Predikce Hodnot Pka Na Základě EEM Atomových Nábojů

MASARYKOVA UNIVERZITA PRˇ I´RODOVEˇ DECKA´ FAKULTA NA´ RODNI´ CENTRUM PRO VY´ZKUM BIOMOLEKUL

Diplomova´pra´ce

BRNO 2013 STANISLAV GEIDL MASARYKOVA UNIVERZITA PRˇ I´RODOVEˇ DECKA´ FAKULTA NA´ RODNI´ CENTRUM PRO VY´ZKUM BIOMOLEKUL

Predikce hodnot pKa na za´kladeˇ EEM atomovy´ch na´boju˚

Diplomova´pra´ce Stanislav Geidl

Vedoucı´pra´ce: prof. RNDr. Jaroslav Kocˇa, DrSc. Konzultant: RNDr. Radka Svobodova´Varˇekova´, Ph.D.

Brno 2013 Bibliograﬁcky´za´znam

Autor: Bc. Stanislav Geidl Prˇı´rodoveˇdecka´fakulta, Masarykova univerzita Na´rodnı´centrum pro vy´zkum biomolekul

Na´zev pra´ce: Predikce hodnot pKa na za´kladeˇEEM atomovy´ch na´boju˚

Studijnı´program: Biochemie

Studijnı´obor: Chemoinformatika a bioinformatika

Vedoucı´pra´ce: prof. RNDr. Jaroslav Kocˇa, DrSc.

Akademicky´rok: 2012/2013

Pocˇet stran: xi + 78

Klı´cˇova´slova: disociacˇnı´konstanta, pKa, QSPR, vı´cerozmeˇrna´linea´rnı´ regrese, atomove´ na´boje, kvantova´ mechanika, EEM, fenoly, karboxylove´kyseliny Bibliographic Entry

Author: Bc. Stanislav Geidl Faculty of Science, Masaryk University National Centre for Biomolecular Research

Title of Thesis: Predicting pKa values from EEM atomic charges

Degree Programme: Biochemistry

Field of Study: Chemoinformatics and Bioinformatics

Supervisor: prof. RNDr. Jaroslav Kocˇa, DrSc.

Academic Year: 2012/2013

Number of Pages: xi + 78

Keywords: dissociation constant, pKa, QSPR, multilinear regression, partial atomic charge, quantum mechanics, EEM, phenols, carboxilic acids Abstrakt

Disociacˇnı´ konstanta pKa je velmi du˚lezˇitou vlastnostı´ molekuly, a proto je vy´voj spolehlivyćh a rychlyćh metod pro predikci pKa jednou z klıćˇovyćh oblastı´ vy´zkumu. Tato praće zjisˇt’uje, jestli lze predikovat pKa pomocı´QSPR modelu˚ vyuzˇı´vajıćıćh empirickeátomoveńa´boje, konkre´tneˇna´boje vypocˇı´tane´metodou EEM (Electronegativity Equalization Method). V ra´mci praće jsme nejdrˇı´ve shro- ma´zˇdili 18 sad EEM parametru˚vytvorˇenyćh pro 8 ru˚znyćh kvantoveˇmechan- ickyćh (QM) na´bojovyćh sche´mat. Pote´jsme si prˇipravili treńinkovou sadu 74 molekul substituovanyćh fenolu˚. Da´le jsme pro kazˇdou molekulu vytvorˇili jejı´ disociovanou formu tak, zˇe jsme odstranili fenolovy´vodı´k. Pro vsˇechny molekuly v treńinkove´sadeˇjsme pak vypocˇı´tali EEM na´boje pomocı´18 sad EEM parametru˚ a QM na´boje pomocı´8 zmıńeˇnyćh na´bojovyćh sche´mat. Pro kazˇdy´typ QM a EEM na´boju˚jsme vytvorˇili jeden QSPR model, vyuzˇı´vajıćıńa´boje z nedisociovane´ molekuly (QSPR model se trˇemi deskriptory), a jeden QSPR model, vyuzˇı´vajıćı´ na´boje z disociovaneí nedisociovane´molekuly (QSPR model s peˇti deskriptory). Pote´jsme vypocˇı´tali krite´ria kvality modelu˚a zhodnotili vsˇechny vytvorˇene´QSPR modely. QSPR modely vyuzˇı´vajıćıÉEM na´boje se uka´zaly jako vhodna´metodika 2 2 pro predikci pKa (63% teˇchto modelu˚ma´ R > 0.9 a nejlepsˇı´model ma´ R = 0.924). Jak bylo ocˇekvańo, QM QSPR modely poskytovaly prˇesneˇjsˇı´predikci pKa nezˇEEM QSPR modely, rozdı´l v prˇesnosti modelu˚vsˇak nebyl prˇı´lisˇvy´razny´. Navıć velkou vy´hodou EEM QSPR modelu˚je, zˇe jejich deskriptory (tj., EEM na´boje) mohou by´t vypocˇı´tańy vy´razneˇrychleji nezˇQM na´boje. Kromeˇtoho jsme zjistili, zˇe EEM QSPR modely nejsou tak silneˇovlivneˇny vy´beˇrem metodiky vy´pocˇtu na´boju˚jako QM QSPR modely. Robustnost EEM QSPR modelu˚byla na´sledneˇpotvrzena cross- validacı´. Aplikovatelnost EEM QSPR modelu˚na dalsˇı´trˇı´dy chemickyćh la´tek jsme uka´zali pomocı´prˇı´padove´studie, zameˇrˇeneńa karboxylove´kyseliny. Souhrnneˇ mu˚zˇeme rˇıći, zˇe EEM QSPR modely poskytujı´rychlou a prˇesnou metodiku pro predikci pKa, a mohou by´t tedy pouzˇity naprˇ. v ra´mci virtua´lnı´ho screeningu. Abstract

