-Br 2.21 2.23 0.02 2.00 -0.21 2.26 0.05 BrCoO Co=O 1.60 1.62 0.02 1.60 0.00 1.36 -0.24 Co-Br 2.19 2.27 0.08 1.63 -0.56 2.08 -0.11

CoBr 2 Co-Br 2.27 2.31 0.04 2.01 -0.25 2.17 -0.10 CoBr 3 Co-Br 2.28 2.28 0.00 2.44 0.15 2.11 -0.17 CoBr 4 Co-Br 2.43 2.33 -0.10 2.25 -0.18 2.27 -0.16 2– CoBr 4 Co-Br 2.40 2.45 0.05 2.70 0.30 2.43 0.03 C4H8N4O5CoBr (BUKPIG) Co-Br 2.36 2.40 0.04 2.14 -0.22 2.35 -0.01 Co-O 1.96 2.06 0.10 2.11 0.15 2.07 0.11 Co-N 1.91 1.98 0.07 1.85 -0.06 2.16 0.25 CoZr Co-Zr 2.16 2.16 0.00 2.47 0.31 3.28 1.12 CoMo Co-Mo 2.33 2.33 0.00 2.23 -0.11 10.82 8.49

CoI 2 Co-I 2.57 2.51 -0.06 1.73 -0.84 2.39 -0.19 CoI 4 Co-I 2.61 2.68 0.07 1.63 -0.98 2.44 -0.17 CoI Co-I 2.39 2.44 0.05 1.66 -0.73 2.37 -0.02 ICoO Co=O 1.60 1.62 0.02 1.60 0.00 1.37 -0.23 Co-I 2.40 2.49 0.09 1.67 -0.73 2.24 -0.16

C10 H15 NS 2CoI (GECVEP) Co-I 2.60 2.61 0.01 2.96 0.36 2.82 0.22 Co-S 2.25 2.40 0.15 2.17 -0.08 2.60 0.35 I-Co-S 95.6 92.2 -3.3 96.5 1.0 58.5 -37.1 S-Co-S 76.5 70.4 -6.1 77.6 1.0 48.9 -27.6 – C4H4N4O4CoI 2 (FIRCOY01) Co-I 2.58 2.57 -0.01 3.31 0.73 2.67 0.09 Co-N 1.88 2.01 0.13 1.90 0.02 2.14 0.26

CoI 3 Co-I 2.42 2.48 0.06 4.13 1.71 2.36 -0.06 CoCH 3ICl Co-I 2.47 2.53 0.06 1.68 -0.79 2.55 0.07 Co-C 1.95 2.07 0.12 1.89 -0.06 1.91 -0.04 Co-Cl 2.14 2.13 -0.01 2.11 -0.03 2.17 0.03 C-Co-I 101.5 120.1 18.7 109.9 8.4 90.2 -11.3 C-Co-Cl 97.1 124.4 27.3 125.2 28.1 168.4 71.3 AM1* PM6 PM5 N=138 MSE bond length 0.04 -0.03 0.36 MUE bond length 0.08 0.16 0.51

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* PM6 PM5 N=28 MSE bond angle -1.5 4.0 5.1 MUE bond angle 9.3 7.1 16.7

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* and PM5 overestimate bond lengths to cobalt-containing compounds systematically by 0.04 and 0.36 Å, respectively, whereas PM6 underestimates them by -0.03 Å. AM1*, with an MUE of 0.08 Å performs quite well for bond lengths, compared with MUEs of 0.16 Å and 0.51 Å for PM6 and PM5, respectively. On the other hand, PM6 (MUE = 7.1°) performs slightly better than AM1* (MUE = 9.3°) and far better than PM5 (MUE = 16.7°) for the bond angles. In general, AM1* gives bond angles for cobalt-containing that are on average 1.5° too small, whereas PM6 and PM5 give bond angles are too large by 4.0° and 5.1°, respectively.

4.4.1.2 Nickel

4.4.1.2.1 Heats of Formation of Nickel Compounds

The results obtained for heats of formation of nickel-containing compounds are shown in Table 4.19. Table 4.19 shows that, for the training set used, AM1* reproduces heats of formation of nickel-containing compounds slightly better than PM6 and far better than PM5. The mean unsigned error between target and AM1*-calculated heats of formation is 21.5 kcal mol −1. For PM6 and PM5, the MUEs are found 27.3 and 53.0 kcal mol −1, respectively. AM1* and PM6 underestimate heats of formation to nickel compounds by -6.7 and -4.3 kcal mol −1, respectively (MSEs). PM5 systematically predicts heats of formation to be too positive with a mean signed error of 21.0 kcal mol −1. The largest positive errors for AM1* are found for the + −1 2+ −1 + compounds NiC 11 N2H21 S2O2 (53.6 kcal mol ), Ni(H 2S) 4 (53.1 kcal mol ), NiH (50.6 −1 −1 −1 kcal mol ), NiCO (48.0 kcal mol ) and NiC 8N4H14 O4 (NIMGLO01) (42.0 kcal mol ). The 3− −1 2− largest negative errors for AM1* are found for Ni(CN) 5 (-108.4 kcal mol ), NiC 2N3S3 −1 2- −1 (CUSJUV) (-79.1 kcal mol ), Ni(CN) 4 (-73.7 kcal mol ). AM1* also gives negative errors for the chlorinated compounds NiCH 3Cl, NiCl 2O, cis - and trans -NiCl 2.(H 2O) 2 and cis - and −1 trans -Ni((CH 3)2S) 2Cl 2 more than 30 kcal mol . Large errors in AM1* are given by the compounds that contain original AM1 elements or AM1 elements with sulfur, and also from the chlorinated compounds. We attribute this to a weakness in the AM1* parameterization for the chlorine and the sulfur, and also general weakness of the original AM1 parameterization.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.19: Calculated AM1*, PM6 and PM5 heats of formation and errors compared with our target values for the nickel-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1. yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The codenames within parentheses indicate the CSD-names of the compounds. Target AM1* PM6 PM5

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error Ni 102.8 102.8 0.0 93.5 -9.3 102.8 0.0 Ni – 76.0 65.3 -10.8 20.2 -55.8 21.8 -54.2 Ni + 276.7 281.8 5.1 266.1 -10.6 319.5 42.8 Ni 2+ 697.2 694.9 -2.3 685.2 -12.0 760.9 63.7 – Ni 2 128.6 87.1 -41.6 49.4 -79.2 148.6 20.0 + Ni 2 428.3 371.6 -56.7 127.7 -300.6 413.7 -14.6 NiH 85.6 85.0 -0.6 87.0 1.4 175.6 90.0 NiH + 254.5 305.0 50.6 292.5 38.0 394.9 140.5

NiH 2 83.5 65.0 -18.5 133.1 49.6 231.0 147.5 NiH 3 36.1 36.1 0.0 54.1 18.0 160.4 124.3 Ni(C 5H5)2 79.7 87.4 7.7 61.1 -18.7 17.8 -61.9 Ni 2(C 5H5)2(CO) 2 -27.0 12.9 39.9 -20.9 6.1 -95.6 -68.6 NiCO 35.1 83.1 48.0 23.2 -11.9 64.4 29.3 NiCO – 17.2 -18.7 -35.9 -0.9 -18.1 -22.1 -39.3

Ni(CO) 2 -39.0 -3.4 35.6 -50.1 -11.1 -12.2 26.8 – Ni(CO) 2 -53.0 -88.7 -35.7 -65.0 -12.0 -56.4 -3.4 Ni(CO) 3 -93.0 -80.5 12.5 -80.0 13.0 -78.9 14.1 – Ni(CO) 3 -118.8 -150.1 -31.3 -106.9 11.9 -169.6 -50.8 Ni(CO) 4 -144.0 -142.2 1.8 -107.1 36.9 -143.6 0.4 NiO 75.0 85.4 10.4 154.0 79.0 71.8 -3.2 NiO – 41.1 20.1 -21.0 44.3 3.2 -21.1 -62.2 – NiO 2 -28.3 -28.5 -0.2 15.3 43.6 -51.3 -23.0 Ni(OH) 2.(H 2O) 2 cis -180.9 -201.9 -21.0 -174.5 6.4 -210.2 -29.3 Ni(OH) 2.(H 2O) 2 trans -177.6 -211.1 -33.5 -165.3 12.3 -218.1 -40.5 + Ni(OH).(H 2O) 3 -36.3 -29.5 6.8 -31.2 5.1 -36.0 0.3 2+ Ni(H 2O) 4 221.9 214.7 -7.2 207.4 -14.5 217.1 -4.8 2+ Ni(H 2O) 6 55.7 54.9 -0.9 45.9 -9.8 11.1 -44.6 2+ NiH 12 O6 (JERNID) 54.4 55.2 0.8 49.0 -5.4 11.1 -43.3 Ni(NH 2)2 39.4 37.1 -2.3 85.1 45.7 187.9 148.6

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

2+ Ni(NH 3)4 319.5 325.0 5.5 309.3 -10.2 587.0 267.5 2+ Ni(NH 3)6 271.4 266.6 -4.8 268.3 -3.1 485.8 214.4 2– Ni(CN) 4 99.1 25.4 -73.7 57.8 -41.3 26.3 -72.8 3– Ni(CN) 5 258.9 150.5 -108.4 290.3 31.4 145.6 -113.3 Ni(CO) 3NO -89.0 -90.8 -1.8 -77.9 11.1 -82.8 6.2 NiC 8N4H14 O4 (NIMGLO10) -37.1 4.9 42.0 -58.3 -21.2 81.4 118.5 NiC 10 N2H12 O8 (Ni-EDTA) -361.5 -374.3 -12.8 -402.2 -40.7 -520.8 -159.3 NiC 13 NH 17 O4 (VAXSUI) -142.3 -137.7 4.6 -94.2 48.1 -154.7 -12.4 NiF 17.5 6.5 -11.0 51.1 33.6 4.9 -12.6

NiF 2 -115.5 -89.4 26.1 -65.2 50.3 -71.9 43.6 2– NiF 4 -211.5 -261.2 -49.7 -212.7 -1.2 -330.9 -119.4 NiCH 3F -8.3 -35.6 -27.3 -11.5 -3.2 -4.3 4.0 NiOF 2 -50.8 -35.4 15.4 -47.2 3.6 -53.4 -2.6 NiF 2.(H 2O) 2 cis -214.2 -213.9 0.3 -202.0 12.2 -188.1 26.1 NiF 2.(H 2O) 2 trans -219.4 -220.5 -1.1 -197.4 22.0 -194.0 25.4 NiAlH 2 56.2 89.1 32.9 60.0 3.8 140.3 84.2 HNiAlH 2 121.3 106.5 -14.8 159.1 37.8 244.6 123.3 NiSiH 3 41.6 53.9 12.3 61.5 19.8 122.2 80.6 HNiSiH 3 98.6 73.7 -24.9 139.3 40.7 226.8 128.2 HNiPH 2 50.7 62.8 12.1 28.6 -22.1 98.7 48.0 Ni(PF 3)4 -953.4 -953.4 0.0 -962.4 -9.0 -959.3 -5.9 NiS 85.4 85.4 0.0 78.6 -6.8 114.2 28.8 NiSH 20.0 35.6 15.6 47.4 27.4 79.0 59.1

NiSH 2 36.4 28.0 -8.4 78.0 41.6 105.7 69.3 2+ Ni(H 2S) 4 384.0 437.1 53.1 300.0 -84.0 449.3 65.3 2– NiC 2N3S3 (CUSJUV) 62.9 -16.2 -79.1 39.4 -23.5 14.3 -48.6 2– NiC 4S4O4 (TOXNIA) -217.9 -228.9 -11.0 -192.6 25.3 -271.2 -53.3 – NiC 8N4S4 (TROPNJ) 92.8 46.2 -46.6 122.2 29.4 84.4 -8.4 NiC 8N2H14 S2 (BAEINI) 12.2 -20.3 -32.5 9.8 -2.4 30.8 18.6 NiC 10 N2H20 S6 (ZOTVUZ) 6.4 29.8 23.4 10.4 4.0 33.9 27.5 + NiC 11 N2H21 S2O2 (Square, 2S and 2N) 72.1 125.7 53.6 96.7 24.6 149.1 77.0 Ni(N 2S2H) 2 95.3 62.9 -32.4 117.1 21.8 200.4 105.1 Ni((CH 3)2S) 2F2 cis -153.5 -130.9 22.6 -135.2 18.3 -158.8 -5.3 Ni((CH 3)2S) 2F2 trans -162.5 -131.4 31.1 -159.3 3.2 -150.2 12.3 NiCl 43.5 45.6 2.1 69.7 26.2 63.6 20.1

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

NiCl 2 -17.7 -17.2 0.5 -18.3 -0.6 19.0 36.6 2– NiCl 4 -130.1 -133.3 -3.2 -130.6 -0.5 -116.8 13.3 NiCH 3Cl 37.2 2.6 -34.6 18.9 -18.3 58.4 21.2 NiCl 2O -0.5 -43.8 -43.3 13.0 13.5 61.3 61.8 – NiCl 3.H 2O -188.1 -190.0 -1.9 -197.2 -9.1 -212.4 -24.3 + NiCl.(H 2O) 3 -19.4 -38.3 -18.9 -20.9 -1.5 -14.4 5.0 NiCl 2.(H 2O) 2 cis -150.9 -199.2 -48.3 -156.6 -5.7 -146.9 4.0 NiCl 2.(H 2O) 2 trans -155.3 -199.2 -43.9 -159.0 -3.7 -165.4 -10.1 Ni((CH 3)2S) 2Cl 2 cis -89.2 -136.9 -47.7 -71.8 17.4 -55.7 33.5 Ni((CH 3)2S) 2Cl 2 trans -96.4 -131.6 -35.2 -79.7 16.7 -70.2 26.2 NiTi 211.0 172.5 -38.5 137.6 -73.4 281.0 69.9 NiV 132.9 132.8 -0.1 141.2 8.3 188.0 55.1 NiCr 105.4 99.4 -6.1 149.7 44.3 -94.1 -199.5 NiCu 137.7 137.7 0.0 122.8 -14.8 78.1 -59.5 NiZn 151.2 147.0 -4.3 -8.0 -159.3 166.1 14.8 NiBr 57.8 68.6 10.8 27.2 -30.6 63.6 5.8

NiBr 2 52.9 76.2 23.3 14.1 -38.8 49.5 -3.4 NiCH 3Br 24.6 12.1 -12.5 23.3 -1.3 45.9 21.3 Ni((CH 3)2S) 2Br 2 cis -70.8 -39.9 30.9 -57.3 13.5 -45.7 25.1 Ni((CH 3)2S) 2Br 2 trans -77.1 -53.2 23.9 -60.5 16.6 -59.7 17.4 + NiC 8N2H20 S3Br (BRUCUB) 75.1 60.9 -14.2 64.8 -10.3 124.2 49.1 NiZr 218.3 179.5 -38.8 120.5 -97.8 340.6 122.3 NiMo 296.6 296.6 0.0 227.3 -69.3 423.0 126.4 NiI 62.3 60.4 -1.9 26.1 -36.2 89.3 27.0

NiI 2 36.5 46.8 10.3 15.0 -21.5 86.6 50.1 NiCH 3I 37.0 42.7 5.7 29.2 -7.8 86.0 49.0 Ni((CH 3)2S) 2I2 cis -42.3 -72.0 -29.7 -31.1 11.2 -12.8 29.5 AM1* PM6 PM5 N=91 Most positive error 53.6 79.0 267.5 Most negative error -108.4 -300.6 -199.5 MSE -6.7 -4.3 21.0 MUE 21.5 27.3 53.0 RMSD 29.9 47.0 74.2

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Results for the PM6 parameterization set ( N=43 ) AM1* PM6 PM5 MSE -12.0 1.0 7.2 MUE 26.2 16.2 47.5 RMSD 35.9 22.6 74.5

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Once again, Table 4.19 shows the results obtained with the three methods for the PM6 training set [72]. AM1* systematically gives heats of formation that are too negative (MSE = -12 kcal mol −1), but otherwise performs similarly for the PM6 subset and the complete dataset. PM6 clearly gives some additional outliers with the AM1* training set that decrease its statistical performance a little, whereas PM5 actually performs slightly better for the AM1* dataset than for the PM6 subset (but worse than the other two methods).

4.4.1.2.2 Ionization Potentials and Dipole Moments of Nickel Compounds

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for the compounds containing nickel are shown in Table 4.20.

Table 4.20: Calculated AM1*, PM6 and PM5 Koopmans’ theorem ionization potentials and dipole moments for nickel-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 PM5 Compound Target Error Error Error Koopmans' Theorem Ionization Potentials for Nickel Compounds (eV) Ni + 18.17 12.59 -5.58 12.28 -5.89 13.94 -4.23 NiH 8.50 8.47 -0.03 8.38 -0.12 6.69 -1.81 NiO 9.50 10.11 0.61 7.82 -1.68 11.33 1.83

NiF 2 11.50 11.82 0.32 9.00 -2.50 13.23 1.73 NiCl 9.28 8.46 -0.82 6.61 -2.67 10.78 1.50

NiCl 2 11.20 11.95 0.75 10.85 -0.35 12.33 1.13 NiCO 7.30 7.30 0.00 7.88 0.58 8.52 1.22

Ni(CO) 2 7.79 8.13 0.34 8.12 0.33 9.02 1.23 Ni(CO) 3 7.69 8.89 1.20 8.14 0.45 9.69 2.00 Ni(CO) 4 8.72 9.41 0.69 8.06 -0.66 10.07 1.35 Ni(Cp) 2 6.51 9.06 2.55 7.02 0.51 8.63 2.12 AM1* PM6 PM5 N=11 MSE 0.00 -1.09 0.73 MUE 1.17 1.43 1.83

Dipole Moments for Nickel Compounds (Debye) NiH 2.40 3.16 0.76 0.33 -2.07 0.09 -2.31 NiH + 0.83 4.24 3.41 0.77 -0.06 1.66 0.83

NiH 3 3.75 5.03 1.28 0.11 -3.64 0.32 -3.43 NiO 4.00 5.97 1.97 9.37 5.37 4.68 0.68 NiO – 3.33 0.16 -3.17 2.15 -1.18 4.05 0.72

Ni(OH) 2.(H 2O) 2 cis 3.50 3.02 -0.48 1.72 -1.78 4.90 1.40 NiCO 3.35 3.95 0.60 0.81 -2.54 1.45 -1.90 NiF 4.49 2.47 -2.02 3.19 -1.30 3.22 -1.27

NiCH 3F 3.59 1.06 -2.54 3.04 -0.55 2.78 -0.82 NiOF 2 1.67 0.98 -0.69 2.58 0.91 3.46 1.79 NiF 2.(H 2O) 2 cis 6.48 3.22 -3.26 5.48 -1.00 8.56 2.08 113

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

NiCl 4.39 2.97 -1.42 2.95 -1.44 5.81 1.42

NiCH 3Cl 4.39 1.72 -2.67 3.85 -0.54 5.27 0.88 NiCl 2O 1.40 0.87 -0.54 0.89 -0.51 0.14 -1.26 NiCl 2.(H 2O) 2 cis 6.70 3.16 -3.54 3.63 -3.07 0.14 -6.56 AM1* PM6 PM5 N=15 MSE -0.82 -0.89 -0.52 MUE 1.89 1.73 1.82

AM1* shows no systematic error-trend in the reproduction of Koopmans’ theorem ionization potentials of nickel-containing compounds for the dataset used. PM6 underestimates ionization potentials to nickel compounds by -1.09 eV, whereas PM5 overestimates them by 0.73 eV. AM1* performs slightly better than PM6 (MUE = 1.43 eV) and PM5 (1.83 eV) with an MUE of 1.17 eV.

The performance of the three methods is comparable for dipole moments. The mean unsigned errors vary in a narrow range from 1.73 (PM6) to 1.89 Debye (AM1*). The PM5 MUE is found to be 1.82 Debye. All three methods systematically underestimate dipole moments of nickel compounds. Mean signed errors are found to be -0.52, -0.82 and -0.89 Debye for PM5, AM1* and PM6, respectively. All the large AM1* errors are found for the compounds either contain original AM1 elements or chlorine.

4.4.1.2.3 Geometries of Nickel Compounds

The geometrical parameters used to parameterize AM1* for nickel and a comparison of the AM1*, PM6 and PM5 results are shown in Table 4.21.

AM1* with a mean unsigned error of 0.09 Å performs slightly better than PM6 (MUE = 0.11 Å) and far better than PM5 (MUE = 0.33 Å) for bond lengths to nickel compounds. PM6 (MSE = 0.01 Å) and AM1* (MSE = 0.04 Å) show no significant systematic trend, whereas PM5 (MSE = 0.24) seriously overestimates bond lengths to nickel.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.21: Calculated AM1*, PM6 and PM5 bond lengths and angles for nickel-containing compounds. The codenames within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 PM5 Compound Variable Target Error Error Error NiH Ni-H 1.61 1.64 0.03 1.71 0.10 3.09 1.47 NiH + Ni-H 1.44 1.63 0.19 1.70 0.26 2.33 0.89

NiH 2 Ni-H 1.64 1.64 -0.01 1.84 0.20 3.16 1.52 H-Ni-H 180.0 180.0 0.0 180.0 0.0 180.0 0.0

NiH 3 Ni-H 1.82 1.88 0.06 2.73 0.91 3.33 1.51 Ni-H(2) 1.52 1.64 0.13 1.70 0.18 3.00 1.48 H-Ni-H 167.7 168.7 0.9 171.9 4.2 173.2 5.5 H-Ni-H 24.5 22.6 -1.9 14.1 -10.4 13.6 -10.9 2– Ni(CN) 4 Ni-C 1.89 1.83 -0.06 1.84 -0.05 1.87 -0.02 C#N 1.19 1.17 -0.02 1.17 -0.02 1.17 -0.02 3– Ni(CN) 5 Ni-C(ap) 2.17 2.01 -0.16 1.92 -0.25 2.34 0.17 Ni-C(ba) 1.87 1.84 -0.03 1.84 -0.03 2.27 0.40 NiCO Ni-C 1.67 1.83 0.16 1.69 0.01 1.71 0.04

Ni(CO) 2 Ni-C 1.84 1.90 0.06 1.75 -0.09 1.77 -0.08 C-Ni-C 180.0 180.0 0.0 180.0 0.0 180.0 0.0 – Ni(CO) 2 Ni-C 1.76 1.92 0.16 1.75 -0.01 1.84 0.08 C-Ni-C 180.0 163.6 -16.4 180.0 0.0 180.0 0.0

Ni(CO) 3 Ni-C 1.82 1.90 0.08 1.78 -0.04 1.79 -0.03 C-Ni-C 120.0 120.0 0.0 120.0 0.0 120.0 0.0 – Ni(CO) 3 Ni-C 1.79 1.87 0.09 1.81 0.02 1.87 0.08 C-Ni-C 120.0 120.0 0.0 147.7 27.7 103.8 -16.2

Ni(CO) 4 Ni-C 1.85 1.93 0.07 1.81 -0.04 1.82 -0.04 C-Ni-C 109.5 109.5 0.0 109.5 0.0 109.5 0.0

Ni(NH2) 2 Ni-N 1.81 1.96 0.15 1.83 0.02 1.83 0.03 N-Ni-N 180.0 179.9 -0.1 180.0 0.0 168.4 -11.6 H-N-Ni 125.5 111.9 -13.7 123.9 -1.6 126.6 1.1 2+ Ni(NH 3)4 Ni-N 2.00 1.97 -0.03 1.96 -0.04 1.97 -0.03 2+ Ni(NH 3)6 Ni-N 1.96 2.06 0.10 1.96 0.00 2.66 0.70 2+ NiC 6N6H24 (Ni(II)(en) 3) Ni-N 2.19 2.15 -0.04 2.09 -0.10 2.50 0.31 2+ NiC 8N6H26 (AEAMNI10) Ni-N 2.14 2.14 0.00 2.05 -0.09 2.53 0.39

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Ni-N' 2.05 2.03 -0.02 1.98 -0.07 2.35 0.30 N-Ni-N' 81.6 84.1 2.5 85.9 4.3 101.9 20.3

NiC 32 N8H16 (Nickel Phthalocyanine) Ni-N 1.92 2.03 0.11 1.93 0.01 1.99 0.07 Ni(CO) 3NO Ni-C 1.81 1.91 0.10 1.81 0.00 1.79 -0.02 Ni-N 1.88 2.09 0.21 1.94 0.06 3.20 1.32 C-Ni-N 108.6 106.5 -2.1 102.6 -6.0 103.2 -5.4

NiC 13 NH 17 O4 (VAXSUI) Ni-N 1.94 2.04 0.10 1.92 -0.02 2.44 0.50 Ni-C 1.97 2.07 0.10 1.93 -0.04 1.98 0.01 C-Ni-N 135.8 138.1 2.3 137.6 1.8 129.5 -6.3 Ni-C' 1.99 2.08 0.09 1.94 -0.05 2.35 0.36

NiC 8N4H14 O4 (NIMGLO10) Ni-N 1.85 2.05 0.20 1.88 0.03 2.67 0.82 N-Ni-N 83.1 81.7 -1.4 84.6 1.5 75.4 -7.7 NiO Ni-O 1.67 1.66 -0.01 1.62 -0.04 1.60 -0.07 NiO – Ni-O 1.68 1.65 -0.03 1.73 0.05 1.63 -0.05 – NiO 2 Ni-O 1.67 1.68 0.02 1.62 -0.05 1.65 -0.02 O-Ni-O 180.0 180.0 0.0 180.0 0.0 180.0 0.0

Ni(OH) 2 Ni-O 1.75 1.82 0.07 1.73 -0.02 1.79 0.04 O-H 0.99 0.96 -0.03 0.84 -0.15 0.97 -0.02

Ni(OH) 2.(H 2O) 2 cis Ni-O 2.01 2.01 0.00 1.94 -0.07 2.07 0.06 Ni-O 1.83 1.84 0.01 1.88 0.05 1.77 -0.07

Ni(OH) 2.(H 2O) 2 trans Ni-O 1.88 1.85 -0.03 1.85 -0.03 1.80 -0.08 Ni-O 1.94 2.12 0.18 2.12 0.18 2.08 0.14 + Ni(OH).(H 2O) 3 Ni-O 1.93 2.01 0.08 1.97 0.04 2.05 0.12 Ni-O 1.80 1.82 0.02 1.83 0.03 1.76 -0.05 2+ Ni(H 2O) 4 Ni-O 1.90 2.04 0.14 2.06 0.16 2.03 0.13 2+ Ni(H 2O) 6 Ni-O 2.09 2.10 0.01 2.10 0.01 2.04 -0.05 2+ NiH 12 O6 (JERNID) Ni-O 2.03 2.09 0.06 2.11 0.08 2.03 0.00 NiC 10 H18 O6 (AQACNI) Ni-O 2.01 2.03 0.02 2.00 -0.01 1.87 -0.14 O-Ni-O 91.6 95.9 4.3 90.7 -1.0 80.4 -11.2 Ni-O(H2) 2.09 2.15 0.06 2.13 0.04 2.18 0.09 NiF Ni-F 1.77 1.81 0.04 1.74 -0.03 1.59 -0.18

NiF 2 Ni-F 1.74 1.79 0.05 1.67 -0.07 1.59 -0.15 F-Ni-F 180.0 180.0 0.0 180.0 0.0 180.0 0.0 2– NiF 6 Ni-F 1.70 1.79 0.09 1.71 0.01 1.70 0.00 4– NiF 6 Ni-F 1.90 1.83 -0.07 1.91 0.01 1.71 -0.19

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

NiCH 3F Ni-F 1.73 1.73 0.00 1.65 -0.08 1.56 -0.17 Ni-C 1.86 1.93 0.07 1.94 0.08 1.87 0.01 F-Ni-C 103.7 180.0 76.3 107.6 3.9 107.2 3.5

NiOF 2 Ni=O 1.61 1.69 0.08 1.52 -0.09 1.66 0.05 Ni-F 1.73 1.72 -0.01 1.66 -0.07 1.57 -0.16 O=Ni-F 117.7 112.1 -5.6 136.5 18.8 107.7 -10.1

NiF 2.(H 2O) 2 cis Ni-O 1.97 2.04 0.07 1.97 0.00 2.09 0.12 Ni-F 1.80 1.75 -0.05 1.68 -0.12 1.71 -0.10

NiF 2.(H 2O) 2 trans Ni-O 1.93 1.87 -0.06 2.09 0.16 2.06 0.13 Ni-F 1.81 1.75 -0.06 1.69 -0.12 1.71 -0.10

NiC 3H8O2F2 Ni-O 2.02 2.17 0.15 1.93 -0.09 2.01 -0.01 O-Ni-O 67.6 60.1 -7.5 74.5 6.9 67.3 -0.3 Ni-F 1.77 1.73 -0.04 1.68 -0.09 1.59 -0.18 F-Ni-O 95.8 95.6 -0.2 98.4 2.6 97.3 1.5 F-Ni-O-O 174.8 173.6 -1.3 175.6 0.7 175.5 0.7

NiAlH 2 Ni-Al 2.33 2.33 0.00 2.25 -0.09 2.41 0.08 Ni-Al-H 122.1 117.3 -4.9 120.0 -2.1 113.7 -8.4

HNiAlH 2 Ni-Al 2.52 2.36 -0.16 2.24 -0.28 2.57 0.05 Ni-H 1.58 1.63 0.06 2.56 0.99 2.22 0.64 H-Ni-Al 180.0 179.9 -0.1 180.0 0.0 179.9 -0.1 Ni-Al-H 123.3 122.3 -1.0 120.1 -3.2 116.4 -6.9

NiSiH 3 Ni-Si 2.26 2.26 0.00 2.55 0.29 2.40 0.14 Ni-Si-H 111.8 107.5 -4.3 109.0 -2.8 107.1 -4.7

HNiSiH 3 Ni-H 1.55 1.64 0.09 2.43 0.88 2.22 0.67 Ni-Si 2.38 2.35 -0.03 2.56 0.18 2.51 0.13 Ni-Si-H 113.3 111.3 -2.0 109.2 -4.1 108.9 -4.4 H-Ni-Si 180.0 179.9 -0.1 179.9 -0.1 180.0 0.0

NiSi 2C14 P2H40 (DILDAD) Ni-P 2.16 2.28 0.12 2.24 0.08 2.09 -0.08 Ni-Si 3.19 3.20 0.01 3.21 0.02 3.08 -0.11 Ni-C 2.07 1.99 -0.08 2.05 -0.02 1.93 -0.14

HNiPH 2 Ni-H 1.45 1.63 0.19 1.68 0.24 3.07 1.62 Ni-P 2.14 2.25 0.11 2.20 0.06 2.29 0.15 Ni-P-H 102.5 88.5 -14.0 101.4 -1.1 116.1 13.6

Ni 2PH Ni-P 2.04 2.10 0.06 2.17 0.14 1.94 -0.10 Ni-P-H 109.0 114.4 5.4 116.0 7.0 137.9 29.0

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

2+ Ni(PH 3)4 Ni-P 2.25 2.26 0.01 2.26 0.01 2.26 0.01 NiS Ni-S 2.00 2.10 0.10 1.92 -0.09 1.94 -0.06 NiSH Ni-S 2.15 1.96 -0.19 2.15 0.00 2.11 -0.04 Ni-S-H 94.0 81.4 -12.7 98.5 4.5 104.3 10.3

NiSH 2 Ni-S 2.08 2.08 0.00 2.12 0.04 2.39 0.30 Ni-H 1.45 1.64 0.19 1.68 0.24 3.01 1.56 Ni-S-H 94.9 91.2 -3.7 100.5 5.6 104.7 9.8 2+ Ni(H 2S) 4 Ni-S 2.27 2.22 -0.05 2.22 -0.05 2.22 -0.05 NiC 6N6H16 S2 (Ni(II)(en) 2(NCS) 2) Ni-N(en) 2.10 2.16 0.06 1.97 -0.13 2.66 0.56 Ni-N(NCS) 2.15 2.04 -0.11 2.44 0.29 3.38 1.23 N-C 1.20 1.18 -0.02 1.17 -0.03 1.17 -0.03 Ni-N-C 140.0 157.4 17.4 88.2 -51.8 100.1 -39.9 C-S 1.64 1.65 0.01 1.65 0.01 1.65 0.01

NiC 8N2H14 S2 (BAEINI) Ni-N 1.85 2.05 0.20 1.88 0.03 1.90 0.04 N-Ni-N 82.9 74.3 -8.6 86.7 3.8 93.3 10.4 Ni-S 2.17 2.19 0.02 2.14 -0.03 2.25 0.08 + NiC 11 N2H21 S2O2 (Square, 2S and 2N) Ni-S 2.20 2.26 0.06 2.26 0.06 2.30 0.10 S-Ni-S 93.5 100.0 6.5 91.9 -1.6 132.2 38.7 Ni-N 1.93 2.09 0.16 1.94 0.01 3.01 1.08 N-Ni-S 84.7 84.0 -0.7 83.2 -1.5 42.9 -41.8 N-Ni-S-S -176.5 -173.3 3.2 -183.9 -7.5 -119.7 56.8 + NiC 11 N2H21 S2O2 (Square, 2S and 2N for Ni-S-C) C-S-Ni 106.5 99.6 -6.9 105.1 -1.3 83.0 -23.5

Ni((CH 3)2S) 2F2 cis Ni-S 2.24 2.30 0.06 2.12 -0.12 2.35 0.11 S-Ni-S 93.2 85.9 -7.3 94.5 1.4 75.4 -17.7 Ni-F 1.82 1.75 -0.07 1.71 -0.11 1.61 -0.21 F-Ni-S 87.6 93.6 6.0 87.2 -0.4 95.8 8.2

Ni((CH 3)2S) 2F2 trans Ni-S 2.23 2.33 0.10 2.12 -0.11 2.28 0.05 Ni-F 1.82 1.76 -0.06 1.68 -0.14 1.68 -0.14 F-Ni-S 89.3 93.7 4.4 87.9 -1.4 92.4 3.1

NiC 7H16 S2F2 (Ni 2S and 2F) Ni-S 2.24 2.36 0.12 2.15 -0.09 2.39 0.15 S-Ni-S 91.0 94.2 3.2 88.0 -3.1 129.8 38.8 Ni-F 1.81 1.78 -0.03 1.68 -0.13 1.65 -0.17 F-Ni-S 88.7 105.1 16.4 92.5 3.8 100.4 11.7 F-Ni-S-S 176.4 130.0 -46.5 173.1 -3.4 111.5 -65.0

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

NiC 8P2H20 S2 (KUSLOZ) Ni-S 2.18 2.11 -0.07 2.24 0.06 2.18 0.00 Ni-P 2.16 2.24 0.08 2.19 0.03 2.08 -0.08 P-Ni-S 88.9 89.6 0.7 87.0 -1.8 96.7 7.8 – NiC 2N3S3 (CUSJUV) Ni-S 2.13 2.15 0.02 2.13 0.00 2.31 0.18 Ni-S' 2.14 2.23 0.09 2.23 0.09 3.36 1.22 S-Ni-S 95.0 97.6 2.6 95.9 0.9 91.7 -3.3 Ni-C 1.85 1.94 0.09 1.82 -0.03 1.84 -0.01

Ni(N 2S2H) 2 Ni-S 2.20 2.22 0.02 2.18 -0.02 2.24 0.04 S-N 1.68 1.68 0.00 1.61 -0.07 1.66 -0.02 N-S 1.59 1.61 0.02 1.63 0.04 1.58 -0.01 Ni-N 1.66 2.11 0.45 1.70 0.04 2.51 0.85 N-H 1.03 0.99 -0.05 1.04 0.01 1.01 -0.02 – NiC 8N4S4 (TROPNJ) Ni-S 2.14 2.20 0.06 2.26 0.12 2.25 0.11 S-Ni-S 92.4 92.7 0.2 91.3 -1.1 97.7 5.3 2– NiC 4S4O4 (TOXNIA) Ni-S 2.19 2.24 0.05 2.22 0.03 2.23 0.04 S-Ni-S 92.5 96.8 4.4 89.5 -3.0 83.7 -8.8

NiC 10 N2H20 S6 (ZOTVUZ) Ni-S 2.44 2.41 -0.03 2.33 -0.11 2.37 -0.07 S-Ni-S 87.6 90.1 2.5 86.2 -1.4 73.5 -14.2 Ni-N 2.02 2.14 0.12 1.93 -0.09 2.44 0.42 NiCl Ni-Cl 2.17 2.18 0.01 2.14 -0.03 2.20 0.03

NiCl 2 Ni-Cl 2.11 2.15 0.04 2.06 -0.05 2.13 0.02 Cl-Ni-Cl 180.0 180.0 0.0 180.0 0.0 180.0 0.0 2– NiCl 4 Ni-Cl 2.29 2.14 -0.15 2.33 0.04 2.30 0.01 NiCH 3Cl Ni-Cl 2.09 2.16 0.07 2.07 -0.02 2.18 0.09 Ni-C 1.94 1.93 -0.01 1.92 -0.02 1.89 -0.05 Cl-Ni-C 163.6 179.9 16.4 102.0 -61.5 179.1 15.6 + NiCl.(H 2O) 3 Ni-O 1.93 2.00 0.07 2.06 0.13 2.05 0.12 Ni-O 1.99 2.00 0.01 2.05 0.06 2.05 0.06 Ni-Cl 2.13 2.17 0.04 2.12 -0.01 2.11 -0.02

NiCl 2O Ni=O 1.62 1.78 0.16 1.58 -0.04 1.60 -0.02 Ni-Cl 2.08 2.19 0.11 2.03 -0.05 2.10 0.02 O=Ni-Cl 116.2 109.3 -6.9 114.5 -1.7 108.8 -7.4

NiCl 2.(H 2O) 2 cis Ni-O 2.01 2.04 0.03 2.09 0.08 2.01 0.00 Ni-Cl 2.16 2.16 0.00 2.18 0.02 2.16 0.00

NiCl 2.(H 2O) 2 trans Ni-O 1.92 2.04 0.12 2.05 0.13 2.06 0.14

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Ni-Cl 2.20 2.17 -0.03 2.14 -0.06 2.16 -0.04

Ni((CH 3)2S) 2Cl 2 cis Ni-S 2.27 2.20 -0.07 2.14 -0.13 2.27 0.00 S-Ni-S 87.3 100.2 12.9 87.6 0.3 89.8 2.5 Ni-Cl 2.19 2.17 -0.02 2.16 -0.03 2.16 -0.03 Cl-Ni-S 173.7 167.5 -6.2 177.6 3.9 135.5 -38.2

Ni((CH 3)2S) 2Cl 2 trans Ni-S 2.26 2.20 -0.06 2.15 -0.11 2.22 -0.04 Ni-Cl 2.20 2.17 -0.03 2.16 -0.04 2.19 -0.01 Cl-Ni-S 87.4 87.2 -0.2 85.7 -1.7 79.3 -8.1

NiC 7H16 S2Cl 2 (Ni 2S and 2Cl) Ni-S 2.27 2.24 -0.03 2.28 0.01 2.31 0.04 S-Ni-S 87.7 110.1 22.4 98.0 10.3 113.4 25.6 Ni-Cl 2.19 2.20 0.01 2.23 0.04 2.22 0.03 Cl-Ni-S 173.8 173.6 -0.2 104.7 -69.1 102.7 -71.1 Cl-Ni-S-S -79.9 -97.4 -17.5 -107.7 -27.8 -110.0 -30.1 – NiCl 3.H 2O Ni-O 2.03 2.13 0.10 2.13 0.10 2.12 0.09 Ni-Cl 2.17 2.23 0.06 2.23 0.06 2.20 0.03 Ni-Cl 2.26 2.29 0.03 2.30 0.04 2.23 -0.03 NiTi Ni-Ti 2.01 2.51 0.50 2.53 0.52 13.40 11.39 NiV Ni-V 2.43 2.43 0.00 2.66 0.23 2.43 0.00 NiCr Ni-Cr 2.13 2.21 0.08 2.67 0.54 1.40 -0.73

Ni 2 Ni-Ni 2.47 2.48 0.00 1.47 -1.00 2.45 -0.02 – Ni 2 Ni-Ni 2.52 2.52 0.00 1.79 -0.73 1.99 -0.54 + Ni 2 Ni-Ni 2.52 2.50 -0.02 1.65 -0.87 2.57 0.04 Ni 2(C 5H5)2(CO) 2 Ni-Ni 2.43 2.86 0.43 2.38 -0.05 2.85 0.42 Ni 3(C 5H5)3(CO) 2 Ni-Ni 2.36 3.44 1.08 2.35 -0.01 2.70 0.34 Ni-C(Cp) 2.17 2.18 0.01 2.12 -0.05 1.90 -0.27 Ni-C(C=O) 1.91 2.01 0.10 1.87 -0.04 2.11 0.20 NiCu Ni-Cu 2.26 2.44 0.18 2.71 0.45 1.91 -0.35 NiZn Ni-Zn 2.22 2.35 0.13 1.97 -0.26 2.88 0.66 NiBr Ni-Br 2.28 2.27 0.00 2.20 -0.07 2.19 -0.08

NiBr 2 Ni-Br 2.22 2.35 0.13 2.18 -0.04 2.21 -0.01 NiCH 3Br Ni-Br 2.19 2.36 0.17 2.22 0.03 2.18 -0.01 Ni-C 1.85 1.93 0.08 1.91 0.06 1.87 0.02 Br-Ni-C 107.7 179.0 71.4 103.4 -4.3 179.4 71.8

NiBr 2O Ni=O 1.62 1.58 -0.05 1.73 0.11 1.60 -0.02 Ni-Br 2.22 2.18 -0.05 2.37 0.15 2.54 0.32

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

O=Ni-Br 115.1 144.0 28.9 52.1 -63.0 123.0 7.9

NiC 3H8Br 2O2 (Ni 2O and 2Br) Ni-O 2.07 2.18 0.11 2.03 -0.04 2.02 -0.05 O-Ni-O 65.8 59.2 -6.6 68.0 2.2 66.1 0.3 Ni-Br 2.26 2.37 0.11 2.30 0.04 2.24 -0.02 Br-Ni-O 164.3 148.1 -16.2 91.0 -73.3 105.0 -59.3 Br-Ni-O-O -16.2 -17.5 -1.3 -109.73 -93.6 -106.7 -90.6 Br-Ni-O 98.9 90.5 -8.4 102.4 3.5 94.5 -4.3 Ni(SH)Br Ni-Br 2.24 2.35 0.11 2.23 -0.01 2.14 -0.10 Ni-S 2.09 2.06 -0.03 2.13 0.04 2.09 0.00 2– Ni(PH 2)(NH 2)(SH)Br Ni-P 2.30 2.29 -0.01 2.28 -0.02 2.25 -0.05 Ni-Br 2.33 2.44 0.11 2.25 -0.08 2.33 0.00 Ni-S 2.20 2.10 -0.10 2.19 -0.01 2.23 0.02 Ni-N 1.83 2.03 0.20 1.87 0.04 2.10 0.27 + NiC 8N2H20 S3Br (BRUCUB) Ni-Br 2.58 2.68 0.10 2.43 -0.15 2.25 -0.33 Ni-N 2.07 2.16 0.09 2.07 0.00 2.69 0.62 N-Ni-Br 89.9 94.1 4.2 70.2 -19.8 88.3 -1.6 Ni-S 2.39 2.31 -0.09 2.30 -0.09 2.28 -0.11 S-Ni-Br 89.4 62.5 -26.9 102.3 13.0 81.8 -7.6

Ni((CH 3)2S) 2Br 2 cis Ni-S 2.29 2.21 -0.08 2.16 -0.13 2.29 0.00 S-Ni-S 86.3 95.6 9.3 82.7 -3.6 75.4 -11.0 Ni-Br 2.33 2.38 0.05 2.31 -0.02 2.21 -0.12 Br-Ni-S 173.8 172.4 -1.4 176.0 2.2 172.3 -1.5

Ni((CH 3)2S) 2Br 2 trans Ni-S 2.26 2.17 -0.09 2.15 -0.11 2.22 -0.04 Ni-Br 2.35 2.38 0.03 2.35 0.00 2.25 -0.10 Br-Ni-S 86.5 75.8 -10.7 84.3 -2.2 76.5 -10.1

NiC 7H16 S2Br 2 (Ni 2S and 2Br) Ni-S 2.28 2.26 -0.02 2.31 0.03 2.31 0.03 S-Ni-S 81.9 106.5 24.6 90.4 8.5 115.0 33.1 Ni-Br 2.33 2.38 0.05 2.33 0.00 2.26 -0.07 Br-Ni-S 94.0 99.5 5.5 106.3 12.3 83.9 -10.1 Br-Ni-S-S 179.8 136.1 -43.7 144.1 -35.8 118.4 -61.5 NiZr Ni-Zr 2.21 2.73 0.52 2.43 0.23 3.49 1.28 NiMo Ni-Mo 2.14 2.20 0.06 2.52 0.38 10.99 8.85 NiI Ni-I 2.39 2.20 -0.19 2.27 -0.12 2.34 -0.05

NiI 2 Ni-I 2.45 2.20 -0.25 2.37 -0.07 2.36 -0.09 NiCH 3I Ni-I 2.39 2.31 -0.08 2.33 -0.06 2.34 -0.05

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Ni-C 1.85 1.93 0.08 1.91 0.06 1.86 0.01 I-Ni-C 107.5 142.9 35.4 107.5 0.0 111.5 4.0 2– NiIF 3 Ni-F 1.88 1.76 -0.12 2.22 0.34 1.81 -0.07 NiICl Ni-I 2.41 2.23 -0.18 2.33 -0.08 2.37 -0.04 Ni-Cl 2.08 2.18 0.10 2.05 -0.03 2.11 0.03 I-Ni-Cl 120.2 79.6 -40.6 113.4 -6.8 75.0 -45.2

NiC 3H8I2O2 (Ni 2O and 2I) Ni-O 2.10 2.10 0.00 2.02 -0.08 1.99 -0.11 O-Ni-O 64.6 63.2 -1.4 69.4 4.8 67.7 3.2 Ni-I 2.47 2.29 -0.18 2.58 0.11 2.69 0.22 I-Ni-O 101.1 102.1 1.0 56.1 -45.0 110.2 9.1 I-Ni-O-O 176.5 176.1 -0.4 237.0 60.5 150.9 -25.6

Ni((CH 3)2S) 2I2 cis Ni-S 2.29 2.16 -0.13 2.16 -0.13 2.26 -0.03 S-Ni-S 85.1 100.0 14.9 80.2 -4.9 82.2 -2.9 Ni-I 2.56 2.29 -0.27 2.52 -0.04 2.46 -0.10 I-Ni-S 167.8 121.3 -46.5 172.7 4.9 173.6 5.8

Ni((CH 3)2S) 2I2 trans Ni-S 2.27 2.18 -0.09 2.13 -0.14 2.20 -0.07 Ni-I 2.58 2.35 -0.23 2.53 -0.05 2.49 -0.09 I-Ni-S 85.4 111.7 26.3 78.8 -6.6 68.9 -16.5 AM1* PM6 PM5 N=177 MSE bond length 0.04 0.01 0.24 MUE bond length 0.09 0.11 0.33 N=80 MSE bond angle 0.2 -5.1 -4.6 MUE bond angle 10.2 10.7 15.9

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

The performance of AM1* for bond angles to nickel compounds is comparable to PM6 and better than PM5. The MUEs for AM1* and PM6 are 10.2° and 10.7°, respectively, and for PM5 15.9°. AM1* shows no significant systematic error with an MSE of 0.2°, whereas PM6 (MSE = -5.1°) and PM5 (MSE = -4.6°) predict the bond angles to be too small.

4.4.2 Conclusions and Outlook

Our new AM1* parameters for cobalt and nickel provide important additional elements especially for catalytic chemistry applications based on organometallic compounds of the two metals [147, 148]. As for our previous parameterizations, we have extended the range of the parameterization dataset and made it more reliable by including results from DFT calculations. For the training set used, AM1* parameterizations for cobalt and nickel give good energetic and electronic results. Additionally, AM1* performs very well for the structural properties.

As published NDDO-based semiempirical molecular orbital techniques that use d-orbitals, both AM1* and PM6 have very similar theoretical frameworks and provide a good opportunity to carry out comparative calculations for many different applications and provide good starting points for the reaction-specific local parameterizations. As for all semiempirical methods, AM1* and PM6 are likely to give large errors that were not revealed during parameterization. This is illustrated well by comparing their performance for the dataset used to parameterize PM6. The additional compounds in the AM1* dataset give slightly larger errors with PM6. The availability of two independently parameterized techniques of similar quality should, however, provide an additional validation possibility for semiempirical MO calculations on transition metal species.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.5 Parameterization of Copper and Zinc

4.5.1 Results

The optimized AM1* parameters for copper and zinc [66] are shown in Table 4.22. Most of the parameters are quite consistent along the second row so far. Geometries were optimized with the new AM1* parameterization and for AM1 and PM3 using VAMP 10.0 [138], while the PM5 calculations used LinMOPAC2.0 [62]. The two programs give essentially identical results for the Hamiltonians that are available in both.

Table 4.22: AM1* parameters for the elements Cu and Zn. Parameter Cu Zn

Uss [eV] -36.7200000 -58.9431927 Upp [eV] -1.5950000 -13.7497019 Udd [eV] -127.6000000 -137.2805579 -1 ζs [bohr ] 2.0732486 1.7935425 -1 ζp [bohr ] 2.8217281 1.4262020 -1 ζd [bohr ] 1.6952738 2.4309843

βs [eV] -10.2346820 -13.5437738

βp [eV] -26.7461824 -4.1232296

βd [eV] -28.8487829 -9.4119204 gss [eV] 6.3524102 2.7500684 gpp [eV] 7.2628066 2.6182526 gsp [eV] 7.8095426 2.9873393 gp2 [eV] 17.0442571 2.8141778 hsp [eV] 1.6767842 1.8427865 -1 zsn [bohr ] 12.5465123 2.2275908 -1 zpn [bohr ] 0.6411768 2.3757534 -1 zdn [bohr ] 1.4560578 1.9389382 ρ(core) [bohr -1] 1.3878582 1.3340000 -1 ∆H° f(atom) [kcal mol ] 80.688 31.171 0 F sd [eV] 3.3465504 4.6842013 2 G sd [eV] 4.5816519 4.0476809 ααα(ij) H 3.7250884 3.9112954 C 3.3514488 3.0416771 N 3.2268224 3.3195694 O 3.9648169 2.6648814 F 4.7295078 2.8884516 Al 2.2854320 2.4006390 Si 2.5793441 3.8488001 P 1.9571093 1.9182580 S 2.4315562 1.2619302 Cl 2.5666738 3.7009365 Ti 2.5672155 2.2550000 Cu 1.8037355 2.8635660 Zn 1.8441671 2.5326653 Zr 2.9455643 3.5988970 Mo 3.5988970 2.3078430

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

δδδ(ij)

H 7.3641345 a 20.2743002 a C 3.7870419 16.5978577 N 51.0306702 3.0545697 O 6.9436125 50.1508315 F 32.3021570 31.3470343 Al 9.3015182 4.7788091 Si 0.8329647 3.6273287 P 1.0453562 0.3620955 S 0.2199399 0.1042134 Cl 1.8004639 29.1814441 Ti 1.7675702 17.6621462 Cu 9.1216919 3.0060503 Zn 3.0060503 3.0150493 Zr 5.3523771 7.1531723 Mo 2.6563480 2.3815000

aDistance-dependent δ [Å -1] according to equation (1)

4.5.1.1 Copper

4.5.1.1.1 Heats of Formation of Copper Compounds

The calculated heats of formation for our training set of copper compounds are shown in Table 4.23. We have compared our results with the only comparable method available in its final form to date, the unpublished PM5 method implemented in Mopac [62].

Table 4.23: Calculated AM1* and PM5 heats of formation and errors compared with our target values for the copper compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. Target AM1* PM5 Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error Cu + 258.8 261.4 2.6 220.6 -38.2 Cu 80.7 80.7 0.0 78.9 a -1.8 Cu - 52.4 46.5 -5.9 362.1 309.7

Cu 2 116.0 115.0 -1.0 61.9 -54.1 + Cu 2 298.2 305.7 7.5 458.8 160.6 - Cu 2 95.4 104.5 9.1 134.8 39.4 - Cu 3 116.7 123.7 7.0 104.0 -12.7 CuH 72.6 57.7 -14.9 17.2 -55.4 CuH + 289.2 286.3 -2.9 261.2 -28.0 CuH - 68.6 78.0 9.4 57.3 -11.3

CuH 2 92.0 90.0 -2.0 5.9 -86.1 CuCH 3 66.8 62.4 -4.4 -3.9 -70.7 Cu(CH 3)2 80.7 89.2 8.4 -29.0 -109.7 CuC 3H5 88.6 77.9 -10.7 13.0 -75.6 125

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Cu 2C2H2 201.1 158.2 -42.8 30.6 -170.5 CuNH 2 106.2 67.9 -38.3 -2.4 -108.6 Cu(NH 2)2 97.3 71.6 -25.7 -7.1 -104.4 Cu 2O 72.0 72.4 0.4 -91.7 -163.7 CuO 55.5 45.6 -10.0 24.8 -30.7 CuO - 35.0 40.1 5.1 -39.0 -74.0

CuO 2 70.3 70.3 0.0 117.8 47.5 CuOH 3.8 3.2 -0.6 -43.0 -46.8

Cu(OH) 2 -63.5 -48.0 15.5 -92.7 -29.2 HCuOH 46.7 30.5 -16.2 -45.2 -91.9 CuF -3.0 -2.9 0.1 -46.8 -43.8

CuF 2 -63.8 -63.8 0.0 -47.5 16.3 CuHF 24.6 31.2 6.6 -35.2 -59.8

FCuCH 3 42.1 30.4 -11.7 -52.8 -94.9 CuAlH 2 99.4 86.9 -12.5 35.6 -63.7 Cu(AlH 2)2 142.8 142.9 0.1 -31.9 -174.7 Cu 3Al 197.7 206.3 8.6 70.2 -127.5 CuSiH 3 84.9 69.9 -15.0 -6.4 -91.2 HCuSiH 3 113.0 98.6 -14.4 -8.8 -121.8 Cu 2SiO 111.3 110.5 -0.8 -47.9 -116.7 CuHSiO 42.1 56.9 14.8 -27.9 -48.6

CuPH 3 78.9 78.0 -0.9 -31.2 -110.1 Cu 2PH 156.7 142.1 -14.6 13.1 -143.6 Cu(PH 2)2 62.5 63.5 0.9 -75.2 -137.7 CuSH 63.8 56.3 -7.5 2.4 -61.4 HCuSH 63.2 89.3 26.2 10.5 -52.7

Cu(SH) 2 63.8 73.4 9.6 15.9 -47.9 Cu 2S 107.4 108.9 1.5 -28.7 -136.1 CuSCH 3 64.6 45.5 -19.1 7.4 -57.2 CuSCN 112.5 81.5 -30.9 49.4 -63.1 CuCl 21.8 27.3 5.6 -4.5 -26.2

CuCl 2 0.0 5.8 5.8 23.6 23.6 Cu 3Cl 3 -61.8 -67.3 -5.5 -69.7 -7.9 CuHCl 65.4 33.9 31.2 7.5 -57.9 CuFCl -35.0 -36.1 -1.1 -12.4 22.6

ClCuCH 3 65.6 43.1 -22.4 -10.9 -76.5 CuTi 166.6 129.8 -36.9 135.1 -31.6

Cu 2Ti 229.4 241.0 11.7 262.4 33.0 CuZr 200.0 140.8 -59.1 250.3 50.3

Cu 2Zr 248.1 248.4 0.3 219.1 -28.9 CuMo 262.6 275.9 13.3 314.9 52.3

AM1* PM5 Most positive error 31.2 309.7 Most negative error -59.1 -174.7 MSE -5.3 -48.2 MUE 11.4 75.7 RMSD 16.8 93.9

aThe heat of formation of the Cu atom with PM5 was calculated using a full CI because the UHF calculations converges to a 2d configuration. The heat of formation of the atom of any element is by definition the experimental value in MNDO-like methods.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* performs remarkably well, even considering that the data shown in Table 4.23 are biased towards AM1* because it was trained on this set of compounds. The mean unsigned error of only 11.4 kcal mol –1 and RMSD of 16.8 kcal mol –1 are very respectable and suggest that AM1* has been parameterized well. The parameterization set for PM5 has not been published, but clearly does not cover the range of compounds used for AM1*.