The acid dissociation constant pKa is a very important molecular property, and there is a strong interest in the development of reliable and fast methods for pKa prediction. We have evaluated the pKa prediction capabilities of QSPR models based on empirical atomic charges calculated by the Electronegativity Equaliza- tion Method (EEM). Specifically, we collected 18 EEM parameter sets created for 8 different quantum mechanical (QM) charge calculation schemes. Afterwards, we prepared a training set of 74 substituted phenols. Additionally, for each molecule we generated its dissociated form by removing the phenolic hydrogen. For all the molecules in the training set, we then calculated EEM charges using the 18 parameter sets, and the QM charges using the 8 above mentioned charge calculation schemes. For each type of QM and EEM charges, we created one QSPR model employing charges from the non-dissociated molecules (three descriptor QSPR models), and one QSPR model based on charges from both dissociated and non-dissociated molecules (QSPR models with five descriptors). Afterwards, we calculated the quality criteria and evaluated all the QSPR models obtained. We found that QSPR models employing the EEM charges proved as a good approach 2 for the prediction of pKa (63% of these models had R > 0.9, while the best 2 had R = 0.924). As expected, QM QSPR models provided more accurate pKa predictions than the EEM QSPR models but the differences were not significant. Furthermore, a big advantage of the EEM QSPR models is that their descriptors (i.e., EEM atomic charges) can be calculated markedly faster than the QM charge descriptors. Moreover, we found that the EEM QSPR models are not so strongly influenced by the selection of the charge calculation approach as the QM QSPR models. The robustness of the EEM QSPR models was subsequently confirmed by cross-validation. The applicability of EEM QSPR models for other chemical classes was illustrated by a case study focused on carboxylic acids. In summary, EEM QSPR models constitute a fast and accurate pKa prediction approach that can be used in assigning charges to compounds in virtual screening.

Podeˇkova´nı´

Ra´d bych na tomto mı´steˇ podeˇkoval sve´mu sˇkoliteli prof. Kocˇovi za jeho podporu a pomoc, bez ktere´by tato praće nemohla vzniknout. Da´le bych ra´d podeˇkoval sveódborne´konzultance Radce Svobobove´za vesˇkerou jejı´pomoc. V neposlednı´ rˇadeˇ bych chteˇl take´ podeˇkovat babicˇce a otci za jejich podporu prˇedevsˇı´m prˇi psanı´praće.

Prohla´sˇenı´

Prohlasˇuji, zˇe jsem svoji diplomovou praći vypracoval samostatneˇs vyuzˇitı´m informacˇnıćh zdroju˚, ktere´jsou v praći citovańy.