The largest errors for AM1* are found for the “exotic” molecules CuTi and CuZr (-36.9 and −1 −1 -59.1 kcal mol , respectively), CuNH 2 (-38.3 kcal mol ), the unsymmetrically substituted −1 molecules ClCuCH 3 and HCuSH (26.2 and -22.4 kcal mol , respectively), Cu(NH 2)2 (-25.7 −1 −1 kcal mol ) and the two molecules with triple bonds, Cu 2C2H2 (-42.8 kcal mol ) and CuSCN (-30.9 kcal mol −1). The last two can be explained by AM1’s known tendency to treat triply bonded species incorrectly, as is shown by the good performance of AM1* for the reaction

Cu + + SCN − → CuSCN (see Table 4.24 below).

4.5.1.1.2 Reaction energies of Copper Compounds

The calculated reaction energies are shown in Table 4.24. As expected from the parameterization procedure and also seen for Ti and Zr [87], AM1* performs significantly better than other methods for these reactions. The largest AM1* error is found to be only 21.2 kcal mol −1 for the reaction below.

Cu + SCH 3 → CuSCH 3

Table 4.24: Calculated AM1* and PM5 heats of reaction and errors compared with our target values for the copper compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. AM1* PM5 Reaction Target Error Error CuH → H + Cu 67.0 75.1 8.1 71.6 4.6 CuO → Cu + O 96.0 112.5 16.5 93.1 -2.9 Cu + + SCN - → CuSCN -160.9 -160.8 0.2 -145.6 15.3

CuCl 2 → CuCl + Cl 54.0 48.6 -5.4 0.9 -53.1

Cu 2 → 2Cu 46.4 46.4 0.0 11.5 -34.9 CuS → Cu + S 66.0 64.9 -1.1 29.4 -36.6 CuF → Cu + F 88.0 102.5 14.5 102.4 14.4

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CS 2 + Cu → CuS + CS 38.5 53.8 15.3 103.3 64.8

Cu + SCH 3 → CuSCH 3 -202.3 -181.2 21.2 -178.4 23.9 CuCl → Cu + Cl 84.0 80.4 -3.6 70.2 -13.8

CuF 2 → CuF + F 95.0 79.8 -15.2 19.6 -75.4

MSE 4.6 -8.5 MUE 9.2 30.9 RMSD 11.7 38.7

4.5.1.1.3 Ionization Potentials and Dipole Moments of Copper Compounds

Table 4.25 shows the calculated Koopmans’ theorem ionization potentials and dipole moments for some copper compounds. AM1* performs significantly better than PM5 for ionization potentials and similarly for dipole moments. AM1* tends to underestimate ionization potentials, whereas they are overestimated severely by PM5. AM1* underestimates dipole moments systematically but gives a better correlation between experimental and target values than PM5, which shows no systematic deviation but correlates poorly. Correcting AM1* for the systematic deviation leads to the equation

∗ = 1.028 + 0.991 4.1 which gives a mean unsigned error of 0.55 Debye and a standard deviation of 0.71 Debye.

Table 4.25: Calculated AM1* and PM5 Koopmans’ theorem ionization potentials and dipole moments for coppercontaining compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. MSE indicates the mean signed error in the appropriate units, MUE the mean unsigned error and R 2 the correlation coefficient between the calculated and target data. AM1* PM5 Compound Target Error Error Koopmans’ Theorem Ionization Potential (eV)

Cu 2 7.97 8.41 0.44 8.64 0.67 CuH 9.52 10.52 1.00 11.84 2.32 CuF 10.80 11.46 0.66 14.24 3.44

CuF 2 13.18 12.48 -0.70 15.22 2.04 CuCl 10.70 9.63 -1.07 11.66 0.96

CuCl 2 11.90 9.25 -2.65 12.57 0.67 CuSCH 3 7.90 7.91 0.02 9.95 2.05 Cu 2S 7.73 7.29 -0.44 10.88 3.15 CuH 2 10.04 7.61 -2.43 14.84 4.80 CuSH 8.58 8.39 -0.18 10.45 1.87

CuAlH 2 8.55 8.62 0.07 9.07 0.52 Cu 3Al 7.05 8.40 1.35 6.42 -0.63 Cu 2PH 5.87 6.88 1.01 9.56 3.69 128

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CuPH 3 8.95 8.05 -0.90 10.93 1.98 CuN 2H4 8.75 8.29 -0.46 10.28 1.53 CuAl 2H4 7.66 7.17 -0.50 7.61 -0.05 MSE -0.30 1.81 MUE 0.87 1.90 R2 0.64 0.66 Dipole Moment (Debye) CuO 4.45 3.31 -1.14 4.58 0.13 CuOH 3.85 3.00 -0.85 2.83 -1.02 CuF 5.70 3.50 -2.20 4.28 -1.42 CuCl 4.97 3.24 -1.73 5.58 0.61

CuCH 3 1.68 0.72 -0.95 2.31 0.63 CuC 3H5 1.66 1.45 -0.20 1.95 0.29 Cu 2O 3.76 2.45 -1.31 2.53 -1.23 CuNH 2 3.30 2.31 -0.99 0.47 -2.83 CuSCN 6.68 5.29 -1.40 7.11 0.43 CuHF 3.32 2.75 -0.57 1.42 -1.90

CuSiH 3 2.66 0.38 -2.28 4.44 1.78 CuAlH 2 2.14 1.40 -0.74 4.86 2.72 Cu 2PH 0.23 0.41 0.18 0.96 0.73 CuPH 3 1.50 0.80 -0.70 1.91 0.41 CuSiH 4 1.55 0.38 -1.17 0.41 -1.14 CuCH 3Cl 3.95 2.17 -1.78 3.50 -0.45 CuCH 3F 3.89 3.30 -0.59 3.19 -0.70 CuH 2.66 0.47 -2.19 3.64 0.98

CuSCH 3 3.43 3.28 -0.15 5.14 1.71 Cu 2S 4.66 3.46 -1.20 3.61 -1.05 CuSH 3.94 3.77 -0.17 5.51 1.57

CuAl 2H4 1.97 1.68 -0.29 1.31 -0.67 CuS 4.31 3.58 -0.73 5.56 1.25 MSE -1.01 0.04 MUE 1.02 1.11 R2 0.79 0.48

4.5.1.1.4 Geometries of Copper Compounds

Table 4.26 shows a comparison of the AM1* and PM5 results for bond lengths and angles of small copper compounds. AM1* performs slightly better than PM5 for bond lengths and bond angles. The mean unsigned errors of 0.06 Å and 7.4° for bond lengths and angles, respectively, are acceptable. AM1* tends to overestimate bond lengths to cooper (by 0.04 Å), whereas PM5 tends to make them too short.

Table 4.26: Calculated AM1* and PM5 bond lengths and angles at the metal for copper-containing compounds. AM1* PM5 Compound Variable Target Error Error

Cu 2 Cu-Cu 2.22 2.44 0.22 2.05 -0.17 - Cu 2 Cu-Cu 2.39 2.67 0.28 1.91 -0.48 - Cu 3 Cu-Cu 2.37 2.51 0.14 1.88 -0.49 CuH Cu-H 1.46 1.57 0.11 1.37 -0.09 129

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CuH - Cu-H 1.59 1.84 0.25 1.48 -0.11 CuH + Cu-H 1.56 1.76 0.20 1.87 0.31

CuH 2 Cu-H 1.56 1.66 0.11 1.33 -0.23 CuCH 3 Cu-C 1.92 1.97 0.04 1.78 -0.15 Cu-C-H 108.3 108.3 0.0 111.1 2.8

CuC 3H5 Cu-C 1.90 1.93 0.03 1.79 -0.10 Cu 2C2H2 Cu-C 1.91 1.94 0.03 1.80 -0.12 CuNH 2 Cu-N 1.88 1.94 0.05 1.56 -0.32 CuO Cu=O 1.72 1.69 -0.03 1.80 0.07

Cu 2O Cu-O 1.81 1.75 -0.05 1.68 -0.13 Cu-O-Cu 104.8 121.0 16.3 144.4 39.7 CuOH Cu-O 1.77 1.75 -0.02 1.72 -0.05 Cu-O-H 110.2 106.3 -3.9 139.7 29.5 CuF Cu-F 1.75 1.69 -0.05 1.68 -0.07

CuF 2 Cu-F 1.75 1.63 -0.12 1.68 -0.07 HCuF Cu-F 1.77 1.69 -0.07 1.60 -0.16 Cu-H 1.52 1.70 0.18 1.33 -0.19

FCuCH 3 Cu-C 1.93 1.92 -0.01 1.72 -0.21 Cu-F 1.78 1.67 -0.11 1.62 -0.16 Cu-C-H 107.8 110.3 2.5 109.2 1.4 FCuCl Cu-Cl 2.09 2.07 -0.02 2.02 -0.07 Cu-F 1.75 1.66 -0.09 1.67 -0.08 CuCl Cu-Cl 2.05 2.11 0.05 2.11 0.06

Cu 3Cl 3 Cu-Cl 2.16 2.17 0.01 2.30 0.14 Cu-Cl-Cu 90.0 100.0 10.0 105.0 15.0 Cl-Cu-Cl 150.0 140.0 -10.0 135.0 -15.0 HCuCl Cu-Cl 2.13 2.36 0.23 1.95 -0.17 Cu-H 1.53 1.57 0.05 1.34 -0.19

ClCuCH 3 Cu-C 1.94 1.95 0.01 1.72 -0.22 Cu-Cl 2.14 2.17 0.03 1.98 -0.16 Cu-C-H 107.7 108.8 1.1 108.6 0.9

Cu 3Al Cu-Al 2.35 2.47 0.12 2.48 0.14 CuAlH 2 Cu-Al 2.34 2.46 0.12 2.30 -0.04 Cu-Al-H 122.2 118.5 -3.7 122.8 0.6

CuSiH 3 Cu-Si 2.26 2.30 0.04 2.19 -0.07 Cu-Si-H 111.8 110.2 -1.6 112.4 0.6

Cu 2SiO Cu-Si 2.31 2.31 0.01 2.25 -0.06 Si-Cu-Si 125.3 116.3 -9.0 146.5 21.2 CuHSiO Cu-Si 2.28 2.28 0.01 2.24 -0.04 Cu-Si-O 117.4 125.1 7.7 111.8 -5.6

Cu 2PH Cu-P 2.26 2.22 -0.03 2.08 -0.17 Cu-P-H 100.6 112.1 11.5 106.8 6.2 Cu-P-Cu 158.7 135.8 -22.9 149.9 -8.8

Cu(PH 2)2 Cu-P 2.27 2.30 0.03 2.03 -0.24 P-Cu-P 149.8 144.4 -5.4 168.4 18.6 Cu-P-H 101.5 103.2 1.7 95.0 -6.5

HCuPH 2 Cu-P 2.28 2.31 0.03 2.04 -0.24 H-Cu-P 138.6 119.8 -18.8 177.2 38.6

Cu 2S Cu-S 2.14 2.17 0.03 2.02 -0.12 Cu-S-Cu 76.05 111.08 35.03 146.12 70.07 CuSH Cu-S 2.15 2.17 0.02 2.06 -0.10 Cu-S-H 93.7 100.7 7.0 100.3 6.6

Cu(SH) 2 Cu-S 2.17 2.14 -0.03 1.97 -0.21 Cu-S-H 95.1 103.1 8.0 94.4 -0.7 HCuSH Cu-S 2.19 2.19 0.00 1.97 -0.23

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CuSCH 3 Cu-S 2.16 2.15 0.01 2.05 -0.10 Cu-S-C 103.8 108.7 5.0 109.2 5.4 CuSCN Cu-S 2.18 2.15 -0.03 2.12 -0.06 Cu-S-C 94.5 105.8 11.3 103.5 9.0 CuTi Cu-Ti 2.48 2.79 0.31 39.86 37.38

Cu 2Ti Cu-Ti 2.43 2.96 0.53 15.66 13.23 CuZr Cu-Zr 2.58 3.07 0.49 3.93 1.35

Cu 2Zr Cu-Zr 2.59 3.19 0.60 3.75 1.16 CuMo Cu-Mo 2.45 2.44 -0.01 14.41 11.96 AM1* PM5 MSE bond lengths 0.077 1.275 MUE bond lengths 0.107 1.524 MSE bond angles 2.0 10.9 MUE bond angles 9.2 14.4

Table 4.27 shows a comparison of the structures optimized for a series of copper compounds (including ion pairs) with the crystal structures taken from the Cambridge Structural Database [107]. The RMSD values were calculated using Quatfit [149] to overlay all the non-hydrogen atoms. Table 4.27: Calculated AM1* and PM5 root-mean-square deviations from the crystal structures for a selection of copper compounds.

RMSD (Å) Cambridge Structural Database Entry AM1* PM5 ABETEH 1.34 1.54 ABUXIE 1.18 0.84 ACITIP 0.98 1.58 ACTHCU 1.16 1.13 AEPYCC10 0.49 2.13 AJEVOA 1.11 0.26 AJILIO 0.18 0.31 AJINIQ 0.19 0.17 AJOROG01 0.73 0.86 AKEVUH 0.17 0.14 AKIYUO 0.54 0.39 ALERUE 0.68 0.90 ALEUCU 0.43 0.56 ALIWUN 0.13 - AMEHOP 0.82 0.38 AMORCU 0.17 1.40 AMPCUC01 0.69 0.19 AMPRCU 0.55 0.55 ANCTCU 0.99 0.50 APBTCU 0.26 0.35 AQCBCU 0.42 1.14 ASTMEC 0.54 1.56 ASUDEX 0.34 0.42 ATEVAW 0.20 1.78 ATISIF 0.58 -

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AVOQIL 0.50 0.60 AVOQOR 0.95 1.05 AVUKIL 0.22 0.33 AWAWAW 0.30 - AWEMAQ 0.67 5.65 AYACOS 0.79 0.41 AZEFUG 0.61 1.50 BUACUM 1.11 2.74 CEFXOA 0.57 - CETCAM 0.49 - DMTCCU 0.26 0.10 ESOXAL 0.18 0.20 FEJMEN 0.67 6.48 GACPOQ 0.32 0.34 UKUYAA 0.92 0.40 Mean RMSD 0.59 1.11 Median RMSD 0.55 0.56 Std. Dev. 0.33 1.37 Largest RMSD 1.34 6.48

A visual comparison of the crystal and AM1*-optimized structures is given in Table S2 of the Supplementary Material [66].

Table S2 reveals some systematic weaknesses of AM1*. The optimized structure for entry ABETEH, for instance, shows a calculated copper coordination that is closer to square planar than the observed distorted tetrahedral geometry from the crystal structure. Eleven examples (ACITIP, ATCHU, EJEVOA, AKIYUO, ALEUCU, ALIWUN, AMPRCU, AQCBCU, ASTMEC, AVOQIL and AVOQOR) contain waters of crystallization that are coordinated either via hydrogen bonds to ligands or interact directly with the copper center. The former are subject to the know AM1 problems with hydrogen-bond geometries [39], whereas the latter (ACTHCU and ALIWUN) tend to bind the waters too tightly to the metal. The structures with both phosphine and cyanide ligands bound to copper (AWEMAQ and FEJMEN) optimize to geometries in which one of the nitrogens of the bipyridyl ligand is slightly dissociated and the cyanide occupies a bridging position above the Cu-P bond.

In general, however, the crystal structures, and especially the coordination at copper, are reproduced remarkably well by AM1*.

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4.5.1.2 Zinc

4.5.1.2.1 Heats of Formation of Zinc Compounds

The results obtained for heats of formation of zinc compounds are shown in Table 4.28. We have compared our results with PM5 [62], PM3 [31, 41, 46], PM3-Zn [150], AM1 [39, 151], MNDO [28, 152] and MNDO/d [34, 135]. The AM1* errors in heats of formation for zinc compounds are significantly lower than for the other methods, even MNDO/d, which normally performs best in our comparisons [69, 87]. The mean unsigned error between experimental and AM1*-calculated heats of formation is only 12.5 kcal mol –1 and the root mean square deviation 21.8 kcal mol –1. These values are 2-3 times smaller than those given by the other published methods except MNDO, which gives only slightly worse agreement with experiment. The only major and consistent deviations in the AM1* results are given by compounds that contain both zinc and either titanium or zirconium, for which we have no experimental data and which are unlikely to be strongly represented in molecules calculated with AM1*, and for Zn(II) solvated by ammonia molecules.

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Table 4.28: Calculated AM1*, PM5, PM3, PM3-Zn, AM1, MNDO/d and MNDO heats of formation and errors compared with our target values for the zinc compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1.

Target AM1* PM5 PM3 PM3-Zn AM1 MNDO/d MNDO

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error Zn 2+ 665.1 664.5 -0.6 665.1 0.0 662.7 -2.4 618.1 -47.0 729.4 64.3 665.0 -0.1 720.1 55.1 Zn + 249.4 251.3 1.9 247.9 -1.5 235.4 -14.0 226.7 -22.7 244.2 -5.2 249.4 0.0 239.6 -9.8 Zn 31.2 31.2 0.0 31.2 0.0 31.2 0.0 31.2 0.0 31.2 0.0 31.2 0.0 31.2 0.0 ZnH 62.7 61.7 -1.0 50.3 -12.4 55.5 -7.2 69.7 7.0 47.9 -14.8 63.9 1.2 41.1 -21.6 ZnH + 246.3 246.9 0.6 235.7 -10.6 266.2 19.9 256.8 10.5 255.1 8.8 247.8 1.5 258.8 12.5

ZnH 2 56.0 72.3 16.3 50.9 -5.1 42.2 -13.8 70.8 14.8 39.3 -16.7 45.0 -11.0 53.2 -2.9

ZnCH 3 46.9 46.4 -0.5 31.2 -15.7 37.2 -9.7 45.6 -1.3 36.1 -10.8 46.5 -0.4 24.7 -22.2 + ZnCH 3 213.9 227.5 13.6 215.1 1.2 227.1 13.2 220.7 6.8 222.3 8.4 227.4 13.5 227.7 13.8

Zn(CH 3)2 12.7 30.7 18.0 15.0 2.3 8.2 -4.5 16.8 4.1 19.8 7.1 8.6 -4.1 19.9 7.2 + Zn(CH 3)2 221.7 222.3 0.6 218.7 -3.0 222.0 0.3 218.9 -2.8 217.8 -3.9 222.2 0.5 236.2 14.5

Zn(C 2H5)2 12.1 10.1 -2.0 8.2 -3.9 5.5 -6.6 12.5 0.4 14.1 2.0 0.2 -11.9 13.0 0.9

Zn(C 3H7)2 -3.3 -3.4 -0.1 -2.9 0.4 -1.6 1.8 4.3 7.6 2.4 5.7 -8.3 -5.0 4.6 7.9

Zn(C 4H9)2 -12.3 -15.8 -3.5 -12.6 -0.3 -9.9 2.4 -4.3 8.0 -9.2 3.1 -16.1 -3.8 -3.2 9.1

Zn(NH 2)2 68.9 55.5 -13.4 4.6 -64.3 29.5 -39.4 27.8 -41.1 44.9 -24.0 29.7 -39.2 26.2 -42.8 ZnO - 12.7 10.7 -2 1.6 -11.1 17.9 5.2 31.7 19 57.7 45 13.7 1 16.8 4.1 ZnF -11.4 -10.5 0.9 -34.6 -23.2 2.8 14.2 -20.8 -9.4 -8.3 3.1 -25.1 -13.7 -53.3 -41.9

ZnF 2 -101.2 -101.2 -0.1 -112.5 -11.3 -43.1 58.0 -109.2 -8.0 -50.6 50.5 -111.9 -10.7 -116.3 -15.2 ZnHF -25.2 -10.4 14.8 -33.2 -8.0 -3.6 21.6 -22.7 2.5 -8.1 17.1 -45.8 -20.6 -35.3 -10.1

ZnAlH 2 98.8 90.6 -8.2 50.5 -48.2 18.4 -80.4 50.2 -48.6 48.4 -50.4 70.2 -28.5 79.3 -19.5

Zn(AlH 2)2 119.3 98.2 -21.1 21.8 -97.5 -0.8 -120.1 113.4 -5.9 37.5 -81.8 58.9 -60.4 94.3 -25.0

HZnAlH 2 94.4 117.7 23.3 51.0 -43.3 111.0 16.6 56.3 -38.0 45.5 -48.8 51.8 -42.6 88.5 -5.9

ZnSiH 3 82.8 62.2 -20.6 37.2 -45.6 36.3 -46.5 57.3 -25.5 39.3 -43.5 65.9 -16.9 57.0 -25.8

Zn(SiH 3)2 90.8 86.8 -4.1 31.6 -59.2 16.9 -73.9 63.3 -27.5 34.6 -56.2 45.9 -44.9 80.2 -10.6

HZnSiH 3 74.2 84.5 10.3 41.4 -32.8 30.1 -44.1 68.4 -5.8 38.4 -35.8 47.1 -27.2 64.3 -9.9

Zn 2PH 122.7 117.8 -4.9 191.6 68.9 12.5 -110.2 47.3 -75.4 70.3 -52.4 92.6 -30.1 70.8 -51.9

HZnPH 2 63.3 79.3 16.0 26.6 -36.7 13.1 -50.3 39.5 -23.9 41.1 -22.2 33.3 -30.1 57.1 -6.3 ZnS 75.4 75.4 0.0 48.5 -26.9 58.8 -16.6 75.4 0.0 78.3 2.9 44.7 -30.7 63.8 -11.6

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ZnSH 53.3 49.4 -3.9 15.7 -37.5 14.7 -38.6 31.9 -21.4 30.5 -22.8 25.7 -27.5 29.0 -24.3 HZnSH 56.6 42.7 -13.9 21.0 -35.6 9.3 -47.4 39.7 -16.9 28.5 -28.1 2.0 -54.7 43.6 -13.1 ZnCl 6.3 -6.4 -12.7 -13.9 -20.2 -2.3 -8.6 -10.0 -16.3 -7.7 -14.0 9.5 3.2 -16.2 -22.5

ZnCl 2 -63.5 -63.2 0.3 -61.5 2.0 -52.8 10.7 -76.3 -12.8 -54.6 8.9 -63.3 0.2 -48.7 14.8 ZnHCl 4.3 3.6 -0.7 -8.5 -12.8 -7.2 -11.5 -6.9 -11.3 -9.7 -14.0 -12.9 -17.2 -0.5 -4.8 ZnClF -71.8 -82.0 -10.3 -87.5 -15.8 -47.6 24.1 -92.6 -20.9 -53.3 18.5 -87.9 -16.1 -83.3 -11.6

Zn 2 57.9 62.4 4.5 60.6 2.7 53.0 -4.9 62.7 4.8 56.5 -1.4 55.7 -2.2 61.2 3.3 2+ Zn(H 2O) 499.9 513.0 13.1 482.4 -17.5 541.5 41.7 479.5 -20.4 559.4 59.5 506.1 6.2 517.2 17.3 2+ Zn(H 2O) 2 347.7 356.5 8.8 348.7 1.0 432.4 84.7 351.7 4.0 429.2 81.5 355.9 8.2 362.6 14.9 2+ Zn(H 2O) 3 228.6 245.5 16.9 238.9 10.3 338.2 109.6 236.9 8.3 326.0 97.4 225.1 -3.5 238.9 10.3 2+ Zn(H 2O) 4 123.3 139.0 15.7 142.4 19.1 253.6 130.3 134.0 10.7 234.8 111.5 111.6 -11.7 139.0 15.7 + Zn (H 2O) 112.3 130.7 18.4 133.1 20.8 166.5 54.2 137.7 25.4 158.4 46.0 147.2 34.8 126.6 14.2 2+ Zn(NH 3) 537.7 523.6 -14.1 491.6 -46.1 534.3 -3.3 499.8 -37.9 546.8 9.2 541.0 3.4 547.0 9.3 2+ Zn(NH 3)2 461.8 396.0 -65.8 382.2 -79.6 429.5 -32.3 404.3 -57.4 430.8 -31.0 222.2 -239.6 438.5 -23.3 2+ Zn(NH 3)3 421.6 353.7 -67.8 308.1 -113.4 347.4 -74.2 330.7 -90.9 356.4 -65.1 356.2 -65.4 368.5 -53.1 2+ Zn(NH 3)4 397.2 313.2 -84.0 252.0 -145.2 277.3 -120.0 272.2 -125.0 302.2 -95.0 291.6 -105.6 321.7 -75.5

Zn(Acac) 2 -233.4 -233.5 -0.1 -229.4 4.0 -117.0 116.4 -226.8 6.6 -92.8 140.6 -196.1 37.3 -168.1 65.3 AM1* PM5 PM3 PM3-Zn AM1 MNDO/d MNDO Most positive error 23.3 68.9 130.3 25.4 140.6 37.3 65.3 Most negative error -84.0 -273.4 -120.1 -125.0 -95.0 -239.6 -75.5 MSE -3.7 -21.6 -5.8 -15.3 1.2 -19.7 -6.2 MUE 12.5 27.7 38.8 21.7 34.8 24.7 19.3 RMSD 21.8 42.6 54.9 33.3 48.2 46.4 26.0 Compounds containing Cu, Ti, Zr and Mo

Zn 2Zr 220.6 178.8 -41.9 -52.8 -273.4 ZnZr 195.7 164.7 -31.0 27.1 -168.6

Zn 2Ti 201.6 180.6 -21.0 238.6 37 ZnTi 204.1 159.3 -44.8 172.9 -31.1 ZnCu 102.0 97.7 -4.3 159.1 57.1 ZnMo 265.5 265.5 0.0 379.2 113.6 AM1* PM5 Most positive error -4.3 113.6 Most negative error -44.8 -273.4

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

MSE -23.8 -44.2 MUE 23.8 113.5 RMSD 29.4 142.4

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

The latter error is disturbing because it implies that the all-important competition between nitrogen and oxygen coordination to Zn(II) in biological systems will not be treated adequately by AM1*. We were, however, unable to remove this error without severely worsening the calculated AM1* structures for zinc compounds in which the metal is coordinated to nitrogen ligands.