Brno 14. kveˇtna 2013 ...... Stanislav Geidl Contents

I Introduction1

II Theory4

1. Acid dissociation constant...... 5 1.1 Deﬁnition...... 5 1.2 Methods for pKa prediction...... 6

2. Atomic charges...... 8 2.1 QM approaches for charge calculation...... 8 2.1.1 Quantum mechanics...... 9 2.1.2 Charge distribution schemes...... 11 2.2 Empirical approaches for charge calculation...... 12 2.2.1 Electronegativity equalization method...... 13

3. Quantitative Structure-Property Relationship (QSPR)...... 15 3.1 Descriptors...... 15 3.2 Parametrization of models...... 16 3.3 Validation of models...... 18 3.3.1 Cross-validation...... 19

III Methods 20

4. Tools...... 21 4.1 NCI database...... 21 4.2 Physprop...... 21 4.3 Gaussian...... 21 4.4 AIMAll...... 22 4.5 EEM solver...... 22 4.6 QSPR designer...... 22 4.7 R...... 22

– ix – IV Results and discussion 23

5. Preparation of input data...... 24 5.1 Data sets...... 24 5.1.1 Data set for phenols...... 24 5.1.2 Data set for carboxylic acids...... 25 5.2 pKa values...... 25 5.3 Charge calculation...... 25 5.3.1 EEM parameter sets...... 25 5.3.2 QSPR model parameterization...... 26

6. Building QSPR models for phenols...... 27 6.1 Selection of descriptors...... 27 6.2 Models...... 27 6.2.1 Prediction of pKa using EEM charges...... 28 6.2.2 Improvement of EEM QSPR models by removing outliers.... 33 6.2.3 Improvement of EEM QSPR models by adding descriptors... 33 6.2.4 Comparison of EEM and QM QSPR models...... 34 6.2.5 Influence of theory level and basis set...... 34 6.2.6 Influence of population analysis...... 34 6.2.7 Influence of the EEM parameter set...... 35

7. Validation QSPR models...... 36 7.1 Cross-validation...... 36 7.2 Comparison with previous work...... 36

8. Case study for carboxylic acids...... 40 8.1 Selection of descriptors...... 40 8.2 Models...... 40

9. Publication outputs...... 42 9.1 QM models for phenols...... 42 9.2 EEM models for phenols...... 42 9.3 My contribution...... 43

V Conclusion 44

VI Appendices 47

A. Content of included CD...... 48

B. List of abbreviations...... 49 C. List of molecules...... 51 Part I

Introduction

– 1 – Introduction

The acid dissociation constant pKa is an important molecular property, and its values are of interest in pharmaceutical, chemical, biological and environmental research. The pKa values have found application in many areas, such as the evaluation and optimization of candidate drug molecules [1–3], ADME proﬁl- ing [4,5], pharmacokinetics [6], understanding protein-ligand interactions [7,8], etc.. Moreover, the key physicochemical properties like lipophilicity, solubility, and permeability are all pKa dependent. For these reasons, pKa values are important for virtual screening. Therefore, both the research community and pharmaceutical companies are interested in the development of reliable and above all fast methods for pKa prediction. Several approaches for pKa prediction have been developed [8–11]. However, the prediction of pKa values still remains a challenge. A very promising approach for pKa prediction is to use QSPR models which employ partial atomic charges as descriptors [12–15]. The partial atomic charges cannot be determined experimentally, and they are also not quantum mechanical observables. For this reason, the rules for determin- ing partial atomic charges depend on their application (e.g. molecular mechanics energy, pKa etc.), and many different methods have been developed for their calculation. The charge calculation methods can be divided into two main groups, namely quantum mechanical (QM) approaches and empirical approaches. The quantum mechanical approaches ﬁrst calculate a molecular wave function by a combination of some theory level and basis set, and then partition this wave function among the atoms [16]. Empirical approaches determine partial atomic charges without calculating a quantum mechanical wave function. A well-known empirical charge calculation method is EEM (Electronegativity Equal- ization Method) [17]. This approach is based on the 3D structure of the molecule, and it employs empirical parameters derived from QM charges. The accuracy of EEM is comparable to the accuracy of the QM charge calculation approach from which the EEM parameters were derived. Additionally, EEM is very fast, as its computational complexity is θ(N3), where N is the number of atoms in the molecule. The prediction of pKa using QSPR models which employ QM atomic charges was described in several studies [12–15]. The studies analyzed the precision of this approach and compared the quality of QSPR models based on different QM charge calculation schemes. All these studies show that QM charges are successful