The reaction energies calculated for zinc compounds (e.g. complexation energies of Zn 2+ with water and ammonia) were used to calculate some of the heats of formation shown in Table 4.28 and are not listed separately.

4.5.1.2.2 Ionization Potentials and Dipole Moments of Zinc Compounds

The calculated Koopmans’ theorem ionization potentials and dipole moments are shown in Table 4.29. For the ionization potentials, PM5 performs significantly better than the other methods and MNDO significantly worse. MNDO/d shows no systematic error, whereas PM3, PM5, AM1 and MNDO show increasingly large positive mean signed errors and AM1* and PM3-Zn negative ones. The correlation coefficients (without Zn +, whose high ionization potential exerts a strong lever effect on the correlation) only vary between 0.81 (MNDO/d) and 0.93 (PM5).

AM1* overestimates dipole moments by about 0.5 Debye, whereas MNDO/d and MNDO underestimate them. Generally, none of the methods perform either very well or very badly for dipole moments of zinc compounds.

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Table 4.29: Calculated Koopmans’ theorem ionization potentials and dipole moments for zinc-containing compounds. AM1* PM3 PM3-Zn PM5 AM1 MNDO/d MNDO Compound Target Error Error Error Error Error Error Error Koopmans’ Theorem Ionization Potential (eV)

Zn 9.39 9.54 0.15 8.85 -0.54 8.48 -0.91 9.40 0.01 9.24 -0.15 9.46 0.07 9.04 -0.35

Zn(CH 3)2 9.40 9.48 0.08 10.28 0.88 9.71 0.31 9.82 0.42 9.74 0.34 10.07 0.67 10.54 1.14 Zn(C 2H5)2 8.60 9.14 0.54 9.46 0.86 9.11 0.51 9.20 0.60 9.14 0.54 9.77 1.17 10.19 1.59 ZnCl 2 11.87 11.42 -0.45 10.95 -0.92 11.27 -0.60 11.72 -0.15 12.20 0.33 11.16 -0.71 12.80 0.93 Zn 2 9.00 9.70 0.70 8.25 -0.75 8.20 -0.80 8.64 -0.36 8.27 -0.73 8.05 -0.95 9.14 0.14 ZnF 2 13.91 11.87 -2.04 15.32 1.41 14.30 0.39 14.08 0.17 14.32 0.41 14.00 0.09 14.37 0.46 ZnH 9.40 8.87 -0.53 9.25 -0.15 8.25 -1.15 9.69 0.29 9.57 0.17 8.11 -1.29 10.39 0.99 ZnO 9.34 9.52 0.18 9.89 0.55 9.17 -0.17 10.58 1.24 10.70 1.36 9.61 0.27 10.83 1.49 Zn + 17.96 17.27 -0.69 18.53 0.57 16.97 -0.99 18.09 0.13 21.04 3.08 18.02 0.06 20.84 2.88 MSE -0.23 0.21 -0.38 0.26 0.59 -0.07 1.03 MUE 0.60 0.74 0.65 0.38 0.79 0.59 1.11 R2 b 0.89 0.85 0.91 0.93 0.91 0.81 0.87 Dipole Moment (Debye) ZnH 0.56 1.91 1.35 2.47 1.91 2.04 1.48 1.33 0.77 1.84 1.28 0.98 0.42 1.23 0.67

Zn(CH 3)2 0.40 0.00 -0.40 0.02 -0.38 0.02 -0.39 0.01 -0.40 0.01 -0.39 0.02 -0.39 0.01 -0.39 Zn(C 2H5)2 0.00 0.11 0.11 0.30 0.30 0.13 0.13 0.06 0.06 0.09 0.09 0.23 0.23 0.13 0.13 Zn(C 3H7)2 0.10 0.15 0.05 0.08 -0.02 0.18 0.08 0.23 0.13 0.19 0.09 0.26 0.16 0.15 0.05 Zn(C 4H9)2 0.00 0.17 0.17 0.07 0.07 0.21 0.21 0.14 0.14 0.20 0.20 0.31 0.31 0.13 0.13 ZnCl 2 3.19 4.60 1.42 4.00 0.81 5.25 2.06 4.25 1.06 3.56 0.37 1.98 -1.21 3.03 -0.16 ZnH + a 2.14 0.96 -1.18 2.95 0.81 2.29 0.15 2.42 0.28 2.05 -0.10 1.87 -0.27 2.34 0.20 ZnO 5.37 4.84 -0.53 3.12 -2.25 4.29 -1.08 3.11 -2.26 3.53 -1.84 2.09 -3.28 2.16 -3.22 ZnS 5.22 8.32 3.10 4.13 -1.10 5.53 0.31 8.06 2.84 6.78 1.56 2.28 -2.95 2.69 -2.53 MSE 0.45 0.02 0.33 0.29 0.14 -0.78 -0.57 MUE 0.92 0.85 0.65 0.88 0.66 1.02 0.83 R2 0.83 0.71 0.84 0.75 0.82 0.83 0.71 aDipole moment relative to the center of mass bExcluding the value for Zn +, whose lever effect increases R 2 unreasonably

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4.5.1.2.3 Geometries of Zinc Compounds

Table 4.30 shows a comparison of the available and finalized methods for the bond lengths and angles of the compounds used for our AM1* parameterization. AM1* performs best for bond lengths to zinc (MUE = 0.068 Å) and moderately well (MUE = 3°), but not as well as PM5 (MUE = 2.2°) for bond angles with a zinc atom involved. The specific reparameterization of PM3 for zinc [150] also does well for these angles (MUE = 3.4°), whereas AM1, MNDO and MNDO/d are slightly worse (MUE 5-7°) and PM3 significantly so. Apart from PM5, which has a MUE of 0.19 Å for the bond lengths to zinc in this set of compounds, all other methods give MUEs between 0.11 and 0.15 Å. Thus, AM1* performs best for its own training set, which is not surprising. The data shown in Table 4.30 are best regarded as an indication of how general the parameterizations are, rather than an absolute measure of the quality of the parameterization. Thus, although AM1* is best for this set of compounds, there may be local compound types for which any of the other methods may perform better.

Table 4.31 shows a comparison of the results obtained by optimizing some zinc-containing structures from the Cambridge Structural Database as isolated molecules or complexes using the available methods. The same reservations about using such comparisons apply as for the corresponding copper cases, but AM1* and the specific PM3-parameterization for zinc give the best results. The AM1* results are shown graphically in Table S3 of the Supporting Material.

As for copper, some of the compounds that show large deviations (ALOPAS, FIPRUR) involve waters moving during the optimization, whereas others (DOLVAB01, DTBZZN10, EXAPYZ, HEPBOT, HOCZEE, IPEHOA01, IZUPAU, MIXZEY, NAGMUE) show difficulties that AM1* suffers in reproducing the coordination of sulfur ligands to zinc. However, some of these effects may be due to missing intermolecular interactions in the calculations. Otherwise, the structures are reproduced remarkably well be AM1* despite some differences distinguishing between square planar and tetrahedral coordination or deviations caused by missing dispersion between monomers in a dimeric structure (DONWAE).

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Table 4.30: Calculated AM1*, PM3, PM3-Zn, PM5, AM1, MNDO/d and MNDO bond lengths and angles at the metal for zinc-containing compounds.

AM1* PM3 PM3-Zn PM5 AM1 MNDO/d MNDO Compound Variable Target Error Error Error Error Error Error Error ZnH Zn-H 1.60 1.76 0.16 1.55 -0.05 1.75 0.15 1.35 -0.25 1.49 -0.11 1.47 -0.13 1.43 -0.16 ZnH + Zn-H 1.52 1.56 0.04 1.53 0.01 1.70 0.19 1.41 -0.10 1.52 0.01 1.39 -0.13 1.51 -0.01

ZnH 2 Zn-H 1.62 1.62 0.00 1.53 -0.09 1.63 0.02 1.37 -0.24 1.47 -0.15 1.43 -0.18 1.43 -0.19

ZnCH 3 Zn-C 2.13 2.12 -0.01 1.97 -0.16 2.01 -0.11 1.87 -0.26 1.93 -0.20 1.95 -0.17 1.90 -0.23 + ZnCH 3 Zn-C 2.02 1.92 -0.10 2.07 0.05 2.03 0.01 1.83 -0.19 1.97 -0.05 1.94 -0.08 1.95 -0.07

Zn(CH 3)2 Zn-C 1.93 1.95 0.02 1.94 0.01 1.88 -0.05 1.88 -0.05 1.90 -0.03 1.90 -0.03 1.88 -0.05 H-C-Zn 111.5 108.2 -3.3 109.5 -2.0 110.9 -0.6 112.1 0.6 109.2 -2.3 111.6 0.1 111.3 -0.2 C-Zn-C 180.0 180.0 0.0 178.8 -1.2 179.7 -0.3 180.0 -0.1 179.8 -0.2 179.3 -0.8 179.8 -0.2 + Zn(CH 3)2 Zn-C 2.12 1.95 -0.17 2.10 -0.02 2.05 -0.07 1.82 -0.30 2.03 -0.09 1.99 -0.13 2.04 -0.08

Zn(C 2H5)2 Zn-C 1.95 1.95 0.00 1.97 0.02 1.90 -0.05 1.89 -0.06 1.93 -0.02 1.92 -0.03 1.90 -0.05 C-C-Zn 114.5 108.3 -6.2 98.3 -16.2 110.2 -4.3 111.8 -2.8 114.6 0.1 116.3 1.8 118.5 4.0 C-Zn-C 180.0 179.1 -0.9 168.7 -11.3 178.4 -1.6 175.7 -4.4 174.2 -5.9 177.5 -2.5 174.6 -5.4 H-C-Zn 108.4 107.0 -1.4 109.6 1.3 108.2 -0.1 109.6 1.2 105.8 -2.5 107.6 -0.8 106.6 -1.8

Zn(C 3H7)2 Zn-C 1.95 1.95 0.00 1.98 0.03 1.91 -0.04 1.89 -0.06 1.94 -0.01 1.92 -0.03 1.91 -0.04 C-C-Zn 114.5 107.7 -6.8 110.1 -4.4 112.4 -2.1 111.2 -3.3 114.8 0.3 116.2 1.7 118.1 3.6 H-C-Zn 108.5 107.4 -1.1 111.4 2.9 108.0 -0.5 109.9 1.4 105.9 -2.6 107.0 -1.5 106.0 -2.5 C-Zn-C 180.0 179.1 -0.9 167.3 -12.8 176.6 -3.4 177.0 -3.0 174.5 -5.5 176.8 -3.2 173.8 -6.2

Zn(C 4H9)2 Zn-C 2.04 1.95 -0.09 1.98 -0.07 1.99 -0.05 1.89 -0.15 1.93 -0.11 1.92 -0.12 1.91 -0.13 2+ Zn(NH 3) Zn-N 1.99 1.71 -0.28 2.03 0.04 2.02 0.04 1.97 0.0 1.96 -0.03 2.01 0.02 1.98 -0.01 Zn-N-H 112.9 108.9 -4.0 108.0 -4.9 110.1 -2.8 111.6 -1.3 109.3 -3.6 111.8 -1.1 110.6 -2.3

Zn(Acac) 2 Zn-O 1.94 2.04 0.10 2.00 0.06 1.96 0.02 1.94 0.00 2.09 0.14 1.96 0.02 1.96 0.01 O-Zn-O 97.2 94.2 -3.0 102.2 5.0 95.1 -2.1 90.7 -6.5 93.4 -3.8 93.4 -3.8 91.1 -6.1 Zn-O-C 122.9 130.0 7.1 116.1 -6.8 123.8 0.9 128.0 5.1 121.8 -1.1 126.3 3.4 128.7 5.8 2+ [Zn(H 2O)] Zn-O 1.90 1.78 -0.12 1.95 0.05 1.94 0.04 1.84 -0.06 2.00 0.10 1.92 0.02 1.84 -0.06 Zn-O-H 125.9 124.9 -1.0 119.4 -6.5 126.1 0.2 125.4 -0.5 115.3 -10.6 125.0 -0.9 124.4 -1.5 ZnF Zn-F 1.81 1.82 0.01 1.77 -0.04 1.87 0.05 1.78 -0.03 1.77 -0.04 1.74 -0.08 1.70 -0.11

ZnF 2 Zn-F 1.74 1.73 -0.01 1.74 0.00 1.68 -0.06 1.74 0.00 1.75 0.01 1.72 -0.02 1.68 -0.06 F-Zn-F 180.0 180.0 0.00 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0

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HZnF Zn-F 1.78 1.76 -0.02 1.75 -0.03 1.86 0.08 1.78 0.00 1.76 -0.02 1.73 -0.05 1.69 -0.09 Zn-H 1.58 1.59 0.01 1.52 -0.06 1.62 0.04 1.35 -0.23 1.46 -0.12 1.40 -0.18 1.42 -0.16 ZnCl Zn-Cl 2.22 1.99 -0.23 2.10 -0.12 2.03 -0.20 2.16 -0.07 2.11 -0.11 2.16 -0.06 2.16 -0.06

ZnCl 2 Zn-Cl 2.07 1.89 -0.18 2.06 -0.01 2.12 0.05 2.13 0.06 2.07 0.00 2.09 0.02 2.12 0.04 Cl-Zn-Cl 180.0 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0 180.0 0.0 HZnCl Zn-Cl 2.16 1.93 -0.23 2.07 -0.10 2.02 -0.14 2.17 0.00 2.08 -0.08 2.12 -0.04 2.13 -0.03 Zn-H 1.59 1.61 0.02 1.52 -0.06 1.62 0.04 1.37 -0.22 1.46 -0.13 1.41 -0.18 1.43 -0.16

ZnAlH 2 Zn-Al 2.79 2.79 0.00 2.43 -0.36 2.49 -0.30 2.09 -0.70 2.35 -0.44 2.44 -0.35 2.51 -0.28

HZnAlH 2 Zn-Al 2.60 2.66 0.06 2.58 -0.01 2.51 -0.09 2.12 -0.48 2.34 -0.26 2.26 -0.34 2.52 -0.07 Zn-H 1.64 1.69 0.05 1.55 -0.09 1.63 -0.01 1.39 -0.26 1.48 -0.17 1.46 -0.18 1.44 -0.20

ZnSiH 3 Zn-Si 2.62 2.45 -0.17 2.25 -0.37 2.17 -0.46 2.11 -0.51 2.30 -0.32 2.37 -0.25 2.32 -0.30 Zn-Si-H 111.0 105.6 -5.4 108.3 -2.7 110.1 -0.9 113.6 2.6 105.9 -5.1 110.8 -0.2 111.9 0.9

HZnSiH 3 Zn-Si 2.45 2.45 0.00 2.26 -0.19 2.25 -0.19 2.14 -0.31 2.30 -0.15 2.28 -0.17 2.32 -0.13 Zn-H 1.63 1.68 0.06 1.54 -0.09 1.64 0.01 1.38 -0.24 1.47 -0.15 1.45 -0.18 1.44 -0.18

Zn(SiH 3)2 Zn-Si 2.47 2.47 0.00 2.27 -0.20 2.24 -0.23 2.15 -0.32 2.29 -0.18 2.28 -0.19 2.32 -0.15

Zn 2PH Zn-P 2.47 2.47 0.00 1.92 -0.55 2.01 -0.46 2.59 0.12 2.23 -0.24 2.14 -0.32 2.13 -0.34 Zn-P-Zn 172.4 177.6 5.2 109.0 -63.4 145.9 -26.5 167.6 -4.8 118.7 -53.7 141.7 -30.7 133.1 -39.3 Zn-P-H 93.8 88.8 -5.0 54.5 -39.3 107.0 13.2 96.2 2.4 71.1 -22.7 108.9 15.1 113.5 19.7

HZnPH 2 Zn-P 2.38 2.52 0.14 1.98 -0.40 2.00 -0.38 2.13 -0.25 2.18 -0.20 2.21 -0.17 2.24 -0.15 Zn-H 1.62 1.67 0.05 1.54 -0.09 1.63 0.01 1.38 -0.25 1.47 -0.15 1.43 -0.19 1.43 -0.19 ZnS Zn-S 2.12 2.17 0.05 2.23 0.10 2.13 0.01 1.83 -0.29 1.90 -0.22 1.84 -0.28 2.14 0.02 Zn2S Zn-S 2.32 2.34 0.02 2.12 -0.20 2.06 -0.27 2.11 -0.21 2.23 -0.09 2.04 -0.28 2.04 -0.28 ZnSH Zn-S 2.35 2.36 0.01 2.18 -0.17 2.10 -0.25 2.17 -0.18 2.27 -0.08 2.08 -0.27 2.13 -0.22 HZnSH Zn-S 2.31 2.33 0.02 2.15 -0.16 2.13 -0.17 2.18 -0.13 2.25 -0.06 2.04 -0.27 2.11 -0.20 Zn-H 1.60 1.59 -0.01 1.53 -0.07 1.63 0.03 1.37 -0.23 1.47 -0.13 1.42 -0.17 1.43 -0.17 H-S-Zn 98.7 103.3 4.6 88.2 -10.5 96.2 -2.5 99.8 1.1 89.9 -8.8 121.1 22.4 105.8 7.1 H-Zn-S 176.4 177.6 1.2 173.8 -2.6 178.7 2.3 177.9 1.5 175.4 -1.0 170.0 -6.4 177.3 0.9 AM1* PM3 PM3-Zn PM5 AM1 MNDO/d MNDO MSE bond lengths -0.022 -0.094 -0.078 -0.180 -0.108 -0.143 -0.126 MUE bond lengths 0.068 0.114 0.121 0.190 0.122 0.148 0.130 MSE bond angles -1.1 -9.2 -1.6 -0.6 -6.8 -0.4 -0.5

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MUE bond angles 3.0 10.2 3.4 2.2 6.8 5.1 5.7

Compounds containing Cu, Ti, Zr and Mo ZnCu Zn-Cu 2.48 2.48 0.00 2.25 -0.23 ZnTi Zn-Ti 2.42 3.14 0.72 35.54 33.12

Zn 2Ti Zn-Ti 2.93 2.93 0.00 11.18 8.24 ZnZr Zn-Zr 2.97 2.97 0.01 2.22 -0.75

Zn 2Zr Zn-Zr 2.99 3.06 0.07 2.33 -0.66 ZnMo Zn-Mo 2.50 2.55 0.05 2.46 -0.04 AM1* PM5 MSE bond lengths 0.141 6.615 MUE bond lengths 0.141 7.174

Table 4.31: Calculated AM1*, PM5, AM1, PM3, PM3-Zn, MNDO and MNDO/d root-mean-square deviations from the crystal structures for a selection of zinc compounds.

RMSD (Å) Cambridge Structural Database Entry AM1* PM5 AM1 PM3 PM3-Zn MNDO MNDO/d ALOJIU 0.75 2.48 2.40 1.45 3.02 2.86 ALOPAS 1.53 1.26 1.23 0.32 0.19 1.75 0.64 AQEROD 0.45 0.31 1.01 0.95 0.55 1.58 0.36 AREWOJ 0.72 12.01 27.06 1.26 1.78 24.38 26.31 AXILUO 0.34 0.15 0.81 2.45 0.20 0.37 0.37 AYEKIY 0.73 0.79 1.13 0.91 0.96 2.77 0.78 BACNEZ 0.53 0.49 0.68 0.63 0.55 0.82 0.52 BAXROH 0.36 0.12 1.14 0.27 0.18 3.00 2.63 BEBCIV 0.95 1.16 2.08 0.35 0.55 0.53 1.14 BEKPUC 0.48 0.14 0.14 0.13 0.19 4.01 1.76 BENLAH 0.39 0.14 0.63 0.22 0.14 0.64 0.16 BIBBEU 1.33 1.69 1.65 1.46 0.40 1.72 1.73 CAPDEC 0.86 0.49 1.31 0.29 0.32 0.78 0.26

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CAPDIG 0.65 0.20 0.56 0.17 0.20 0.69 0.13 CEAMZN01 0.66 0.44 0.93 0.77 0.19 0.34 0.15 DIYXUE 0.48 1.01 0.56 3.03 0.88 0.49 0.46 DOLVAB01 1.43 0.97 1.08 0.85 0.93 0.99 1.20 DONWAE 1.91 0.36 0.60 1.66 0.93 1.29 1.50 DTBZZN10 0.76 0.09 0.19 0.13 0.17 0.53 0.77 DUVKOU 0.56 0.39 1.13 0.30 0.34 0.43 0.42 EXAPYZ 0.94 0.32 0.54 0.38 0.38 0.69 1.84 FESBOV 0.27 0.10 0.20 0.15 0.15 2.43 0.24 FIDWOF 0.25 0.09 0.31 0.16 0.13 2.20 0.09 FIPRUR 1.14 0.27 0.33 0.23 0.31 0.29 0.28 FODMEQ 0.28 0.07 0.18 0.13 0.12 2.81 0.13 HADVIR 0.75 0.14 2.18 0.54 0.49 4.53 1.64 HEPBOT 1.37 0.22 0.34 0.46 0.39 0.44 2.23 HIJSOI 0.40 0.28 0.88 0.25 0.29 2.49 0.22 HITPUV 0.23 0.07 0.23 0.22 0.25 0.24 0.44 HOCZEE 0.83 0.37 0.32 0.43 0.43 0.36 2.33 HODZIJ01 0.89 0.83 0.70 0.67 0.48 0.64 0.86 HOPBUJ 0.84 0.48 0.48 0.49 0.50 0.55 0.56 INICZN 0.39 0.23 0.28 1.22 0.18 0.58 0.57 IPEHOA01 1.62 0.64 0.78 0.87 0.86 0.66 1.65 IZUPAU 1.27 0.80 0.88 1.03 1.20 0.97 1.70 JIZCAW10 0.29 0.19 2.50 0.18 0.16 2.34 0.27 KUJRAI 0.44 0.29 2.13 0.56 0.54 1.81 0.40 KUJREM 0.52 0.32 2.49 1.85 1.05 2.59 0.64 LAJMIS 0.28 0.20 0.22 0.22 0.21 3.92 0.21 LAJMUE 0.16 0.07 0.11 0.57 0.49 2.35 0.15 LIVYOE 0.45 0.20 0.35 0.19 0.14 2.13 0.20 MIXZEY 0.83 0.20 0.22 0.32 0.35 0.30 2.96 MPEZNC 0.38 0.19 0.18 0.13 0.15 0.15 0.15 NAGMUE 1.12 0.53 1.39 1.32 1.58 16.00 1.18 NENMAU 1.37 0.09 0.59 0.56 0.31 0.99 0.93 ROPZOL 1.35 0.06 0.33 0.90 0.57 2.25 0.40 SUNXOO 0.14 0.24 0.37 0.47 0.30 0.75 0.40 SUPDIQ 0.51 0.10 2.16 0.34 0.29 2.99 0.32

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UCATIB 0.86 0.22 0.32 0.44 0.45 1.20 2.43 ULIRUC 0.61 0.08 1.04 0.34 0.15 1.06 1.08 VOGFIG 0.19 0.51 1.05 0.56 0.53 2.48 0.46 VOTGAM 0.70 0.39 0.72 0.53 0.49 0.83 0.73 WEZXEE 0.26 1.58 1.55 1.43 1.96 25.06 0.28 XAJLOJ 0.20 0.13 2.17 0.26 0.30 3.52 0.32 ZNTPBZ 0.76 0.29 1.23 1.21 1.29 1.46 0.65

Mean RMSD 0.70 0.61 1.38 0.69 0.52 2.62 1.33 Median RMSD 0.65 0.28 0.72 0.47 0.38 1.20 0.56 Std. Dev. 0.42 1.61 3.56 0.63 0.44 4.84 3.49 Largest RMSD 1.91 12.01 27.06 3.03 1.96 25.06 26.31

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4.5.2 Conclusions and Outlook

As for our previous parameterization for AM1*, we have extended the range of the parameterization dataset by including results from DFT and ab initio calculations. Our aim thereby is to produce a parameter set that is more robust and generally applicable than those trained only on the experimental data. The results for our training dataset suggest that this objective has been achieved, although we warn against drawing too many conclusions by comparing calculational methods with each other based on training compounds used for only one of the methods. Nevertheless, our data suggest that the AM1* parameterizations for copper and zinc give surprisingly good energetic results and are acceptable for the “electronic” properties (ionization potential and dipole moment) to the other methods available.

Using twelve valence electrons for zinc apparently allows gives better results than those obtained by the other methods, which use only two valence electrons. This, however, may also simply be the effect of comparing the other methods with our own training set. However, using twelve valence electrons allows us to produce consistent parameterizations across the first transition-metal series at the cost of making AM1* slightly slower for zinc than the other methods. Note that none of the other methods use either occupied or virtual d-orbitals for zinc.

As with all semiempirical MO-techniques reported so far, we expect that there will be cases in which AM1* gives large deviations from experiment or higher-level calculations. However, by using a diverse training set that includes data obtained from DFT and ab initio calculations, we have attempted to make the parameterization as robust and generally applicable as possible. This is apparently possible without sacrificing accuracy for the more commonplace compounds for which reliable experimental data are available.

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4.6 Parameterization of Bromine and Iodine

4.6.1 Results

The optimized AM1* parameters for bromine and iodine [67] are shown in Table 4.32. Geometries were optimized with the new AM1* parameterization and for AM1, PM3, MNDO and MNDO/d using VAMP 10.0 [138], while the PM5 calculations used LinMOPAC2.0 [62] and those with PM6 used MOPAC2007 [139]. The three programs give essentially identical results for the Hamiltonians that are available in all three. We have compared our results with MNDO [28, 152], MNDO/d [34, 135], AM1 [39, 151], PM3 [31, 41, 46], PM5 [62] and PM6 [72].

Table 4.32: AM1* parameters for the elements Br and I. Parameter Br I

Uss [eV] -65.40253456 -60.75271210 Upp [eV] -54.55391930 -47.18041426 Udd [eV] -15.51056900 -9.49851860 -1 ζs [bohr ] 2.5905411 4.0425168 -1 ζp [bohr ] 2.3308566 2.8124603 -1 ζd [bohr ] 1.3573612 1.6540802 βs [eV] -8.3149757 -6.5019618 βp [eV] -10.5070410 -7.9162569 βd [eV] -0.9625993 -3.4072650 gss [eV] 7.4008761 8.9163551 gpp [eV] 9.2274222 3.6086821 gsp [eV] 7.5365165 9.1817156 gp2 [eV] 7.9550041 5.7144226 hsp [eV] 3.6616527 2.9958452 -1 zsn [bohr ] 0.4804244 0.1695950 -1 zpn [bohr ] 3.7665928 2.2521795 -1 zdn [bohr ] 4.8057603 4.1070512 ρ(core) [bohr -1] 1.7542911 1.3865333 -1 ∆H° f(atom) [kcal mol ] 26.7400000 25.5160000 0 F sd [eV] 4.6747381 5.7882291 2 G sd [eV] 26.6113981 15.4899237 ααα(ij) H 3.7096163 3.8684681 C 2.5775014 2.8992533 N 2.8846137 2.9170659 O 3.5223744 2.4445019 F 2.4787667 2.3108956 Al 2.5933836 3.2803001 Si 4.0281236 3.5099969 P 1.4090763 3.2419093 S 2.4234321 1.8500840 Cl 1.9658508 3.4260883 Ti 3.1288615 3.7234443 Cu 4.2315726 4.1756457 Zn 7.2212087 4.6581564 146

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Br 3.1162216 2.1827496 Zr 3.6415408 3.3752957 Mo 3.4837054 3.7083736 I 2.1827496 3.6483792 δδδ(ij) H -7.1316792 -15.2888133 C 3.0538542 9.9695358 N 5.7893235 9.0153552 O 11.8870965 2.6996725 F 1.6319315 1.8755240 Al 4.9508713 84.6788616 Si 72.6409601 68.6752217 P 0.6387116 50.7461936 S 3.1922391 2.1902606 Cl 1.0877097 30.6262179 Ti 8.5729464 87.8970995 Cu 61.7791246 91.5204213 Zn 3.0808859 77.1375232 Br 13.8079448 2.4789698 Zr 42.0142732 47.7961015 Mo 60.0988582 98.1745836 I 2.4789698 -40.7622533

4.6.1.1 Bromine

4.6.1.1.1 Heats of Formation of Bromine Compounds

The calculated heats of formation for our training set of bromine compounds are shown in Table 4.33. We have compared our results with the available published methods available and the unpublished PM5 method implemented in LinMopac [62]. As Stewart’s PM6 parameters are now published [72] we have also compared our results with this method.

AM1* can be seen to reproduce heats of formation for the training set of bromine compounds (excluding compounds of Ti, Cu, Zr and Mo, which are only available in AM1*, PM5 and PM6) slightly better than PM3, PM5 or PM6, far better than MNDO and AM1 and slightly worse than MNDO/d. These results are roughly what we expect as AM1* uses the unchanged AM1 parameterization for the elements H, C, N, O and F, which limits the possible accuracy of the parameterization. This interpretation is partly justified by the relatively large negative AM1* error (-10.9 kcal mol −1) for BrOH and for the large negative errors found for BrF (- −1 −1 13.4 kcal mol ), CBrClF 2 (-26.0 kcal mol ), and the very large positive error (68.4 kcal −1 mol ) for BrFO 3. It does not, however, explain the large negative errors for Br 2S2 (-15.5 kcal −1 −1 mol ) BrSi and Br 3Si (-12.3 and -13.0 kcal mol , respectively) and the phosphorus anion 147

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

− −1 Br 4P (-17.0) and the large positive one (39.6 kcal mol ) for Br3P=O. With the exception the oxygen in Br 3P=O, these compounds contain only “pure” AM1* elements. We note, however, − that all methods give negative errors for Br 4P . A particularly annoying example is, however, −1 ZnBr 2, for which AM1* gives an error of 49.4 kcal mol . This error represents a necessary compromise in the parameterization as the Zn-Br bond length is also in error by 0.11 Å. Quite generally, we find disappointing results for compounds that contain two or more “pure” AM1* elements. This is likely to be a consequence of our sequential parameterization strategy, in contrast to the simultaneous parameterization used for PM6 [72], aggravated by using the original AM1 parameters for H, C, N, O and F. Nevertheless, on aggregate AM1* performs at the level expected of a modern NDDO-based technique for the heats of formation of bromine compounds.

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Table 4.33: Calculated AM1*, MNDO/d, MNDO, AM1, PM3, PM5 and PM6 heats of formation and errors compared with our target values for the bromine compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1. yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. Target AM1* MNDO/d MNDO AM1 PM3 PM5 PM6

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error Br 26.7 26.7 0.0 26.7 0.0 26.7 0.0 26.7 0.0 26.7 0.0 26.7 0.0 26.7 0.0 Br - -50.9 -50.9 0.0 -50.9 0.0 -37.5 13.4 -20.4 30.5 -56.2 -5.3 -53.5 -2.6 -55.1 -4.2 Br + 273.2 273.2 0.0 264.3 -8.9 301.8 28.7 284.7 11.6 284.6 11.4 279.3 6.1 286 12.8

Br 2 7.4 7.9 0.5 6.7 -0.7 -1.7 -9.1 -5.3 -12.7 4.9 -2.5 -5.6 -13.0 2.5 -4.9 BrH -8.7 -8.8 -0.1 2.8 11.5 3.6 12.3 -10.5 -1.8 5.3 14.0 -7.8 0.9 -15.7 -7.0

CH 3Br -8.5 -6.2 2.3 -8.0 0.5 -10.4 -1.9 -6.2 2.3 -2.0 6.5 -7.5 1.0 -5.7 2.8

CH 2Br 2 0.0 -0.4 -0.4 -0.3 -0.3 -5.1 -5.1 -1.0 -1.0 7.9 7.9 -0.5 -0.5 2.8 2.8

CHBr 3 5.7 6.6 0.9 10.2 4.5 3.1 -2.6 6.4 0.7 17.6 11.9 9.3 3.6 12.4 6.7 CBr 4 20.1 14.0 -6.1 23.3 3.2 13.8 -6.3 15.9 -4.2 32.9 12.8 21.0 0.9 23.1 3.0

C2H5Br -14.9 -14.3 0.6 -15.3 -0.4 -17.0 -2.1 -13.1 1.8 -11.4 3.5 -14.5 0.4 -13.0 1.9

CH 2Br-CH 2Br -9.8 -9.5 0.3 -9.6 -0.2 -13.4 -3.6 -7.9 1.9 -3.4 6.4 -12.9 -3.1 -7.5 2.3

CHBr=CH 2 18.9 21.9 3.0 16.2 -2.7 15.8 -3.1 18.0 -0.9 23.8 4.9 16.8 -2.1 17.3 -1.6 1-C3H7Br -20.8 -21.0 -0.2 -19.7 1.1 -21.6 -0.8 -19.5 1.3 -16.4 4.4 -20.0 0.8 -18.2 2.6

2-C3H7Br -23.8 -20.3 3.5 -19.7 4.1 -20.6 3.2 -19.7 4.1 -20.8 3.0 -21.9 1.9 -21.9 1.9

1,2-C3H6Br 2 -17.1 -15.4 1.7 -13.0 4.1 -16.3 0.8 -12.1 5.0 -12.5 4.6 -19.6 -2.5 -17.5 -0.4

1,3-C3H6Br 2 -17.0 -16.4 0.6 -13.8 3.2 -17.9 -0.9 -14.5 2.5 -9.2 7.8 -17.7 -0.7 -13.7 3.3 (CH 2Br)HC=CH 2 10.8 11.2 0.4 8.5 -2.3 7.0 -3.8 11.0 0.2 13.4 2.6 9.1 -1.7 11.2 0.4

CH 3HC=CHBr cis 10.5 9.9 -0.6 6.2 -4.3 5.6 -4.9 7.9 -2.6 13.6 3.1 8.1 -2.4 9.9 -0.6

CH 3HC=CHBr trans 9.8 11.2 1.4 6.8 -3.0 6.4 -3.4 8.4 -1.4 17.8 8.0 9.1 -0.7 11.2 1.4

1-C4H9Br -25.6 -27.8 -2.2 -24.9 0.7 -26.7 -1.1 -26.8 -1.2 -22.1 3.5 -25.6 0.0 -23.1 2.5 2-C4H9Br -28.8 -25.9 2.9 -23.2 5.6 -24.2 4.6 -23.7 5.1 -25.6 3.2 -25.4 3.4 -24.4 4.4

C(CH 3)3Br -31.6 -24.1 7.5 -20.4 11.2 -20.5 11.1 -20.6 11.0 -30.3 1.3 -29.5 2.1 -31.7 -0.1

1-C5H11 Br -30.8 -34.7 -3.9 -29.6 1.2 -31.4 -0.6 -33.6 -2.8 -27.5 3.3 -31.1 -0.3 -28.1 2.7

C6H5Br 25.2 30.8 5.6 23.2 -2.0 23.9 -1.3 26.8 1.6 31.0 5.8 25.6 0.4 25.7 0.5 BrCN 44.4 47.8 3.4 40.2 -4.2 40.0 -4.4 32.5 -11.9 53.6 9.2 38.8 -5.6 35.1 -9.3 BrNO 19.6 19.6 0.0 8.0 -11.6 1.9 -17.7 21.3 1.7 6.6 -13.0 13.5 -6.1 -0.1 -19.7 BrO 30.1 30.1 0.0 29.9 -0.2 35.3 5.2 35.7 5.6 20.8 -9.3 25.9 -4.2 36.5 6.4 BrOH -20.0 -30.9 -10.9 -24.0 -4.0 -22.7 -2.7 -24.7 -4.7 -33.9 -13.9 -19.6 0.4 -21.6 -1.6

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

O=CBr 2 -27.1 -25.8 1.3 -29.0 -1.9 -31.6 -4.5 -17.8 9.3 -25.3 1.8 -26.0 1.1 -25.7 1.4

CH 3COBr -45.5 -40.4 5.1 -42.7 2.8 -43.2 2.3 -34.3 11.2 -43.5 2.0 -43.4 2.1 -44.6 0.9 CH 3COCH 2Br -43.3 -42.8 0.5 -42.9 0.4 -43.2 0.1 -41.5 1.8 -42.9 0.4 -46.6 -3.3 -46.9 -3.6

C6H5-COBr -11.6 -6.2 5.4 -7.5 4.1 -7.7 3.9 0.8 12.4 -7.7 3.9 -10.5 1.1 -7.6 4.0

p-Br-C6H4-COOH -69.4 -57.9 11.5 -64.9 4.5 -64.3 5.1 -62.3 7.1 -57.9 11.5 -64.3 5.1 -62.1 7.3 BrF -14.0 -27.4 -13.4 -26.0 -12.0 -5.8 8.2 -7.2 6.8 -21.2 -7.2 -10.6 3.4 -25.9 -11.9

BrF 2 -27.1 -34.8 -7.7 -28.7 -1.6 22.0 49.1 14.1 41.2 -11.7 15.4 -13.6 13.5 -33.9 -6.8

BrF 3 -61.1 -59.1 2.0 -59.6 1.5 22.9 84.0 24.9 86.0 -47.1 14.0 -51.3 9.8 -68.7 -7.6

BrF 5 -102.5 -102.5 0.0 -103.6 -1.1 107.7 210.2 83.4 185.9 -74.8 27.7 -108.9 -6.4 -81.3 21.2

CBrF 3 -155.1 -155.8 -0.7 -154.0 1.1 146.6 301.7 -144.6 10.5 -157.8 -2.7 -151.5 3.6 -150.2 4.9 CBr 2F2 -91.0 -92.7 -1.7 -94.8 -3.8 -86.1 4.9 -74.1 16.9 -94.1 -3.1 -86.2 4.8 -84.3 6.7

CHBrF 2 -101.6 -105.9 -4.3 -105.1 -3.5 -101.1 0.5 -96.8 4.8 -99.4 2.2 -100.1 1.5 -95.8 5.8

CBrF 2-CBrF 2 -189.0 -184.2 4.8 -181.9 7.1 172.2 361.2 -165.3 23.7 -193.4 -4.4 -182.2 6.8 -184.5 4.5

CF 2Br-CH 2Br -103.0 -94.2 8.8 -96.0 7.0 -92.9 10.1 -88.6 14.4 -100.3 2.7 -90.9 12.1 -90.2 12.8 CH 2F-CH 2Br -60.0 -60.6 -0.6 -58.7 1.3 -60.8 -0.8 -60.7 -0.7 -51.2 8.8 -59.6 0.4 -56.8 3.2

C6F5Br -191.3 -179.0 12.3 -193.9 -2.5 -192.0 -0.6 -179.7 11.6 -176.0 15.3 -178.8 12.5 -189.4 1.9

BrFO 3 32.8 101.2 68.4 31.5 -1.3 263.6 230.8 202.7 169.9 140.1 107.3 48.0 15.2 91.5 58.7 BrCl 3.5 3.5 0.0 0.0 -3.5 -9.5 -13.0 -10.6 -14.1 -3.2 -6.7 -8.3 -11.8 4.8 1.3

CBr 2Cl 2 2.0 0.4 -1.7 -3.5 -5.5 -5.1 -7.1 -2.7 -4.7 -1.6 -3.6 -0.3 -2.3 11.0 9.0

CBrCl 3 -10.0 -17.9 -7.9 -17.8 -7.8 -15.1 -5.1 -14.7 -4.7 -14.1 -4.1 -12.0 -2.0 -3.5 6.5

CHBr 2Cl 2.0 1.8 -0.2 -2.2 -4.2 -7.2 -9.2 -3.7 -5.7 3.2 1.2 -1.2 -3.2 6.9 4.9

CHBrCl 2 -12.0 -10.8 1.2 -15.3 -3.3 -17.9 -5.9 -15.5 -3.5 -9.0 3.0 -12.4 -0.4 -4.2 7.8 CH 3-CHClBr -20.0 -15.9 4.1 -18.4 1.6 -21.2 -1.2 -17.5 2.5 -15.9 4.1 -19.5 0.5 -16.5 3.5

CH 2Cl-CH 2Br -19.4 -18.7 0.7 -19.3 0.1 -23.7 -4.3 -20.2 -0.8 -12.9 6.5 -22.8 -3.4 -16.4 3.0 CHBrCl-CHBrCl -8.8 -8.6 0.2 -9.7 -0.9 -15.6 -6.8 -12.8 -4.0 -8.9 -0.1 -15.5 -6.7 -5.1 3.7

CBrClF 2 -105.0 -131.0 -26.0 -106.2 -1.2 -98.0 7.0 -90.0 15.0 -104.8 0.2 -99.6 5.4 -100.6 4.4 AlBr 3.8 4.4 0.6 4.5 0.7 0.7 -3.1 -0.3 -4.1 7.8 4.0 4.0 0.2 -3.7 -7.5

AlBr 3 -98.1 -88.9 9.2 -104.3 -6.2 -60.3 37.8 -96.4 1.7 -85.8 12.3 -94.7 3.4 -100.3 -2.2

Al 2Br 6 -224.0 -224.0 0.0 -222.9 1.1 -132.6 91.4 -248.9 -24.9 -224.9 -0.9 -224.4 -0.4 -222.5 1.5 BrSi 50.0 37.7 -12.3 50.1 0.1 79.3 29.3 46.1 -3.9 75.9 25.9 56.2 6.2 54.4 4.4

Br 2Si -12.5 -15.0 -2.5 -3.7 8.8 11.2 23.7 -18.9 -6.4 -27.4 -14.9 -19.3 -6.8 -8.5 4.0

Br 3Si -48.2 -61.2 -13.0 -34.7 13.5 -16.3 31.9 -66.8 -18.5 -61.6 -13.4 -54.3 -6.1 -48.1 0.1

Br 4Si -99.3 -99.3 0.0 -73.1 26.2 -50.4 48.9 -94.5 4.8 -107.9 -8.6 -98.3 1.0 -98.9 0.4

BrH 3Si -15.3 -15.0 0.3 -11.1 4.2 -18.0 -2.7 -21.1 -5.8 -16.0 -0.7 -18.4 -3.1 -17.7 -2.4

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Br 2H2Si -43.2 -41.4 1.8 -31.6 11.6 -32.0 11.2 -45.8 -2.6 -47.2 -4.0 -45.9 -2.7 -44.5 -1.3

Br 3HSi -72.5 -70.0 2.5 -52.2 20.3 -42.4 30.1 -70.2 2.3 -79.5 -7.0 -72.3 0.2 -72.2 0.3 BrP 38.9 39.9 1.0 65.0 26.1 38.1 -0.8 32.7 -6.2 40.3 1.4 80.8 41.9 36.1 -2.8

Br 3P -33.2 -20.2 13.1 -25.2 8.0 -38.1 -4.9 -23.3 9.9 -28.2 5.0 -53.9 -20.7 -47.0 -13.8 - Br 3P -70.0 -87.0 -17.0 -85.7 -15.7 -114.4 -44.4 -98.1 -28.1 -107.1 -37.1 -130.4 -60.4 -92.7 -22.7 - Br 4P -99.7 -106.2 -6.5 -107.9 -8.2 -147.4 -47.7 -111.3 -11.6 -138.6 -38.9 -170.9 -71.2 -118.2 -18.5 Br 3PO -97.0 -57.4 39.6 -82.5 14.5 -28.6 68.4 -29.0 68.0 -79.8 17.2 -91.2 5.8 -93.9 3.1

Br 2S -3.0 -1.0 2.0 11.1 14.1 -0.2 2.8 -6.8 -3.8 24.4 27.4 -3.1 -0.1 -3.0 0.0

Br 2S2 7.4 -8.1 -15.5 10.7 3.3 1.5 -5.9 -4.4 -11.8 21.8 14.4 -5.1 -12.5 -1.2 -8.6 - SO 2Br -141.1 -141.1 0.0 -127.8 13.3 -74.2 66.9 -122.0 19.2 -137.5 3.6 -252.3 -111.2 -131.2 9.9 ZnBr 29.0 30.9 1.9 23.9 -5.1 10.6 -18.4 -12.8 -41.8 6.8 -22.3 -1.0 -30.0 -17.3 -46.3

ZnBr 2 -44.4 5.0 49.4 -35.7 8.7 2.7 47.1 -63.1 -18.7 -21.2 23.2 -35.1 9.3 -32.5 11.9 AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 Most positive error 68.4 26.2 361.2 185.9 107.3 41.9 58.7 Most negative error -26.0 -15.7 -47.7 -41.8 -38.9 -111.2 -46.3 MSE 1.7 1.7 21.4 7.5 3.8 -3.0 0.9 MUE 5.9 5.3 28.5 14.8 9.8 8.1 6.4 RMSD 12.5 7.7 70.0 34.1 17.1 18.8 11.2 Compounds Containing Ti, Cu, Zr and Mo. TiBr 51.0 1.5 -49.5 -1.0 -52.0 12.7 -38.3

TiBr 2 -30.0 -66.9 -36.9 -53.6 -23.6 -34.9 -4.9

TiBr 3 -90.0 -90.0 0.0 -95.7 -5.7 -88.8 1.2 TiBr 4 -132.0 -99.3 32.7 -130.5 1.5 -130.1 1.9 CuBr 41.3 34.3 -7.0 32.5 -8.8 16.0 -8.8

CuBr 2 22.4 34.1 11.7 -10.5 -32.9 29.1 6.7 CuOBr 15.7 22.5 6.8 47.8 32.1 66.0 50.3 ZrBr 80.0 32.3 -47.7 55.8 -24.2 64.3 -15.7

ZrBr 2 -7.5 -14.5 -7.0 -38.4 -30.9 -27.4 -19.9

ZrBr 3 -80.0 -79.4 0.6 -102.8 -22.8 -97.8 -17.8

ZrBr 4 -142.0 -113.8 28.2 -171.7 -29.7 -132.4 9.6 MoBr 109.3 139.1 29.8 185.2 75.9 126.3 17.0

MoBr 2 40.0 37.5 -2.5 109.0 69.0 68.4 28.4

MoBr 3 -2.0 0.5 2.5 -10.6 -8.6 15.9 17.9

MoBr 4 -40.9 -42.4 -1.5 -37.2 3.7 -44.8 -3.9

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* PM5 PM6 Most positive error 32.7 75.9 50.3 Most negative error -49.5 -52.0 -38.3 MSE -2.7 -3.8 1.6 MUE 17.6 28.1 16.1 RMSD 24.7 35.6 21.0

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.6.1.1.2 Ionization Potentials and Dipole Moments of Bromine Compounds

Table 4.34 shows a comparison of the calculated and experimental ionization potentials and dipole moments. AM1* underestimates ionization potentials of the test set of bromine compounds by about -0.07 eV. The AM1* MUE is only slightly worse than MNDO/d and AM1 and better than MNDO or PM3. In this respect, PM5 and PM6 perform by far the best of the methods investigated. We note, however, that all the large AM1* errors (-1.03, -1.55 and -1.58 eV for BrF, BrF 3 and CBrF 2-CBrF 2, respectively) are given by fluorine-containing compounds, so that they may be an indirect result of the original AM1 parameterization for fluorine.

Both AM1* and MNDO/d tend to overestimate dipole moments for the bromine compounds in the training set slightly (by 0.1-0.2 Debye). The mean unsigned errors vary over a relatively small range from 0.24 (MNDO/d) to 0.52 (PM5). The AM1* value of 0.35 Debye lies in the middle of this range. AM1* seriously overestimates the dipole moment of SiH 3Br and BrF 3.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.34: Calculated AM1*, MNDO/d, MNDO, AM1, PM3, PM5 and PM6 Koopmans’ theorem ionization potentials and dipole moments for bromine-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0.

AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 Compound Target Error Error Error Error Error Error Error Koopmans' Theorem Ionization Potentials for Bromine Compounds (eV)

Br 2 10.56 10.91 0.35 10.33 -0.23 11.66 1.10 10.94 0.38 11.24 0.68 10.80 0.24 10.71 0.15 BrH 11.71 10.89 -0.82 10.58 -1.13 12.10 0.39 11.46 -0.25 12.13 0.42 11.31 -0.40 11.14 -0.57

CH 3Br 10.54 10.43 -0.11 10.30 -0.24 11.56 1.02 10.80 0.26 11.01 0.47 10.51 -0.03 10.62 0.08

CH 2Br 2 10.61 10.77 0.16 10.48 -0.13 11.70 1.09 10.96 0.35 10.59 -0.02 10.59 -0.02 10.60 -0.01 CHBr 3 10.47 11.10 0.63 10.61 0.14 11.87 1.40 11.07 0.60 10.84 0.37 10.67 0.20 10.75 0.28 CBr 4 10.40 11.38 0.98 10.74 0.34 12.03 1.63 11.22 0.82 11.22 0.82 10.72 0.32 10.93 0.53

C2H5Br 10.28 10.33 0.05 10.24 -0.04 11.48 1.20 10.69 0.41 10.91 0.63 10.40 0.12 10.47 0.19 CHBr=CH 2 9.80 10.10 0.30 9.69 -0.11 10.25 0.45 10.15 0.35 10.44 0.64 10.06 0.26 10.22 0.42 1-C3H7Br 10.18 10.33 0.15 10.23 0.05 11.46 1.28 10.65 0.47 10.85 0.67 10.40 0.22 10.48 0.30

1-C4H9Br 10.15 10.33 0.18 10.23 0.08 11.47 1.32 10.69 0.54 10.92 0.77 10.40 0.25 10.48 0.33 C6H5Br 9.25 9.68 0.43 9.28 0.03 9.55 0.30 9.60 0.35 9.81 0.56 9.45 0.20 9.65 0.40 BrCN 11.88 11.40 -0.48 10.85 -1.03 12.40 0.52 11.92 0.04 11.72 -0.16 11.41 -0.47 11.74 -0.14

O=CBr 2 11.00 11.18 0.18 10.88 -0.12 11.89 0.89 11.31 0.31 10.95 -0.05 11.21 0.21 10.92 -0.08 CH 3COBr 10.55 10.72 0.17 10.66 0.11 11.43 0.88 11.18 0.63 11.20 0.65 11.05 0.50 10.88 0.33 BrF 11.87 10.84 -1.03 10.80 -1.07 12.65 0.78 11.77 -0.10 11.64 -0.23 11.56 -0.31 11.53 -0.34

BrF 3 12.38 10.83 -1.55 11.45 -0.93 13.89 1.51 12.51 0.13 12.46 0.08 12.37 -0.01 12.10 -0.28 CBrF 3 12.10 11.52 -0.58 11.56 -0.54 13.25 1.15 12.33 0.23 12.23 0.13 12.26 0.16 12.00 -0.10 CBrF 2-CBrF 2 12.76 11.18 -1.58 11.42 -1.34 12.77 0.01 11.49 -1.27 11.03 -1.73 11.71 -1.05 11.55 -1.21

AlBr 3 10.91 11.59 0.68 10.85 -0.06 12.04 1.13 11.50 0.59 14.31 3.40 11.11 0.20 10.92 0.01 Br 2H2Si 10.92 10.92 0.00 11.21 0.29 11.75 0.83 11.11 0.19 11.45 0.53 10.50 -0.42 10.65 -0.28 Br 3PO 11.08 11.92 0.84 11.57 0.49 12.18 1.10 12.09 1.01 12.70 1.62 11.91 0.83 11.46 0.38 BrCl 11.10 10.76 -0.34 10.51 -0.59 12.01 0.91 11.22 0.12 10.92 -0.18 10.87 -0.23 10.82 -0.28

ZnBr 2 11.06 10.90 -0.16 10.48 -0.58 11.76 0.70 11.36 0.30 12.62 1.56 11.17 0.11 11.07 0.01 MSE -0.07 -0.29 0.94 0.28 0.51 0.04 0.01 MUE 0.51 0.42 0.94 0.42 0.71 0.29 0.29 Dipole Moments for Bromine Containing Compounds (Debye) BrH 0.83 0.95 0.12 1.16 0.33 1.07 0.24 1.38 0.55 1.27 0.44 1.32 0.49 1.16 0.33

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

CH 3Br 1.82 1.61 -0.21 1.87 0.05 1.56 -0.26 1.47 -0.35 1.55 -0.27 1.80 -0.02 1.58 -0.24

CH 2Br 2 1.43 1.34 -0.09 1.60 0.17 1.37 -0.06 1.32 -0.11 1.45 0.02 1.48 0.05 1.42 -0.01 CHBr 3 0.99 0.89 -0.10 1.06 0.07 0.91 -0.08 0.91 -0.08 0.96 -0.03 0.94 -0.05 1.00 0.01 C2H5Br 2.03 1.94 -0.09 1.98 -0.05 1.66 -0.37 1.66 -0.37 1.85 -0.18 2.20 0.17 2.09 0.06

CHBr=CH 2 1.42 1.67 0.25 1.62 0.20 1.31 -0.11 1.30 -0.12 1.33 -0.09 1.58 0.16 1.51 0.09 1-C3H7Br 2.18 1.99 -0.19 1.97 -0.21 1.64 -0.54 1.65 -0.53 1.80 -0.38 2.19 0.01 2.14 -0.04 2-C3H7Br 2.21 2.18 -0.03 2.07 -0.14 1.72 -0.49 1.79 -0.42 2.05 -0.16 2.49 0.28 2.62 0.41

1-C4H9Br 2.10 2.02 -0.08 2.06 -0.04 1.73 -0.37 1.72 -0.38 1.82 -0.28 2.21 0.11 2.14 0.04 1-C5H11 Br 2.13 2.05 -0.08 2.08 -0.05 1.75 -0.38 1.74 -0.39 1.84 -0.29 2.24 0.11 2.20 0.07 C6H5Br 1.70 1.87 0.17 1.70 0.00 1.80 0.10 1.41 -0.29 1.45 -0.25 1.50 -0.20 1.78 0.08 BrNO 1.80 2.43 0.63 1.19 -0.61 1.19 -0.61 0.95 -0.85 0.87 -0.93 1.26 -0.54 2.39 0.59 BrO 1.55 1.22 -0.33 1.52 -0.03 1.19 -0.36 2.36 0.81 2.08 0.53 2.78 1.23 1.95 0.40

CH 3COBr 2.43 3.00 0.57 2.57 0.14 2.45 0.02 2.59 0.16 2.95 0.52 3.34 0.91 3.38 0.95 BrF 1.42 1.35 -0.07 1.50 0.08 2.10 0.68 1.46 0.04 2.25 0.83 2.54 1.12 0.80 -0.62

BrF 3 1.19 2.32 1.13 2.78 1.59 0.00 -1.19 2.53 1.34 0.00 -1.19 0.00 -1.19 0.02 -1.17 BrHCF 2 1.31 1.71 0.40 1.85 0.54 1.74 0.43 1.55 0.24 1.57 0.26 2.19 0.88 1.56 0.25

CBr 2F2 0.66 0.45 -0.21 0.77 0.11 0.83 0.17 0.60 -0.06 0.54 -0.12 1.42 0.76 0.63 -0.03 CBrF 3 0.63 0.63 0.00 0.96 0.33 1.18 0.55 1.02 0.39 0.91 0.28 1.50 0.87 0.99 0.36 BrH 3Si 1.32 3.62 2.30 1.56 0.24 3.45 2.13 1.81 0.49 2.26 0.94 2.62 1.30 1.62 0.30 BrCl 0.52 0.86 0.34 0.43 -0.09 0.75 0.23 0.45 -0.07 0.06 -0.46 0.89 0.37 0.60 0.08 MSE 0.21 0.13 -0.01 0.00 -0.04 0.32 0.09 MUE 0.35 0.24 0.45 0.38 0.40 0.52 0.29

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.6.1.1.3 Geometries of Bromine Compounds

Table 4.35 shows the performance of the different methods in reproducing the geometries (bond lengths and angles) of bromine-containing compounds. MNDO and PM3 underestimate bond lengths to bromine systematically, as does AM1*. The AM1* mean signed error is, however, only -0.02 Å. MNDO/d and PM6 give the smallest mean unsigned errors for bond lengths (0.03 and 0.04 Å, respectively) and PM3 the largest (0.08 Å). The other four methods, including AM1*, give mean unsigned errors of 0.05-0.06 Å.

PM3 systematically underestimates bond angles to bromine (by -2.5°), as does AM1* (but only by -1.0°). The other methods all systematically overestimate these angles with mean signed errors between 1.0° (MNDO/d) and 3.0° (MNDO). MNDO/d gives the lowest mean unsigned error (1.8°) followed by AM1* and AM1 (2.6°). PM3 gives by far the largest mean unsigned error (8.5°).

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Table 4.35: Calculated AM1*, MNDO/d, MNDO, AM1, PM3, PM5 and PM6 bond lengths and angles for bromine-containing compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 Compound Variable Target Error Error Error Error Error Error Error BrH Br-H 1.42 1.42 0.00 1.44 0.03 1.44 0.02 1.42 0.01 1.47 0.05 1.38 -0.04 1.45 0.03

CH 3Br Br-C 1.93 1.91 -0.02 1.92 -0.02 1.88 -0.06 1.90 -0.03 1.95 0.02 2.50 0.56 1.95 0.01 CH 2Br 2 Br-C 1.93 1.90 -0.03 1.92 -0.01 1.87 -0.06 1.90 -0.02 1.91 -0.01 1.92 -0.01 1.94 0.01 Br-C-Br 112.9 109.4 -3.5 113.1 0.2 111.7 -1.2 113.7 0.8 94.4 -18.5 109 -3.9 111.5 -1.4 Br-C-H 109.0 108.0 -1.0 108.4 -0.6 108.6 -0.4 108.2 -0.8 112.5 3.5 108.6 -0.4 108.8 -0.2

CHBr 3 Br-C 1.92 1.90 -0.03 1.92 0.00 1.86 -0.06 1.91 -0.02 1.87 -0.05 1.91 -0.02 1.93 0.01 Br-C-Br 111.7 109.7 -2.0 111.4 -0.3 110.7 -1.0 111.7 0.0 98.4 -13.3 109.3 -2.4 110.7 -1.0

CBr 4 Br-C 1.93 1.90 -0.03 1.93 0.00 1.86 -0.07 1.92 -0.01 1.84 -0.09 1.90 -0.03 1.94 0.01 CBrCl 3 Br-C 1.93 1.97 0.04 1.95 0.02 1.87 -0.05 1.96 0.03 1.91 -0.01 1.93 0.00 1.96 0.03 Br-C-Cl 109.2 110.7 1.5 110.3 1.1 109.6 0.4 109.3 0.1 105.3 -3.9 108.6 -0.6 110.6 1.4

CBrF 3 Br-C 1.92 1.95 0.03 1.95 0.03 1.94 0.01 2.04 0.12 1.96 0.04 1.99 0.06 1.98 0.06 C2H5Br Br-C 1.95 1.93 -0.02 1.93 -0.02 1.89 -0.06 1.93 -0.02 1.96 0.01 1.96 0.01 1.98 0.03 Br-C-C 111.0 110.6 -0.4 112.5 1.5 112.7 1.7 113.5 2.5 104.4 -6.6 108 -3.0 111.2 0.2

CH 2Br-CH 2Br Br-C 1.95 1.93 -0.02 1.93 -0.02 1.89 -0.06 1.93 -0.02 1.96 0.01 1.96 0.01 1.97 0.02 Br-C-C 109.5 109.0 -0.5 111.0 1.5 111.2 1.7 112.0 2.5 103.9 -5.6 105.8 -3.7 109.4 -0.1

CH 2=CHBr Br-C 1.88 1.88 0.00 1.87 -0.02 1.83 -0.05 1.86 -0.02 1.90 0.01 1.90 0.02 1.91 0.03 Br-C=C 122.8 121.4 -1.4 123.3 0.5 123.8 1.0 125.1 2.3 116.2 -6.6 119.7 -3.1 122.4 -0.4

1-C3H7Br Br-C 1.97 1.93 -0.04 1.93 -0.04 1.89 -0.08 1.93 -0.04 1.96 -0.01 1.96 0.01 1.97 0.00 Br-C-C 111.0 110.4 -0.6 113.4 2.4 113.8 2.8 114.5 3.5 105.2 -5.8 107.7 -3.3 110.8 -0.2

2-C3H7Br Br-C 1.96 1.95 -0.01 1.94 -0.02 1.90 -0.05 1.95 0.00 1.96 0.01 1.98 0.02 2.01 0.06 Br-C-C 111.0 108.3 -2.7 109.5 -1.5 109.4 -1.6 111.0 0.0 103.9 -7.1 106.3 -4.7 108.5 -2.5

1,3-C3H6Br 2 Br-C 1.96 1.93 -0.03 1.93 -0.03 1.89 -0.07 1.93 -0.03 1.96 0.00 1.95 -0.01 1.97 0.01 Br-C-C 112.0 110.0 -2.0 113.3 1.3 113.6 1.6 114.3 2.3 105.1 -6.9 107.4 -4.6 110.5 -1.5

(CH 3)HC=CHBr trans Br-C 1.88 1.93 0.04 1.86 -0.02 1.83 -0.05 1.86 -0.03 1.89 0.01 1.96 0.08 1.97 0.08 Br-C=C 122.1 114.3 -7.8 126.0 3.9 126.7 4.6 127.3 5.2 119.7 -2.4 112.6 -9.5 115.3 -6.8

(CH 2Br)HC=CH 2 Br-C 1.96 1.93 -0.03 1.93 -0.03 1.90 -0.07 1.93 -0.03 1.96 0.00 1.96 0.00 1.97 0.01 Br-C-C 111.5 114.2 2.7 110.5 -1.0 111.0 -0.5 112.0 0.5 104.0 -7.5 112.7 1.2 115.2 3.7

1-C4H9Br Br-C 1.95 1.93 -0.02 1.93 -0.02 1.89 -0.06 1.93 -0.02 1.96 0.01 1.96 0.01 1.97 0.02 Br-C-C 111.0 110.3 -0.7 111.8 0.8 112.0 1.0 113.3 2.3 104.2 -6.8 107.5 -3.5 110.8 -0.2

(CH 3)3CBr Br-C 1.98 1.97 -0.01 1.96 -0.02 1.92 -0.05 1.98 0.00 1.96 -0.01 2.00 0.02 2.05 0.07

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

C6H5Br Br-C 1.85 1.88 0.03 1.86 0.01 1.83 -0.02 1.87 0.02 1.87 0.02 1.88 0.03 1.92 0.06 O=CBr 2 Br-C 1.92 1.89 -0.03 1.90 -0.02 1.85 -0.06 1.92 0.00 1.90 -0.02 1.90 -0.02 1.94 0.02 Br-C-Br 112.3 112.7 0.4 115.6 3.3 111.2 -1.1 110.6 -1.7 97.4 -14.9 125.9 13.6 109.9 -2.4

CH 3COBr Br-C 1.97 1.93 -0.04 1.92 -0.05 1.89 -0.09 1.95 -0.03 1.97 -0.01 1.96 -0.02 2.00 0.03 Br-C=O 121.9 116.3 -5.6 118.2 -3.7 119.8 -2.1 122.5 0.6 119.3 -2.6 119.6 -2.3 120.6 -1.3 Br-C-C 111.0 113.1 2.1 114.3 3.3 112.9 1.9 113.3 2.3 106.3 -4.7 108.1 -2.9 110.8 -0.2 BrCN Br-C 1.79 1.81 0.02 1.78 -0.01 1.74 -0.05 1.76 -0.03 1.80 0.01 1.78 -0.01 1.77 -0.02 BrNO Br-N 2.14 2.07 -0.07 1.91 -0.23 1.87 -0.27 1.92 -0.22 1.89 -0.25 1.92 -0.22 2.05 -0.09 Br-N=O 114.5 113.2 -1.3 117.5 3.0 118.9 4.4 122.5 8.0 120.8 6.3 120.3 5.8 119.9 5.4 BrO Br-O 1.72 1.85 0.13 1.69 -0.02 1.70 -0.02 1.79 0.08 1.76 0.04 1.71 -0.01 1.79 0.07 BrF Br-F 1.76 1.72 -0.03 1.76 0.00 1.73 -0.03 1.78 0.02 1.77 0.02 1.76 0.00 1.77 0.01

BrF 3 Br-Fax 1.73 1.73 0.00 1.77 0.04 1.76 0.03 1.81 0.08 1.79 0.06 1.74 0.01 1.77 0.04 Br-Feq 1.81 1.76 -0.05 1.82 0.02 1.76 -0.05 1.82 0.01 1.79 -0.02 1.74 -0.07 1.77 -0.04 Fax -Br-Feq 85.0 83.1 -2.0 83.3 -1.7 120.0 35.0 81.4 -3.6 120.0 35.0 120 35.0 120.6 35.6

BrF 5 Br-Fax 1.70 1.72 0.02 1.78 0.09 1.77 0.07 1.82 0.13 1.76 0.06 1.69 -0.01 1.78 0.08 Br-Feq 1.77 1.74 -0.03 1.81 0.04 1.77 0.00 1.80 0.03 1.77 0.01 1.70 -0.06 1.76 -0.01 Fax -Br-Feq 84.8 84.8 0.00 83.6 -1.2 104.7 19.9 85.2 0.4 103.6 18.8 103 18.2 88.7 3.9

BrFO 3 Br-F 1.71 1.71 0.00 1.77 0.06 1.78 0.08 1.81 0.10 1.78 0.08 1.71 0.00 1.70 -0.01 Br=O 1.58 1.83 0.25 1.62 0.04 1.79 0.21 1.87 0.29 1.78 0.19 1.72 0.14 1.49 -0.09 F-Br=O 103.3 98.9 -4.4 102.5 -0.8 105.7 2.4 98.5 -4.8 108.2 4.9 102.1 -1.2 100.1 -3.2 O=Br=O 114.9 107.3 -7.6 115.5 0.6 113.0 -1.9 117.8 2.9 110.7 -4.2 114.1 -0.8 105.5 -9.4 BrCl Br-Cl 2.14 1.97 -0.17 2.11 -0.02 2.08 -0.06 2.06 -0.07 2.18 0.04 2.11 -0.02 2.18 0.04

Br 2 Br-Br 2.28 2.28 0.00 2.27 -0.01 2.17 -0.11 2.18 -0.10 2.44 0.16 2.24 -0.04 2.33 0.05 AlBr Br-Al 2.30 2.08 -0.22 2.27 -0.03 2.20 -0.09 2.26 -0.03 2.29 0.00 2.22 -0.07 2.29 0.00

Al 2Br 6 Br-Al 2.22 2.08 -0.14 2.23 0.01 2.18 -0.04 2.27 0.04 1.84 -0.38 2.18 -0.04 2.23 0.01 Br-Al (2) 2.38 2.24 -0.14 2.49 0.11 2.39 0.01 2.40 0.02 2.46 0.08 2.39 0.00 2.44 0.06 Br-Al-Br 118.0 126.0 8.0 123.1 5.1 122.1 4.1 119.4 1.4 104.2 -13.8 122.1 4.1 124.2 6.2 BrSi Br-Si 2.25 2.25 0.00 2.21 -0.04 2.20 -0.06 2.17 -0.08 1.85 -0.40 2.02 -0.23 2.26 0.01

Br 2Si Br-Si 2.24 2.24 0.00 2.24 -0.01 2.21 -0.03 2.20 -0.05 1.86 -0.39 2.23 -0.01 2.10 -0.14 Br 4Si Br-Si 2.18 2.26 0.07 2.22 0.04 2.19 0.01 2.24 0.06 1.80 -0.39 2.22 0.04 2.17 -0.01 BrH 3Si Br-Si 2.21 2.30 0.09 2.24 0.03 2.23 0.02 2.24 0.03 1.90 -0.31 2.27 0.06 2.23 0.02 Br-Si-H 108.2 104.9 -3.3 108.3 0.1 106.9 -1.3 110.4 2.2 108.3 0.1 106.1 -2.1 108.9 0.7

Br 3P Br-P 2.22 1.96 -0.26 2.18 -0.04 2.09 -0.13 2.10 -0.12 2.09 -0.13 2.22 0.00 2.19 -0.03 Br-P-Br 101.0 107.7 6.7 105.3 4.3 105.7 4.7 106.8 5.8 87.1 -13.9 104.6 3.6 104.6 3.6

Br 3PO Br-P 2.17 1.99 -0.18 2.21 0.03 2.13 -0.05 2.16 -0.01 2.05 -0.12 2.21 0.04 2.18 0.01

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O=P 1.46 1.50 0.04 1.49 0.03 1.48 0.02 1.48 0.02 1.41 -0.05 1.36 -0.10 1.49 0.03 O=P-Br 114.2 113.1 -1.1 114.8 0.6 113.8 -0.4 115.2 1.0 125.5 11.3 115.2 1.0 114.5 0.3

Br 2S2 Br-S 2.24 2.22 -0.02 2.17 -0.07 2.07 -0.17 2.12 -0.13 2.25 0.01 2.17 -0.07 2.11 -0.13 Br 2SO Br-S 2.23 2.24 0.00 2.24 0.00 2.14 -0.09 2.21 -0.03 2.33 0.10 2.21 -0.03 2.17 -0.06 S=O 1.45 1.53 0.08 1.50 0.05 1.47 0.02 1.46 0.01 1.45 0.00 1.43 -0.02 1.44 -0.01 O=S-Br 107.6 108.9 1.3 108.5 0.9 108.0 0.4 111.0 3.4 103.4 -4.2 109.9 2.3 114.0 6.4 Br-S-Br 98.2 97.2 -1.0 101.2 3.0 103.6 5.4 103.8 5.6 99.7 1.5 107.5 9.3 100.2 2.0

ZnBr 2 Br-Zn 2.20 2.09 -0.11 2.17 -0.04 2.24 0.03 2.11 -0.09 2.10 -0.11 2.24 0.04 2.21 0.01 AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 MSE bond length -0.02 0.00 -0.04 0.00 -0.04 0.00 0.01 MUE bond length 0.06 0.03 0.06 0.05 0.08 0.05 0.04 MSE bond angle -1.0 1.0 3.0 1.7 -2.5 1.6 1.4 MUE bond angle 2.6 1.8 3.9 2.5 8.5 5.4 3.7 Compounds Containing Ti, Cu, Zr and Mo. TiBr Br-Ti 2.35 2.21 -0.14 2.33 -0.02 2.35 0.00 CuBr Br-Cu 2.29 2.27 -0.01 2.13 -0.16 2.13 -0.16 ZrBr Br-Zr 2.55 2.42 -0.13 2.67 0.12 2.39 -0.16 MoBr Br-Mo 2.45 2.45 0.00 2.44 -0.01 2.47 0.02 AM1* PM5 PM6 MSE bond length -0.07 -0.02 -0.07 MUE bond length 0.07 0.08 0.08

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4.6.1.2 Iodine

4.6.1.2.1 Heats of Formation of Iodine Compounds

The results obtained for heats of formation of iodine compounds are shown in Table 4.36. Table 4.36 shows clearly that the three newest methods, AM1*, PM5 and PM6 give the best results. They perform very similarly with mean unsigned errors ranging from 8.7 to 10.2 kcal mol −1. PM5 and PM6 give slightly too negative heats of formation with mean signed errors of -3.8 and -3.9 kcal mol −1, respectively, whereas AM1* deviates slightly less (2.6 kcal mol −1) in −1 the opposite direction. Large AM1* errors are found for CI 4 (-15.8 kcal mol ), mononuclear −1 −1 aluminum iodides (49.8 kcal mol for AlI and 85.5 kcal mol for AlI 3), SiH 3I (21.5 kcal −1 − − −1 mol ) and zinc and bromine iodides (ZnI 2 103.8, Br 2I -25.7 and HBrI 12.3 kcal mol ). Quite generally, AM1* does not do well for poly-halogen compounds but otherwise its performance is acceptable.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.36: Calculated AM1*, MNDO/d, MNDO, AM1, PM3, PM5 and PM6 heats of formation and errors compared with our target values for the iodine compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol −1, yellow 10-20 kcal mol −1 and pink those greater than 20 kcal mol −1. AM1* MNDO/d MNDO AM1 PM3 PM5 PM6

Compound Target ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error ∆∆∆H° f Error I 25.5 25.5 0.0 25.5 0.0 25.5 0.0 25.5 0.0 25.5 0.0 25.5 0.0 25.5 0.0 I+ 266.6 256.3 -10.3 239.3 -27.3 271.8 5.2 267.7 1.0 238.0 -28.6 257.8 -8.8 258.2 -8.4 I- -44.9 -49.2 -4.3 -45.0 -0.1 -6.4 38.5 -2.2 42.7 -64.6 -19.7 -46.5 -1.6 -43.1 1.8

I2 14.9 7.6 -7.3 24.2 9.3 21.2 6.3 19.8 4.9 20.7 5.8 5.0 -9.9 16.6 1.7 IH 6.3 6.7 0.4 22.8 16.5 15.7 9.4 7.9 1.6 28.8 22.5 -2.2 -8.5 2.1 -4.2

CH 3I 3.5 8.9 5.4 4.6 1.1 1.9 -1.6 5.7 2.2 9.4 5.9 7.6 4.1 7.5 4.0 CH 2I2 28.0 24.1 -3.9 22.9 -5.1 16.8 -11.2 21.5 -6.5 33.5 5.5 27.1 -0.9 29.7 1.7 CHI 3 50.4 36.8 -13.6 41.6 -8.8 32.0 -18.4 37.8 -12.6 60.6 10.2 47.3 -3.1 54.3 3.9 CI 4 62.4 46.6 -15.8 60.7 -1.7 46.8 -15.6 54.2 -8.2 100.8 38.4 68.0 5.6 82.1 19.7 C2H5I -1.8 -1.8 0.0 -2.8 -1.0 -4.5 -2.7 -1.1 0.7 2.1 3.9 0.4 2.2 1.3 3.1 CH 2I-CH 2I 17.5 11.1 -6.4 15.1 -2.4 11.5 -6.0 15.7 -1.8 23.3 5.8 14.3 -3.2 18.3 0.8 CHI=CH 2 31.0 35.9 4.9 28.5 -2.5 24.5 -6.5 29.8 -1.2 35.2 4.2 31.6 0.6 31.6 0.6 CHI=CHI cis 49.6 52.4 2.8 43.6 -6.0 35.1 -14.5 43.5 -6.1 62.8 13.2 46.5 -3.1 49.2 -0.4 CHI=CHI trans 49.6 53.2 3.6 42.8 -6.8 35.2 -14.4 44.1 -5.5 55.0 5.4 47.4 -2.2 47.9 -1.7

1-C3H7I -7.2 -8.4 -1.2 -6.8 0.4 -8.8 -1.6 -7.2 0.0 -0.6 6.6 -5.0 2.2 -4.0 3.2 2-C3H7I -9.6 -10.5 -0.9 -7.1 2.5 -7.5 2.1 -5.7 3.9 -5.3 4.3 -7.3 2.3 -6.7 2.9 1,2-C3H6I2 8.5 4.6 -3.9 12.2 3.7 9.7 1.2 12.0 3.5 18.6 10.1 13.3 4.8 10.6 2.1 (CH 2I)HC=CH 2 21.9 22.2 0.3 20.8 -1.1 19.5 -2.4 22.4 0.5 27.2 5.3 23.8 1.9 22.9 1.0 (CH 3)HC=CHI (E) 22.3 26.3 4.0 18.7 -3.6 14.5 -7.8 19.7 -2.6 25.4 3.1 23.3 1.1 21.2 -1.1 (CH 3)HC=CHI (Z) 20.7 25.8 5.1 19.5 -1.2 15.3 -5.4 20.5 -0.2 29.2 8.5 23.4 2.7 21.2 0.5 1,2-C4H8I2 2.9 -5.2 -8.1 9.5 6.6 6.1 3.2 5.6 2.7 22.2 19.3 2.6 -0.3 7.3 4.4 C(CH 3)3I -17.2 -17.2 0.0 -7.7 9.5 -6.5 10.7 -8.3 8.9 -12.5 4.7 -15.2 2.0 -15.8 1.4 C6H5I 39.4 41.0 1.6 35.8 -3.6 32.5 -6.9 38.1 -1.3 44.7 5.3 40.3 0.9 40.0 0.6 cyclo-C6H11 I -11.9 -24.1 -12.2 -16.0 -4.1 -17.0 -5.1 -20.0 -8.1 -11.7 0.2 -19.6 -7.7 -13.7 -1.8 o-C6H4I2 60.2 58.1 -2.1 52.0 -8.2 44.8 -15.4 54.0 -6.2 73.8 13.6 56.5 -3.7 58.3 -1.9 C6H5-CH 2I 25.0 27.6 2.6 30.2 5.2 28.7 3.7 30.9 5.9 37.6 12.6 30.1 5.1 32.0 7.0 o-I-C6H4-CH 3 31.7 32.9 1.2 30.1 -1.6 27.0 -4.7 31.9 0.2 38.9 7.2 32.5 0.8 30.1 -1.6 m-I-C6H4-CH 3 31.9 33.4 1.5 28.1 -3.8 24.8 -7.1 30.5 -1.4 35.4 3.5 32.1 0.2 29.9 -2.0 p-I-C6H4-CH 3 28.9 33.5 4.6 28.0 -0.9 24.7 -4.2 30.4 1.5 35.4 6.5 32.1 3.2 29.8 0.9

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

1-I-naphthalene 55.9 59.1 3.2 55.1 -0.8 52.0 -3.9 58.5 2.6 66.0 10.1 56.7 0.8 56.8 0.9 2-I-naphthalene 56.2 59.4 3.2 52.9 -3.3 49.6 -6.6 56.8 0.6 61.9 5.7 55.8 -0.4 56.1 -0.1 IO 41.8 41.2 -0.6 39.7 -2.1 46.7 4.9 37.0 -4.8 31.0 -10.8 35.8 -6.0 41.1 -0.7

CH 3COI -30.2 -21.6 8.6 -26.6 3.6 -26.9 3.3 -20.7 9.5 -29.9 0.3 -27.9 2.3 -30.2 0.0 CH 3COCH 2I -31.2 -34.8 -3.6 -28.2 3.0 -30.5 0.7 -29.1 2.1 -26.3 4.9 -33.7 -2.5 -34.5 -3.3 C6H5-COI 2.5 11.4 8.9 5.8 3.3 5.1 2.6 14.1 11.6 8.0 5.5 5.0 2.5 6.5 4.0 p-I-C6H4-COOH -54.5 -49.6 4.9 -52.3 2.2 -55.6 -1.1 -50.9 3.6 -44.4 10.1 -49.7 4.8 -47.5 7.0 ICN 53.7 50.5 -3.2 49.0 -4.7 39.6 -14.1 42.6 -11.1 63.5 9.8 49.4 -4.3 54.0 0.3 INO 26.8 26.8 0.0 20.0 -6.8 20.9 -5.9 32.3 5.5 18.2 -8.6 25.9 -0.9 26.2 -0.6 IF -22.7 -27.3 -4.6 -28.4 -5.7 -9.3 13.4 -9.1 13.6 -8.0 14.7 -14.2 8.5 -32.7 -10.0

IF 5 -200.7 -205.1 -4.4 -198.3 2.4 97.9 298.6 67.0 267.7 -201.1 -0.4 -157.7 43.0 -207.9 -7.2 IF 7 -229.7 -229.6 0.1 -228.0 1.7 236.1 465.8 193.3 423.0 -12.2 217.5 -179.5 50.2 -222.4 7.3 CF 3I -140.5 -153.0 -12.5 -133.2 7.3 -128.2 12.3 -132.6 7.9 -137.9 2.6 -136.1 4.4 -141.1 -0.6 ICl 4.2 -11.9 -16.1 0.5 -3.7 -6.9 -11.1 -4.6 -8.8 10.8 6.6 -6.8 -11.0 3.0 -1.2 ICl - -51.4 -60.0 -8.6 0.5 51.9 -6.9 44.5 -4.6 46.8 10.8 62.2 -78.8 -27.4 -76.4 -25.0 - ICl 2 -94.0 -79.8 14.2 28.6 122.6 0.5 94.5 3.0 97.0 -55.7 38.3 -109.7 -15.7 -95.0 -1.0 - ICl 4 -150.8 -150.9 -0.1 62.0 212.8 -18.6 132.3 -16.3 134.5 -64.4 86.4 -128.3 22.6 -98.4 52.4 Cl-CH 2-CH 2-I -11.4 -9.7 1.7 -7.8 3.6 -12.4 -1.0 -9.0 2.4 -0.3 11.1 -8.8 2.6 -5.7 5.7 IAl 16.2 66.0 49.8 25.3 9.1 31.2 15.0 29.0 12.8 11.9 -4.3 25.5 9.3 18.4 2.2

AlI 3 -46.2 39.3 85.5 -47.3 -1.1 11.6 57.8 -29.7 16.5 -22.1 24.1 -38.2 8.0 -46.4 -0.2 Al 2I6 -117.0 -117.0 0.0 -126.0 -9.0 7.5 124.5 -107.9 9.1 -59.1 57.9 -118.9 -1.9 -119.2 -2.2 SiI 76.4 76.3 -0.1 71.3 -5.1 107.9 31.5 92.2 15.8 68.5 -7.9 67.3 -9.1 68.8 -7.6

SiI 2 22.0 20.9 -1.1 38.9 16.9 82.1 60.1 57.5 35.5 18.0 -4.0 19.3 -2.7 29.4 7.4 SiI 3 8.4 8.5 0.0 24.4 15.9 43.6 35.2 9.6 1.1 -50.3 -58.7 -8.9 -17.3 1.1 -7.3 SiI 4 -26.4 -35.6 -9.2 4.0 30.4 42.4 68.8 1.6 28.0 -14.2 12.2 -27.1 -0.7 -16.9 9.5 SiIH 3 -0.5 21.0 21.5 10.1 10.6 11.0 11.5 4.9 5.4 3.1 3.6 1.9 2.4 2.3 2.8 SiI 2H2 -9.1 8.9 18.0 10.5 19.6 23.0 32.1 5.0 14.1 -3.5 5.6 -6.7 2.4 -3.8 5.3 SiI 3H -17.8 -11.1 6.7 8.8 26.6 34.1 51.9 3.9 21.7 -9.0 8.8 -16.3 1.5 -10.6 7.2 IP 64.8 59.5 -5.3 59.6 -5.2 61.6 -3.2 56.2 -8.6 55.9 -9.0 42.0 -22.8 28.7 -36.1

I2P 57.5 34.8 -22.7 32.6 -24.9 34.9 -22.6 34.2 -23.3 -9.2 -66.7 12.1 -45.5 -16.0 -73.5 I3P 1.1 1.1 0.0 20.4 19.3 25.3 24.2 24.4 23.3 38.8 37.7 -13.4 -14.5 -57.3 -58.4 IOP -30.8 -20.1 10.7 -35.9 -5.1 -24.6 6.2 -15.7 15.1 -43.6 -12.8 -26.6 4.2 -49.0 -18.1 IS - 11.2 11.2 0.0 -21.0 -32.2 -10.0 -21.2 -19.8 -31.0 -25.6 -36.8 -43.5 -54.7 -39.7 -50.9

I2S 61.8 61.1 -0.7 24.2 -37.6 29.6 -32.3 21.7 -40.1 51.6 -10.2 12.2 -49.6 19.3 -42.5 C2H5SI 6.4 13.1 6.7 10.0 3.6 -1.7 -8.1 6.4 0.0 13.8 7.4 10.8 4.4 13.4 7.0

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ZnI 2 -15.6 88.2 103.8 0.2 15.8 42.7 58.3 4.7 20.3 15.7 31.3 -2.1 13.5 -15.9 -0.3 2- ZnI 4 -99.0 -99.0 -0.1 -183.5 -84.5 -2.6 96.4 -68.1 30.8 -152.0 -53.0 -119.8 -20.8 -112.0 -13.1 BrI 9.8 2.4 -7.4 12.4 2.6 7.2 -2.5 6.0 -3.8 15.7 5.9 -2.0 -11.8 9.6 -0.1 BrI - -49.0 -49.0 0.0 -53.9 -4.9 -53.2 -4.2 -43.1 5.9 -104.2 -55.2 -76.6 -27.6 -75.1 -26.1 - Br 2I -60.0 -85.7 -25.7 -72.4 -12.4 -84.9 -24.9 -70.9 -10.9 -84.5 -24.5 -120.0 -60.0 -104.1 -44.1 HBrI - -69.8 -57.6 12.3 -32.4 37.5 -39.9 29.9 -33.0 36.8 -43.4 26.5 -94.4 -24.6 -67.5 2.3 - CH 3BrI -62.5 -56.2 6.3 -51.6 10.9 -44.8 17.7 -34.1 28.4 -65.6 -3.1 -76.3 -13.8 -70.1 -7.6 AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 Most positive error 103.8 212.8 465.8 423.0 217.5 50.2 52.4 Most negative error -25.7 -84.5 -32.3 -40.1 -66.7 -60.0 -73.5 MSE 2.6 4.9 22.0 17.3 7.4 -3.8 -3.9 MUE 8.7 14.5 30.8 23.0 19.1 10.2 9.1 RMSD 18.8 33.6 74.1 64.4 35.5 17.4 17.8 Compounds Containing Ti, Cu, Zr and Mo. TiI 66.0 24.2 -41.8 11.0 -55.0 30.8 -35.2

TiI 2 -5.0 -1.9 3.1 -27.0 -22.0 0.8 5.8 TiI 3 -43.0 17.7 60.7 -42.7 0.3 -31.7 11.3 TiI 4 -66.0 -3.1 63.0 -62.4 3.6 -49.0 17.0 CuI 43.5 43.2 -0.3 44.1 0.6 25.7 -17.8

CuI 2 32.0 53.9 21.9 -1.9 -33.9 13.9 -18.1 ZrI 92.0 37.5 -54.5 65.6 -26.4 76.0 -16.0

ZrI 2 21.0 20.4 -0.6 -15.8 -36.8 -4.0 -25.0 ZrI 3 -35.0 19.7 54.7 -49.7 -14.7 -55.3 -20.3 ZrI 4 -87.0 26.4 113.4 -95.8 -8.8 -86.4 0.6 MoI 119.2 157.5 38.3 187.5 68.3 135.4 16.2

MoI 2 61.6 101.6 40.0 131.4 69.8 97.2 35.6 MoI 3 43.7 44.9 1.2 46.2 2.5 38.2 -5.5 MoI 4 29.8 26.6 -3.2 30.7 0.9 19.3 -10.5 AM1* PM5 PM6 Most positive error 113.4 69.8 35.6 Most negative error -54.5 -55.0 -35.2 MSE 21.1 -3.7 -4.4 MUE 35.5 24.5 16.8 RMSD 47.7 34.4 19.4

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4.6.1.2.2 Ionization Potentials and Dipole Moments of Iodine Compounds

Table 4.37 shows a comparison of the calculated and experimental ionization potentials and dipole moments for the training compounds containing iodine.

MNDO and AM1 significantly and systematically overestimate ionization potentials, but once again the performance of the other methods is comparable. MNDO/d (MUE = 0.24 eV) and PM3 (MUE = 0.30 eV) perform best, although PM3 tends to overestimate the ionization potentials (MSE = 0.14 eV). The three newer methods give comparable mean unsigned errors (0.42, 0.45 and 0.44 eV for PM5, PM6 and AM1*, respectively), although PM5 and PM6 systematically give values that are too high (MUE ≈ 0.4 eV) and AM1* ones that are too low (MUE = -0.21 eV).

AM1* performs very poorly for dipole moments, although the errors are concentrated on compounds containing several halogen atoms and on HI. The dipole moments for these compounds are all seriously overestimated, giving an MUE for AM1* of 1.98 Debye, far larger than any of the other techniques. AM1* cannot, therefore, be recommended for calculating dipole moments of iodine compounds and the molecular electrostatic potential should also be treated with caution, although AM1* usually performs very well in this respect [153].

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Table 4.37: Calculated AM1*, MNDO/d, MNDO, AM1, PM3, PM5 and PM6 Koopmans’ theorem ionization potentials and dipole moments for iodine-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 Compound Target Error Error Error Error Error Error Error Koopmans' Theorem Ionization Potentials for Iodine Compounds (eV) IH 10.39 9.42 -0.97 9.56 -0.83 11.21 0.82 10.91 0.52 9.97 -0.42 10.39 0.00 10.19 -0.21

CH 3I 9.54 9.29 -0.25 9.38 -0.16 10.85 1.31 10.51 0.97 9.47 -0.07 9.83 0.29 9.88 0.34 CH 2I2 9.46 9.09 -0.37 9.44 -0.02 10.87 1.41 10.56 1.10 8.98 -0.48 9.40 -0.06 9.75 0.29 C2H5I 9.34 9.27 -0.07 9.34 0.00 10.81 1.47 10.43 1.09 9.44 0.10 9.72 0.38 9.72 0.38 CH 2I-CH 2I 9.50 8.67 -0.83 9.59 0.09 11.02 1.52 10.71 1.21 9.66 0.16 9.88 0.38 10.05 0.55 1-C3H7I 9.27 9.28 0.01 9.33 0.06 10.80 1.53 10.39 1.12 9.42 0.15 9.74 0.47 9.74 0.47 2-C3H7I 9.40 9.26 -0.14 9.30 -0.10 10.79 1.39 10.40 1.00 9.43 0.03 9.63 0.23 9.57 0.17 C6H5I 8.78 9.03 0.25 8.89 0.11 9.55 0.77 9.65 0.87 9.04 0.26 9.30 0.52 9.41 0.63 cyclo-C6H11 I 8.91 9.26 0.35 9.28 0.37 10.77 1.86 10.38 1.47 9.42 0.51 9.64 0.73 9.59 0.68 C6H5-CH 2I 8.91 8.70 -0.21 9.20 0.29 9.46 0.55 9.51 0.60 9.35 0.44 9.10 0.19 9.32 0.41 o-I-C6H4-CH 3 8.53 8.96 0.43 8.90 0.37 9.51 0.98 9.52 0.99 9.02 0.49 9.21 0.68 9.29 0.76 m-I-C6H4-CH 3 8.55 8.95 0.40 8.89 0.34 9.51 0.96 9.52 0.97 9.01 0.46 9.19 0.64 9.32 0.77 p-I-C6H4-CH 3 8.38 8.87 0.49 8.87 0.49 9.45 1.07 9.41 1.03 8.94 0.56 9.08 0.70 9.17 0.79 CF 3I 10.45 10.24 -0.21 10.40 -0.05 12.48 2.03 11.97 1.52 10.28 -0.17 11.35 0.90 11.01 0.56 AlI 3 9.66 8.17 -1.49 9.88 0.22 10.98 1.32 10.94 1.28 9.91 0.25 9.97 0.31 9.95 0.29 ICl 10.10 9.75 -0.35 9.70 -0.40 11.58 1.48 11.12 1.02 9.74 -0.36 10.34 0.24 10.26 0.16

ZnI 2 9.73 8.40 -1.33 9.45 -0.28 10.62 0.89 10.49 0.76 10.26 0.53 10.03 0.30 10.16 0.43 BrI 9.85 10.02 0.17 9.75 -0.10 11.28 1.43 10.84 0.99 9.84 -0.01 10.28 0.43 10.18 0.33

I2 9.34 9.46 0.12 9.57 0.23 10.87 1.53 10.67 1.33 9.53 0.19 9.87 0.53 9.73 0.39 MSE -0.21 0.03 1.28 1.04 0.14 0.41 0.43 MUE 0.44 0.24 1.28 1.04 0.30 0.42 0.45 Dipole Moments for Iodine Containing Compounds (Debye) IH 0.45 1.83 1.38 0.93 0.48 1.01 0.56 1.27 0.82 0.97 0.52 0.43 -0.02 1.08 0.63

CH 3I 1.65 1.63 -0.02 1.80 0.15 1.37 -0.28 1.35 -0.30 1.44 -0.21 1.17 -0.48 1.22 -0.44 CH 2I2 1.62 1.88 0.26 1.41 -0.21 1.15 -0.47 1.12 -0.50 1.20 -0.42 0.74 -0.88 0.97 -0.65 C2H5I 1.91 1.49 -0.42 1.92 0.01 1.42 -0.49 1.50 -0.41 1.83 -0.08 1.68 -0.23 1.88 -0.03 1-C3H7I 2.04 1.51 -0.53 1.92 -0.12 1.42 -0.62 1.51 -0.53 1.81 -0.23 1.64 -0.41 1.89 -0.15 C6H5I 1.70 2.51 0.81 1.79 0.09 1.60 -0.10 1.43 -0.27 0.79 -0.91 0.94 -0.76 1.63 -0.07 IF 1.95 4.16 2.21 2.29 0.34 2.18 0.23 1.65 -0.30 2.59 0.64 3.87 1.92 1.93 -0.02

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CF 3I 1.04 5.89 4.85 1.85 0.81 2.14 1.10 1.67 0.63 1.55 0.51 3.09 2.05 1.50 0.46 ICl 1.24 5.51 4.27 1.26 0.02 1.34 0.10 0.95 -0.29 0.48 -0.76 2.25 1.01 1.20 -0.04 BrI 0.74 5.82 5.08 0.91 0.17 0.72 -0.02 0.63 -0.11 0.53 -0.21 1.50 0.76 0.72 -0.02 MSE 1.79 0.17 0.00 -0.13 -0.12 0.30 -0.03 MUE 1.98 0.24 0.40 0.42 0.45 0.85 0.25

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4.6.1.2.3 Geometries of Iodine Compounds

Table 4.38 shows the calculated bond lengths and angles to iodine for the training compounds using the different methods.

The mean unsigned errors for calculated bond lengths range from 0.07 Å (PM6) to 0.18 Å (MNDO). AM1* performs relatively well, with an MUE of 0.08 Å. In contrast to all the other methods, AM1* systematically overestimates bond lengths to iodine (MSE = 0.05 Å). Surprisingly, the newer methods PM5, PM6 and AM1* perform significantly worse for bond angles (MUEs of 3.6, 3.8 and 6.8° for AM1*, PM6 and PM5, respectively) than the older ones (MUEs of 1.1, 2.8 and 2.9° for MNDO/d, AM1 and MNDO, respectively). The exception is PM3, which has an MUE of 6.5°, almost as large as PM5. AM1* performs differently to PM6 in that the latter systematically overestimates bond angles to iodine (the MSE is 3.2°, compared with the MUE of 3.8°), whereas AM1* shows almost no strong systematic trend (MSE = -1.0°).

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.38: Calculated AM1*, MNDO/d, MNDO, AM1, PM3, PM5 and PM6 bond lengths and angles for iodine-containing compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 Compound Variable Target Error Error Error Error Error Error Error IH I-H 1.61 1.61 0.00 1.59 -0.01 1.57 -0.04 1.59 -0.02 1.68 0.07 1.21 -0.40 1.64 0.03

CH 3I I-C 2.14 2.16 0.02 2.08 -0.05 2.02 -0.12 2.05 -0.09 2.03 -0.11 2.16 0.02 2.13 -0.01 I-C-H 107.5 105.4 -2.1 109.0 1.5 110.5 3.0 109.2 1.7 109.1 1.6 106.7 -0.8 109.2 1.7

CHI 3 I-C 2.12 2.13 0.01 2.08 -0.04 2.01 -0.12 2.04 -0.08 1.96 -0.16 2.10 -0.02 2.13 0.01 I-C-I 113.0 107.9 -5.1 111.4 -1.6 111.6 -1.4 111.1 -1.9 97.5 -15.5 106.9 -6.1 113.2 0.2

C2H5I I-C 2.14 2.17 0.04 2.10 -0.04 2.03 -0.11 2.07 -0.07 2.04 -0.10 2.18 0.04 2.18 0.04 I-C-C 112.2 108.4 -3.8 112.5 0.3 115.0 2.8 113.5 1.3 106.3 -5.9 107.5 -4.7 112.2 0.0

(CH 2I)HC=CH 2 I-C 2.19 2.17 -0.02 2.10 -0.09 2.03 -0.16 2.07 -0.12 2.04 -0.15 2.18 -0.01 2.17 -0.02 I-C-C 107.6 112.0 4.4 110.5 2.9 112.9 5.3 111.4 3.8 106.9 -0.7 113.4 5.8 116.9 9.3

C6H5I I-C 2.08 2.15 0.07 2.03 -0.05 1.98 -0.11 2.02 -0.06 1.97 -0.11 2.09 0.01 2.12 0.04 CH 3COI I-C 2.22 2.21 -0.01 2.11 -0.11 2.04 -0.18 2.09 -0.13 2.05 -0.17 2.18 -0.04 2.21 -0.01 I-C-C 111.8 112.7 0.9 113.1 1.3 114.4 2.6 113.1 1.3 106.9 -4.9 106.2 -5.6 109.9 -1.9 I-C=O 119.4 119.5 0.1 120.3 0.9 122.9 3.5 123.4 4.0 120.8 1.4 122.1 2.7 121.3 1.9 ICN I-C 1.99 2.15 0.16 1.94 -0.05 1.89 -0.10 1.93 -0.06 1.91 -0.08 1.98 -0.01 2.02 0.03 INO I-N 2.30 2.27 -0.03 2.14 -0.16 2.06 -0.24 2.08 -0.23 1.96 -0.34 2.14 -0.16 1.92 -0.38 I-N-O 120.6 116.1 -4.5 119.2 -1.4 121.7 1.1 123.1 2.5 124.6 4.0 127.7 7.1 133.3 12.7 IO I-O 1.87 1.99 0.12 1.89 0.02 1.89 0.02 1.90 0.03 1.86 -0.01 1.91 0.04 1.97 0.10

CF 3I I-C 2.14 2.26 0.11 2.16 0.01 2.13 -0.02 2.18 0.03 2.05 -0.09 2.22 0.07 2.15 0.01 IF I-F 1.91 1.91 0.00 1.95 0.04 1.90 -0.01 1.88 -0.03 1.89 -0.02 1.88 -0.03 1.92 0.01

IF 5 I-Fax 1.81 1.92 0.11 1.93 0.12 1.98 0.17 1.93 0.12 1.87 0.06 1.95 0.14 1.91 0.10 I-Feq 1.87 1.91 0.03 1.96 0.08 1.96 0.09 1.90 0.03 1.88 0.01 1.30 -0.57 1.84 -0.03 Fax -I-Feq 83.0 89.9 6.9 82.3 -0.7 78.1 -4.9 77.3 -5.7 102.5 19.5 94.4 11.4 90.0 7.0

IF 7 I-Fax 1.79 1.90 0.12 1.91 0.12 1.98 0.19 1.93 0.15 1.88 0.10 1.79 0.00 1.84 0.05 I-Feq 1.86 1.92 0.06 1.95 0.09 2.03 0.17 1.97 0.11 1.92 0.06 1.88 0.02 1.92 0.06

O=IF 5 I-Fax 1.86 1.91 0.04 1.93 0.06 2.00 0.14 1.96 0.09 1.87 0.01 1.26 -0.61 1.79 -0.08 I-Feq 1.82 1.89 0.08 1.92 0.11 1.97 0.15 1.92 0.10 1.88 0.07 1.22 -0.60 1.77 -0.05 I=O 1.72 2.09 0.38 1.78 0.07 2.19 0.47 2.06 0.34 2.86 1.15 2.39 0.68 1.67 -0.05

O=I-Feq 98.0 90.4 -7.6 97.7 -0.3 101.5 3.5 101.5 3.5 86.9 -11.1 75.0 -23.0 96.7 -1.3 ICl I-Cl 2.32 2.32 0.00 2.31 -0.01 2.26 -0.06 2.22 -0.10 2.19 -0.13 2.33 0.01 2.34 0.02 IBr I-Br 2.49 2.43 -0.06 2.46 -0.03 2.35 -0.14 2.35 -0.13 2.56 0.08 2.45 -0.04 2.49 0.00

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I2 I-I 2.67 2.64 -0.03 2.64 -0.03 2.52 -0.15 2.54 -0.13 2.67 0.00 2.63 -0.04 2.57 -0.09 AlI I-Al 2.54 2.71 0.17 2.47 -0.06 2.36 -0.18 2.42 -0.12 2.47 -0.07 2.43 -0.11 2.59 0.06

AlI 3 I-Al 2.50 2.58 0.08 2.39 -0.11 2.33 -0.17 2.39 -0.11 2.61 0.11 2.37 -0.13 2.49 -0.01 Al 2I6 I-Al 2.45 2.49 0.04 2.39 -0.06 2.34 -0.11 2.40 -0.05 2.63 0.18 2.37 -0.08 2.50 0.05 SiI I-Si 2.44 2.74 0.30 2.42 -0.02 3.31 0.87 2.27 -0.17 1.92 -0.52 2.16 -0.28 2.37 -0.07

SiI 4 I-Si 2.43 2.52 0.09 2.40 -0.03 2.33 -0.10 2.43 -0.01 2.47 0.04 2.43 0.00 2.40 -0.03 SiIH 3 I-Si 2.44 2.57 0.14 2.44 0.01 2.39 -0.05 2.43 0.00 2.01 -0.42 2.48 0.05 2.45 0.01 Si-H 1.49 1.44 -0.05 1.41 -0.08 1.37 -0.12 1.47 -0.02 1.49 0.01 1.37 -0.12 1.49 0.00 I-Si-H 107.8 108.8 1.0 107.4 -0.4 108.4 0.6 109.8 2.0 107.9 0.1 106.9 -0.9 109.6 1.8 IPO I-P 2.69 2.55 -0.14 2.41 -0.28 2.30 -0.39 2.30 -0.39 2.43 -0.26 2.43 -0.26 2.55 -0.14

I3P I-P 2.46 2.50 0.04 2.37 -0.09 2.26 -0.20 2.25 -0.21 2.36 -0.10 2.40 -0.06 2.52 0.06 IS - I-S 2.66 2.56 -0.11 2.30 -0.36 2.22 -0.44 2.30 -0.36 2.86 0.20 2.38 -0.28 2.39 -0.27

I2S I-S 2.59 2.67 0.08 2.34 -0.25 2.24 -0.35 2.33 -0.26 2.20 -0.39 2.30 -0.29 2.38 -0.21 ZnI 2 I-Zn 2.53 2.53 0.00 2.23 -0.30 2.38 -0.15 2.35 -0.18 2.40 -0.13 2.40 -0.13 2.35 -0.18 AM1* MNDO/d MNDO AM1 PM3 PM5 PM6 MSE bond length 0.05 -0.05 -0.05 -0.06 -0.04 -0.09 -0.03 MUE bond length 0.08 0.09 0.18 0.12 0.16 0.16 0.07 MSE bond angle -1.0 0.3 1.6 1.3 -1.2 -1.4 3.2 MUE bond angle 3.6 1.1 2.9 2.8 6.5 6.8 3.8 Compounds Containing Ti, Cu, Zr and Mo.

TiI 2 I-Ti 2.63 2.63 0.00 2.73 0.11 2.60 -0.03 CuI I-Cu 2.44 2.42 -0.02 2.34 -0.10 2.36 -0.08

CuI 2 I-Cu 2.48 2.50 0.01 2.31 -0.18 2.51 0.03 ZrI 2 I-Zr 2.77 2.67 -0.10 2.90 0.13 2.76 -0.01 MoI I-Mo 2.63 2.48 -0.15 2.69 0.06 1.96 -0.67 AM1* PM5 PM6 MSE bond length -0.05 0.00 -0.15 MUE bond length 0.06 0.11 0.16

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.6.2 Conclusions and Outlook

The AM1* parameters for bromine and iodine provide important additional elements, both for classical organic chemistry applications and for parameterizing the transition metals, for which data for bromides and iodides are often available. AM1* performs comparably to the more modern of the available methods and better than those that only use s- and p-orbital basis sets. Because of the relatively large amount of available experimental data, our parameterization data for Br and I is far more similar to those used for MNDO/d and PM6 than is the case for the transition metals. The similar performances of the different methods are therefore probably not coincidental, but rather reflect the accuracy attainable within the current theoretical framework, which is for instance very similar for PM6 and AM1*.

The availability of PM6 and AM1* (and for some elements MNDO/d) as published semiempirical techniques that use s-, p-, d-basis sets and have very similar theoretical frameworks now opens the opportunity to carry out comparison calculations for many applications in order to assess the reliability of the technique for the problem in hand.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

4.7 Parameterization of Gold

4.7.1 Results

The optimized AM1* parameters for gold [154] are shown in Table 4.39. Geometries were optimized with the new AM1* parameterization using VAMP 10.0 [138], while the PM6 calculations used MOPAC2009 [144]. The two programs give essentially identical results for the Hamiltonians that are available in both.

Table 4.39: AM1* parameters for Au. Parameter Au

Uss [eV] -87.9070798 Upp [eV] -105.2325082 Udd [eV] -86.3002150 -1 ζs [bohr ] 2.9612383 -1 ζp [bohr ] 2.0921916 -1 ζd [bohr ] 4.2954046 βs [eV] -10.5044093 βp [eV] -2.9212915 βd [eV] -26.0306918 gss [eV] 12.8779541 gpp [eV] 41.6610633 gsp [eV] 10.4094935 gp2 [eV] 37.2533670 hsp [eV] 0.2611095 -1 zsn [bohr ] 3.3536714 -1 zpn [bohr ] 7.8813347 -1 zdn [bohr ] 1.7991401 ρ(core) [bohr -1] 1.3923445 -1 ∆H° f(atom) [kcal mol ] 88.0 0 F sd [eV] 7.7583836 2 G sd [eV] 6.0090661 ααα(ij) H 2.6891239 C 3.1012172 N 2.5099816 O 3.3201280 F 2.5990722 Al 1.9195605 Si 1.4489186 P 3.3822499 S 2.4757345 Cl 2.5963772 Ti 0.8968304 V 3.9464525 Cr 2.0645066 Co 2.4940667 Ni 3.9231603 Cu 2.2444292 Zn 4.3646875

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Br 2.2685919 Zr 1.3454899 Mo 1.3740902 I 4.3466246 Au 2.7869271 δδδ(ij) H -2.3071373 C 7.7686410 N 2.0238749 O 8.1526001 F 2.0413648 Al 1.6916486 Si 0.2684171 P 22.0561933 S 2.0695945 Cl 3.0310645 Ti 0.2436297 V 195.3767955 Cr 1.7484764 Co 3.7260808 Ni 51.9934681 Cu 1.4743149 Zn 51.6768894 Br 1.2652966 Zr 0.5332656 Mo 0.6104390 I 178.8807263 Au 6.0750313

4.7.1.1 Heats of Formation of Gold Compounds

The calculated heats of formation for our training set of gold compounds are shown in Table 4.40. Results have been compared with the only comparable method available Stewart’s PM6 [72].

Table 4.40: Calculated AM1* and PM6 heats of formation and errors compared with our target values for the gold-containing compounds used to parameterize AM1* (all values kcal mol -1). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol -1, yellow 10-20 kcal mol -1 and pink those greater than 20 kcal mol -1. The codenames within parentheses indicate the CSD-names of the compounds. Target AM1* PM6

Compound ∆∆∆H° f ∆∆∆H° f Error ∆∆∆H° f Error Au 88.0 88.0 0.0 77.5 -10.5 Au – 20.0 8.3 -11.7 33.0 13.0 Au + 300.7 286.0 -14.7 286.6 -14.1

Au 2 87.0 114.1 27.1 84.7 -2.3 AuH 78.7 82.5 3.8 67.5 -11.2 172

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AuH 3 149.1 128.7 -20.5 136.5 -12.6 AuCH 3 67.3 73.1 5.8 77.4 10.1 Au(CH 3)3 84.7 88.1 3.4 61.8 -22.9 AuNH 2 93.9 96.1 2.2 95.8 1.9 Au(CH 3)2(NH 2) 83.9 98.8 14.9 99.7 15.8 – Au(CN) 2 54.9 50.5 -4.5 65.5 10.6 Au(NH 2)3 126.0 121.9 -4.1 131.3 5.3 + Au(NH 3)4 154.5 174.1 19.6 166.6 12.1 2+ Au(NH 3)6 355.1 346.9 -8.2 367.0 11.9 (Au(CH 3)2(CN)) 4 362.7 361.3 -1.4 364.2 1.5 AuO – 57.1 54.4 -2.7 46.0 -11.1 AuOH 57.8 46.0 -11.8 50.2 -7.6

Au(CH 3)2(OH) 45.7 45.2 -0.5 66.9 21.2 + Au(H 2O) 4 -37.8 -43.7 -5.9 9.7 47.5 + Au(CO) 4 141.1 168.5 27.4 108.8 -32.3 AuF 50.0 55.4 5.4 83.6 33.6

AuF 3 12.7 12.7 0.0 39.1 26.4 – AuF 4 -79.7 -82.5 -2.8 -113.5 -33.8 Au(CH 3)F 2 -10.0 37.0 47.0 25.4 35.4 AuAlH 2 90.6 90.5 -0.1 163.8 73.2 AuSiH 3 84.1 84.1 0.0 125.1 41.0 + AuPH 3 260.8 212.6 -48.2 192.6 -68.2 + AuSH 2 269.1 246.6 -22.5 243.2 -25.9 AuF 2(SH) 7.6 17.0 9.4 23.2 15.6 Au(Me 2S) 2 148.8 148.6 -0.2 154.6 5.8 AuCl 60.2 67.6 7.4 69.5 9.3 – AuCl 2 -67.1 -35.5 31.6 -70.4 -3.3 AuCl 3 65.1 51.4 -13.7 58.0 -7.1 – AuCl 4 -89.7 -89.7 0.0 -92.9 -3.2 AuTi 145.7 145.7 0.0 111.2 -34.5 AuV 100.2 107.0 6.8 203.3 103.1 AuCr 137.0 136.1 -0.9 173.2 36.2 AuCo 141.5 141.6 0.1 132.4 -9.1 AuNi 77.8 77.8 0.0 178.8 101.0 AuCu 117.7 117.7 0.0 200.1 82.4 AuZnH 94.5 94.5 0.0 82.7 -11.8 AuBr 62.8 68.7 5.9 68.9 6.1 – AuBr 2 -56.3 -50.9 5.4 -50.1 6.2 – AuBr 4 -66.4 -71.5 -5.1 -70.0 -3.6 AuZrH 173.0 91.1 -81.9 166.7 -6.3 AuMo 251.5 216.1 -35.4 209.6 -41.9 AuI 69.0 92.5 23.5 79.0 10.0 – AuI 2 -38.1 -22.5 15.6 -24.5 13.6 – AuI 4 -26.8 -27.9 -1.1 -37.5 -10.7 AM1* PM6 N=49 Most positive error 47.0 103.1 Most negative error -81.9 -68.2 MSE -0.7 7.5 MUE 11.4 23.1 RMSD 19.4 33.7

Results for the PM6 parameterization set ( N=32 ) MSE 5.2 2.4 MUE 10.7 12.8 RMSD 15.6 15.9 173

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* reproduces the heats of formation of the training set, consisting of 49 gold compounds, used in parameterization better than PM6. AM1* shows no significant systematic error trend with a mean signed error (MSE) of -0.7 kcal mol −1, whereas PM6 tends to overestimate heats of formation to gold compounds by 7.5 kcal mol −1. The mean unsigned error (MUE) between experimental and AM1*-calculated heats of formation is only 11.4 kcal mol −1 and the root mean square deviation (RMSD) is found 19.4 kcal mol−1. These values are smaller than those given by PM6 as 23.1 kcal mol −1 (MUE) and 33.7 kcal mol −1 (RMSD). PM6 produces large errors for the compounds that were not included in its original training set. For example, PM6 −1 reproduces heats of formation with more than 50 kcal mol error for the compounds AuAlH 2, + AuPH 3 , AuV, AuNi and AuCu. However, Table 4.40 also shows the performance of AM1* and PM6 for only the PM6 parameterization dataset, consisting of 32 gold-containing compounds [72]. The AM1* mean unsigned error of only 10.7 kcal mol −1 and RMSD of 15.6 kcal mol −1 compared with 12.8 kcal mol −1 (MUE) and 15.9 kcal mol −1 (RMSD) for PM6 are very respectable and suggest that AM1* is parameterized well and performs better than PM6 for PM6 parameterization subset as well.

−1 − The large positive errors for AM1* are found for Au(CH 3)F 2 (47.0 kcal mol ), AuCl 2 (31.6 −1 + −1 kcal mol ) and Au(CO) 4 (27.4 kcal mol ). The largest negative errors are found for AuZrH −1 + −1 −1 (-81.9 kcal mol ), AuPH 3 (-48.2 kcal mol ) and AuMo (-35.4 kcal mol ). The large errors + with Au(CH 3)F 2 and Au(CO) 4 are not very surprising, since AM1* uses the unchanged AM1 parameterization for the elements H, C, N, O and F, and this limits the possible accuracy of − the parameterization. However, this does not explain the large error with AuCl 2 , AuZrH, + + AuPH 3 and AuMo. With the exception of the hydrogen in AuZrH and AuPH 3 these compounds contain only pure AM1* elements. As found for other metals, the large errors in these pure AM1* element-containing compounds is likely to be a consequence of our sequential parameterization strategy, in contrast to the simultaneous parameterization used for PM6 [72].

4.7.1.2 Ionization Potentials and Dipole Moments of Gold Compounds

Table 4.41 shows a comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for AM1* and PM6.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Table 4.41: Calculated AM1* and PM6 Koopmans’ theorem ionization potentials and dipole moments for gold- containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0. AM1* PM6 Compound Target Error Error Koopmans' Theorem Ionization Potentials for Cobalt Compounds (eV) Au 9.22 9.42 0.20 9.07 -0.15

Au 2 8.70 8.69 -0.01 11.42 2.72 AuAl 7.60 8.23 0.63 8.01 0.41

AuAl 2 6.20 6.71 0.51 5.79 -0.41 Au 2Al 7.70 8.40 0.70 8.89 1.19 AuSi 9.50 9.17 -0.33 7.72 -1.78

Au(CH 3)P(CH 3)3 7.70 7.26 -0.44 6.27 -1.43 Au(CH 3)3P(CH 3)3 7.80 7.55 -0.25 9.23 1.43 AM1* PM6 N=8 MSE 0.13 0.25 MUE 0.38 1.19 Dipole Moments for Cobalt Compounds (Debye) AuH 0.95 1.16 0.21 0.08 -0.87

AuCH 3 0.46 0.05 -0.41 0.38 -0.08 Au(CH 3)3 1.78 0.65 -1.13 0.41 -1.37 AuNH 2 1.63 1.70 0.07 2.73 1.10 Au(CH 3)2(NH 2) 0.34 0.42 0.08 1.19 0.85 Au(NH 2)3 3.02 0.96 -2.06 5.76 2.74 AuOH 2.53 3.31 0.78 2.62 0.09

Au(CH 3)2(OH) 3.74 2.64 -1.10 3.04 -0.70 AuF 4.04 2.85 -1.19 5.47 1.43

Au(CH 3)F 2 2.46 0.96 -1.50 2.85 0.39 AuF 2(SH) 1.60 1.32 -0.28 1.93 0.33 AuCl 3.48 3.86 0.38 3.35 -0.13 AuBr 2.87 2.89 0.02 2.11 -0.76 AuI 2.21 3.74 1.53 2.11 -0.10 AM1* PM6 N=14 MSE -0.33 0.21 MUE 0.77 0.78

AM1* performs marginally better than PM6 for the ionization potentials with an MUE of 0.38 eV comparing with 1.19 eV for PM6. Here, one must notice that all the experimental ionization potential data taken from NIST Webbook [109] and either there was no experimental data used or statistics not published for ionization potentials in the original PM6 parameterization of gold [72]. On the other hand, only Au and Au 2 were used in the training set of AM1* parameterization and the rest was used for the test step. The large AM1* errors, more than 0.5 eV, are found for AuAl, AuAl 2 and Au 2Al (0.63, 0.51 and 0.70 eV, respectively). Both AM1* and PM6 tend to give positive systematic errors to ionization potentials of gold-containing compounds with MSEs 0.13 and 0.25 eV, respectively. 175

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AM1* training set for dipole moments, consisting of 14 compounds, directly taken from PM6 parameterization dataset and has not been extended. For this dataset, AM1* underestimates dipole moments of gold-containing compounds by -0.33 Debye, while PM6 tends to give positive systematic errors with an MSE of 0.21 Debye. The performance of both methods is comparable for dipole moments. The mean unsigned errors are found to be 0.77 Debye and 0.78 Debye for AM1* and PM6, respectively. All the large AM1* errors, more than 1.0

Debye, are found for the compounds Au(NH 2)3 (-2.06 Debye), AuI (1.53 Debye), Au(CH 3)F 2

(-1.50 Debye), AuF (1.19 Debye), Au(CH 3)3 (-1.13 Debye), Au(CH 3)2(OH) (-1.10 Debye). With the only exception AuI, these compounds contain original AM1 elements H, C, N, O and F, which limits the possible accuracy of the parameterization. The large error with AuI is also not very surprising and just a result of the known weakness of AM1* parameterization for iodine in reproducing dipole moments [67].

4.7.1.3 Geometries of Gold Compounds

The geometrical parameters used to parameterize AM1* for gold and a comparison and statistical analysis of the AM1* and PM6 results are shown in Table 4.42.

Table 4.42: Calculated AM1* and PM6 bond lengths and angles for gold-containing compounds. The codenames within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°. AM1* PM6 Compound Variable Target Error Error

Au 2 Au-Au 2.63 2.63 0.00 2.24 -0.39 – Au 2 Au-Au 2.73 2.67 -0.07 2.49 -0.24 AuH Au-H 1.52 1.52 0.00 1.53 0.01

AuH 3 Au-H 1.70 1.58 -0.13 1.71 0.01 H-Au-H 120.0 119.4 -0.6 120.0 0.0

AuCH 3 Au-C 2.08 2.11 0.03 2.07 -0.01 H-C-Au 107.2 107.3 0.1 107.1 -0.1

Au(CH 3)3 Au-C 2.06 2.10 0.04 2.00 -0.06 Au-C' 2.12 2.11 -0.01 2.02 -0.11 C-Au-C 176.1 160.1 -16.0 169.4 -6.7

AuNH 2 Au-N 2.09 2.00 -0.09 1.53 -0.56 Au(CH 3)2(NH 2) Au-C 2.13 2.10 -0.03 2.06 -0.07 C-Au-C 80.1 86.5 6.4 105.3 25.2 Au-N 2.04 1.99 -0.05 1.60 -0.44 – Au(CN) 2 Au-C 2.04 2.08 0.04 2.09 0.05 C-Au-C 180.0 180.0 0.0 180.0 0.0 – Au(CN) 2 (JEYXAM) Au-C 2.02 2.05 0.03 2.09 0.07 C-N 1.11 1.16 0.05 1.15 0.04

AuC 3N2H3 (CYMIAU) Au-C(N) 2.00 2.13 0.13 2.05 0.05 Au-C(NCH3) 1.98 2.05 0.07 2.15 0.17

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Au(NH 2)3 Au-N 2.08 1.99 -0.09 1.42 -0.66 N-Au-N 158.1 156.0 -2.1 139.3 -18.9 Au-N' 2.11 2.05 -0.06 2.03 -0.08 3+ Au(NH 3)4 Au-N 2.17 2.17 0.00 2.14 -0.03 + Au(NH 3)4 Au-N 2.50 2.56 0.06 2.35 -0.15 + AuC 14 N4H22 (AZEGIV) Au-N 1.99 2.03 0.04 2.14 0.15 Au-N' 1.97 2.03 0.06 2.02 0.05 N-Au-N 95.6 94.7 -0.9 86.2 -9.4 2+ Au(NH 3)6 Au-N 2.67 2.47 -0.20 2.47 -0.20 Au-N' 2.24 2.45 0.21 2.61 0.37

Au 2C6N2H20 (DEVLUL) Au-N 2.14 2.21 0.07 2.18 0.04 Au-C 2.04 2.10 0.06 2.00 -0.04 C-Au-N 97.1 93.2 -3.9 95.2 -1.9

(Au(CH 3)2(CN)) 4 Au-Au 5.50 5.53 0.03 5.53 0.03 Au-C(CN) 2.03 2.10 0.07 2.11 0.08 Au-N 2.14 2.22 0.08 2.28 0.14 Au-C(Me) 2.11 2.15 0.04 1.98 -0.13 AuO – Au-O 1.98 1.98 0.00 1.43 -0.55 AuOH Au-O 1.98 2.08 0.10 1.42 -0.56

Au(CH 3)2(OH) Au-O 2.09 2.10 0.01 1.88 -0.21 Au-C 2.10 2.10 0.00 2.00 -0.10 O-Au-C 106.0 135.1 29.1 98.2 -7.8 + Au(H 2O) 2 O-Au-O 176.8 172.1 -4.7 176.9 0.1 + Au(H 2O) 4 Au-O 2.46 2.46 0.00 2.39 -0.07 Au-O' 2.45 2.45 0.00 2.36 -0.09 + Au(CO) 4 Au-C 2.28 2.34 0.06 2.30 0.02 AuF Au-F 2.07 1.95 -0.12 1.92 -0.15

Au(CH 3)F 2 Au-F 1.96 1.98 0.02 2.06 0.11 Au-C 2.05 2.04 -0.01 1.94 -0.11 C-Au-F 91.6 99.7 8.1 96.7 5.1

AuF 3 Au-F 2.01 2.04 0.03 2.04 0.03 Au-F' 2.02 1.98 -0.04 1.94 -0.08 F-Au-F' 95.0 99.2 4.2 102.5 7.5 – AuF 4 Au-F 1.97 2.00 0.03 2.03 0.07 AuAlH 2 Au-Al 2.38 2.42 0.03 3.01 0.63 AuSiH 3 Au-Si 2.32 2.32 0.00 3.38 1.06 + AuPH 3 Au-P 2.28 2.39 0.11 2.11 -0.17 AuPH 2 Au-P 2.33 2.28 -0.05 2.09 -0.24 AuP 2– Au ≡P 2.28 2.20 -0.08 1.59 -0.69 + Au(PH 3)2 Au-P 2.38 2.34 -0.04 2.20 -0.18 + Au 2C10 P4H28 (DUKREG01) Au-P 2.30 2.39 0.09 2.39 0.09 P-Au-P 176.8 177.0 0.3 91.0 -85.8 AuSH Au-S 2.30 2.29 -0.01 2.18 -0.12 + AuSH 2 Au-S 2.37 2.48 0.12 2.13 -0.24 Au 2C8H22 S2 (CULYIR) Au-Au 3.46 3.59 0.13 3.51 0.05 Au-S 2.41 2.42 0.01 2.32 -0.09 Au-C 2.13 2.11 -0.02 2.00 -0.13 C-Au-Au 134.8 131.2 -3.6 132.8 -1.9

AuF 2(SH) Au-S 2.34 2.26 -0.08 2.16 -0.18 Au-F 2.02 1.99 -0.03 2.04 0.02 S-Au-F 89.4 97.3 7.9 87.0 -2.3 + AuC 2N4H8S2 (AFAWUZ) Au-S 2.28 2.25 -0.03 2.28 0.00 AuC 12 H8S4 (JEKGAH) Au-S 2.30 2.27 -0.03 2.25 -0.05 S-Au-S 89.9 92.7 2.9 92.9 3.0 + Au(Me 2S) 2 Au-S 2.40 2.36 -0.04 2.30 -0.10 177

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

AuCl Au-Cl 2.33 2.26 -0.07 2.34 0.01 – AuCl 2 (GANJOU) Au-Cl 2.28 2.28 0.00 2.42 0.14 AuCl 3 Au-Cl 2.32 2.22 -0.10 2.20 -0.12 Au-Cl 2.30 2.23 -0.07 2.06 -0.25 – AuCl 4 (BENYAU) Au-Cl 2.27 2.25 -0.02 2.27 0.00 2+ AuC 4N3H13 Cl (AEMAUP) Au-Cl 2.27 2.20 -0.07 2.13 -0.14 Au-N 1.97 2.20 0.23 2.21 0.24 N-Au-Cl 93.7 99.1 5.4 90.5 -3.2 Au-N' 2.05 2.26 0.21 2.06 0.01

AuC 2H6SCl (GOJLAS) Au-S 2.27 2.35 0.08 2.33 0.06 Au-Cl 2.29 2.25 -0.04 2.38 0.09

Au(CH 3)Cl 2 Au-Cl 2.35 2.23 -0.12 2.31 -0.04 C-Au-Cl 93.0 93.6 0.6 93.8 0.8 Cl-Au-Cl 177.9 175.7 -2.2 177.9 0.0 + AuC 11 N2H10 Cl 2O2 (BATTOF) Au-Cl 2.26 2.31 0.05 2.16 -0.10 Cl-Au-Cl 89.6 138.6 49.0 99.3 9.7 Au-N 2.08 2.36 0.28 2.19 0.11

AuC 6NH 3Cl 2O3 (KUDNAY) Au-Cl 2.25 2.23 -0.02 2.41 0.16 Au-N 2.04 2.04 0.00 2.35 0.31 Au-O 1.99 2.07 0.08 1.42 -0.57

AuC 5NH 5Cl 3 (PYAUCL10) Au-Cl 2.29 2.25 -0.04 2.28 -0.01 Au-Cl 2.26 2.22 -0.04 2.16 -0.10 Au-Cl 2.28 2.24 -0.04 2.27 -0.01 Au-N 2.00 2.25 0.25 2.17 0.17

AuC 6NH 7Cl 3O (HIHCIK) Au-Cl 2.27 2.31 0.04 2.26 -0.01 Au-N 2.02 2.07 0.05 2.13 0.11

Au 2C12 P2H28 Cl 2 (EMPLAU) Au-Cl 2.38 2.32 -0.06 2.45 0.07 Au-C 2.05 2.17 0.12 2.23 0.18 Cl-Au-C 85.8 88.4 2.7 93.1 7.3 Au-Au 2.59 2.65 0.06 3.13 0.54 AuTi Au-Ti 2.52 2.52 0.00 3.60 1.07 AuV Au-V 2.53 2.53 0.00 3.60 1.07 AuCr Au-Cr 2.54 2.54 0.00 5.54 3.00 AuCo Au-Co 2.44 2.43 0.00 3.51 1.08 AuNi Au-Ni 2.41 2.40 -0.01 6.34 3.93 AuCu Au-Cu 2.39 2.40 0.00 3.78 1.39 AuZn Au-Zn 2.50 2.58 0.08 2.80 0.30 AuZnH Au-Zn 2.42 2.36 -0.06 2.80 0.38 AuBr Au-Br 2.44 2.30 -0.15 2.26 -0.18 – AuBr 2 (DOYMAF) Au-Br 2.38 2.33 -0.05 2.43 0.05 – AuBr 4 Au-Br 2.55 2.35 -0.20 2.28 -0.27 AuC 2H6SBr (GIGWAU) Au-Br 2.40 2.30 -0.10 2.34 -0.06 Au-S 2.28 2.35 0.07 2.32 0.04

AuC 3PH 9Br 3 (BRMPAU) Au-Br 2.51 2.82 0.31 2.49 -0.02 Au-Br' 2.48 2.29 -0.19 2.97 0.49 Au-P 2.48 2.54 0.06 2.08 -0.40

AuC 2H6SBr 3 (GIGWEY) Au-Br 2.42 2.42 0.00 2.84 0.42 Au-S 2.35 2.32 -0.03 2.39 0.04 AuZrH Au-Zr 2.70 2.70 0.00 3.19 0.49 AuMo Au-Mo 2.62 2.62 0.00 3.70 1.08 AuI Au-I 2.61 2.80 0.19 2.57 -0.04 – AuI 2 (GANJUA) Au-I 2.53 2.54 0.01 2.67 0.14 – AuI 4 (GEJQUH) Au-I 2.63 2.55 -0.08 2.91 0.28 Au 2C9P2H23 I (BIBPIL) Au-Au 2.70 3.16 0.46 3.22 0.52 Au-I 2.89 2.53 -0.36 2.67 -0.22 178

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

Au-C 2.13 2.12 -0.01 2.11 -0.02 Au-C(P) 2.09 2.17 0.08 2.11 0.02 C-Au-Au 88.8 87.3 -1.5 121.3 32.5

Au 2C6P2H18 I2 (FUWFIM) Au-I 2.58 2.53 -0.06 2.65 0.07 Au-P 2.26 2.39 0.13 2.32 0.06 AM1* PM6 N=113 MSE bond length 0.01 0.10 MUE bond length 0.07 0.28 N=22 MSE bond angle 3.7 -2.1 MUE bond angle 6.9 10.4

AM1* shows no significant systematic error to gold with an MSE of 0.01 Å. In contrast to AM1*, PM6 with an MSE of 0.10 Å, predicts the bond lengths of the gold-containing compounds to be too long. AM1* with an MUE of 0.07 Å performs far better than PM6 (MUE = 0.28 Å) for the training set, consisting of 75 compounds, used. Once again, as in heats of formations, large errors for PM6 originated from the compounds not included in original PM6 parameterization dataset. For the bond angles, AM1* performs quite well (MUE = 6.9°) comparing with PM6 (MUE = 10.4°). AM1* overestimates bond angles to gold systematically with an MSE of 3.7°, whereas PM6 underestimates by -2.1°. However, AM1* not only performs well for its own extended dataset, it also performs better for PM6 parameterization subset which consists of 50 compounds [72]. For PM6 training set, AM1* gives MUEs 0.08 Å for bond lengths and 7.5° for bond angles, whereas PM6 produces 0.15 Å and 12.4° for bond lengths and angles, respectively.

Fig. 4.1 : AM1* (upper row) and PM6 (lower row) optimized structures of neutral gold clusters with 4 to 9 atoms.

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RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

The AM1* and PM6 optimized ground state structures of neutral gold clusters with 4 to 9 atoms are represented in Fig. 4.1. PM6 predicts neutral gold clusters up to 9 atoms to be planar as it has been reported by Stewart before [72]. AM1* produces planar structures up to 7 atoms. Starting from 8 atoms, AM1* predicts neutral gold clusters to be dispersed 3D structures. This finding is in good agreement with Häkkinen and Landman’s results [155]. On the other hand, Gruene et al. [156] proposed that for neutral Au 7 a planar edge-capped triangle with C s symmetry to be lowest in energy, in contrast to Häkkinen and Landman’s hexagonal planar structure [155] and Wang et al.’s 3D pentagonal bipyramidal structure [157] proposals.

Fig. 4.2: AM1* (a) and PM6 (b) optimized structure of planar edge-capped triangle Au 7 with C s symmetry.

As represented in Fig. 4.2, AM1* reproduces planar edge-capped triangle Au 7 structure very well, but with 7.38 kcal mol −1 higher in energy comparing with hexagonal structure. PM6 reproduces this isomer structure not that successfully, but 0.23 kcal mol −1 lower in energy comparing with hexagonal structure.

Very recently Botana et al. [158] found that the global energy minimum for Au 8 is obtained for planar D 4h tetra-capped square structure. A non-planar D 2d bi-capped octahedron structure 180

RESULTS OF AM1* PARAMETERIZATIONS Chapter 4

is found as the second lowest energy structure. They performed ab initio calculations within the density functional theory frame using linear combinations of Gaussian-type orbitals within the Kohn-Sham density functional methology (LCGTO-KSDFM) [159]. Wang et al [157] proposed T d bicapped octahedron structure using a relativistic effective core potential (ECP) and a double numerical basis with a d-polarization function which is in consistent with Häkkinen and Landman’s generalized gradient approximation (GGA) results [155]. On the other hand, Olson and Gordon [160] found that non-planar D 2d bi-capped octahedron structure is the lowest energy neutral Au 8 isomer, using Møller-Plesset perturbation theory (MP2) [161] regardless of basis set or contributions from core-valence correlation. They additionally proposed that CCSD [123] calculations (with some exceptions due to core-valence correlation effects) give tetra-capped square structure as the minimum energy structure.

Since there are many different proposals originating from different level of calculations, both AM1* and PM6 can be consistent or inconsistent with some of them.

4.7.2 Conclusions and Outlook

The new AM1* parameterization for gold, for which the parameterization dataset has been extended by including results from DFT calculations to produce a parameter set that is more robust and more reliable, provides an important additional element especially for catalytic chemistry and biochemistry applications [162, 163]. AM1* parameterization for gold gives very good results for energetic, electronic and structural properties. AM1* performs very well for its own training set and also for PM6 parameterization subset. In addition, for small neutral gold clusters, AM1* performs very well especially for the structural properties. Naturally, as for all semiempirical methods, there can be some cases that both AM1* and PM6 might show large deviations from experiment. As published NDDO-based methods including d-orbitals, both AM1* and PM6 provide opportunity to perform comparative calculations for different applications and good starting points for reaction specific local parameterizations.

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PUBLICATIONS AND PRESENTATIONS

Publications

Kayi H, Clark T (2010) J Mol Model 16:29-47; AM1* parameters for cobalt and nickel.

Kayi H, Clark T (2009) J Mol Model (online first) DOI: 10.1007/s00894-009-0614-y; AM1* parameters for manganese and iron.

Kayi H (2009) J Mol Model (online first) DOI: 10.1007/s00894-009-0613-z; AM1* parameters for gold.

Kayi H, Clark T (2009) J Mol Model 15:1253-1269; AM1* parameters for vanadium and chromium.

Kayi H, Clark T (2009) J Mol Model 15:295-308; AM1* parameters for bromine and iodine.

Serbest K, Kayi H, Er M, Sancak K, Degirmencioglu I (2008) Heteroatom Chemistry 19(7):700-712; Ni(II), Cu(II) and Zn(II) complexes of tetradentate schiff base containing two thiadiazoles units: structural, spectroscopic, magnetic properties and molecular modeling studies.

Kayi H, Clark T (2007) J Mol Model 13:965-979; AM1* parameters for copper and zinc.

Kayi H, Elkamel A, Tuncel A, Alper E (2005) J Mol Model 11:55-60; Prediction of lower critical solution temperature of N-isopropylacrylamide-acrylic acid copolymer by an artificial neural network model.

Kayi H (2004) “Fluorimetry”, Instrumental Analysis Laboratory , Eds. Ayhan H & Kocum C, Aydan Publishings, Ankara, ISBN:975-98530-0-0, p. 29-36.

Uguzdogan E, Kayi H, Denkbas EB, Patir S, Tuncel A (2003) Polymer International 52(5):649-657; Stimuli-responsive properties of aminophenylboronic acid-carrying thermosensitive copolymers.

Oral Presentations

th Molecular Modeling Workshop and Model(l)ing’09 Conference, 6-11 September 2009, Erlangen, Germany; “Parameterization of AM1*”.

UKMK-8, 26-29 August 2008, Inönü University, Malatya, Turkey; “Prediction of drying time in fluidized bed dryer by an artificial neural network model” (by Olgac Bavbek).

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Graduate College GK-312: Homogeneous and Heterogeneous Electron Transfer Final Report Seminar, 2005, Erlangen, Germany; “Parameterization of Copper and Zinc for AM1* Molecular Orbital Theory”.

DFG - Graduate College GK-312: Homogeneous and Heterogeneous Electron Transfer Symposium, 2004, Veilbron, Germany; “Parameterization of new elements for AM1*”.

UKMK-5 (National Chemical Eng. Congress), 2-5 September 2002, Ankara University, Ankara, Turkey; “Prediction of lower critical solution temperature of N-isopropylacrylamide-acrylic acid copolymer by an artificial neural network model”.

Poster Presentations

Darmstadt Molecular Modeling Workshop in Erlangen, 29-30 April 2008, Computer- Chemistry-Centrum, Erlangen, Germany; “Parameterization of Bromine and Iodine for AM1*”.

Darmstadt Molecular Modeling Workshop in Erlangen, 15-16 May 2007, Compute- Chemistry-Centrum, Erlangen, Germany; “Parameterization of Zinc for AM1*”.

Darmstadt Molecular Modeling Workshop in Erlangen, 23-24 May 2006, Computer- Chemistry-Centrum, Erlangen, Germany; “Parameterization of Copper for AM1*”.

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Curriculum Vitae

Name : Hakan Kayi

Year of Birth : 1978

Place of Birth : Bursa, Turkey

Education

Doctor rerum naturalium

2009 Friedrich-Alexander Universität Erlangen-Nürnberg, Germany

Computer-Chemie-Centrum and Interdisciplinary Center for Molecular Materials

Master of Science

2003 Hacettepe University, Ankara, Turkey

Chemical Engineering Department

Bachelor of Science

2000 Hacettepe University, Ankara, Turkey

Chemical Engineering Department

Work Experience

Research Assistant

2004-2009 Friedrich-Alexander Universität Erlangen-Nürnberg, Germany

Computer-Chemie-Centrum and Interdisciplinary Center for Molecular Materials

Research and Teaching Assistant

2001-2004 Hacettepe University, Ankara, Turkey

Chemical Engineering Department

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