– 2 – Introduction 3 descriptors for pKa prediction, as the QSPR models based on QM atomic charges are able to calculate pKa with high accuracy. The weak point of QM charges is that their calculation is very slow, as the computational complexity is at least θ(B4), where B is the number of basis functions used during the QM calculation. There- fore, B is greater than the number of electrons in the molecule. For this reason, pKa prediction by QSPR models based on QM charges cannot be applied in virtual screening, as it is not feasible to compute QM atomic charges for hundreds of thousands of compounds in a reasonable time. This issue can be avoided if empirical charges are used instead of QM charges. Since the conformation of the atoms surrounding the dissociating hydrogens strongly inﬂuences the dissociation process and therefore pKa, it is important that the atomic charges used as descriptors correctly account for the effect of the conformation. Employing EEM charges as descriptors of QSPR models is a promising solution for pKa prediction during virtual screening, because EEM charges consider the inﬂuence of the molecule’s conformation on the atomic charges, whiletheir calculation remains very inexpensive. Therefore, the present thesis focuses on pKa prediction using QSPR models which employ EEM charges as descriptors. The particular goals of the work are:

• Preparation of a training set containing phenol molecules.

• Retrieval of published EEM parameter sets from literature.

• Calculation of EEM atomic charges using all available EEM parameter sets.

• Calculation of corresponding QM charges.

• Creation of a QSPR model for each set of EEM and QM atomic charges, and prediction of pKa using all obtained QSPR models.

• Discussion of the accuracy of the predicted pKa values. Part II

Theory

– 4 – 1

Acid dissociation constant

The acid dissociation constant is a physicochemical property which describes the strength of an acid in solution. This property plays an important role in pharmaceutical, chemical, biological and environmental research. In particular, it can be used in the evaluation and optimization of candidate drug molecules [1–3], ADME proﬁling [4,5], pharmacokinetics [6], understanding protein-ligand interactions [7,8], etc..

1.1 Deﬁnition

The acid dissociation constant [18, 19](Ka) is the equilibrium constant for the dissociation of an acid. According to the Brønstred–Lowry theory [18, 19], an acid is a compound that can donate a proton, while a base is a compound that can receive a proton:

− + HA (acid) + H2O (base) A + H3O (1.1)

This equilibrium can be described using equilibrium concentrations, or using the change in standard Gibbs energy for the reaction:

[A−] K = [H O+] (1.2) a [HA] 3

−∆G◦ Ka = e RT (1.3) Because acid dissociation constants span many orders of magnitude, it is con- venient to report them as their decimal logarithm:

pKa = log10 Ka (1.4)

Examples of pKa values for common molecules are given in Table 1.1.

– 5 – Chapter 1. Acid dissociation constant 6

◦ 1 Table 1.1: Table of common acids and the values of their pKa at 25 C .

Name Molecular formula pKa Name Molecular formula pKa

Hydrochloric acid HCl -6.3 Formic acid HCO2H 3.74

Nitrous acid HNO2 3.35 Benzoic acid C6H5CO2H 4.19

Hydroﬂuoric acid HF 3.46 Acetic acid CH3CO2H 4.74

Hydrocyanic acid HCN 9.31 Phenol C6H5OH 9.99

1.2 Methods for pKa prediction

Several approaches for pKa prediction have been developed [8–11]. Common methods include:

LFER (Linear Free Energy Relationships) method [21, 22]: This is one of the ﬁrst methods developed, and it is based on the fact that there is a linear relation between free energy and pKa. It uses the Hammett and Taft equations, and it is still used in the programs ACD/pKa [23], EPIK [24] and SPARC [25].

Database methods [26, 27]: These methods use databases of known pKa values. The pKa value of a compound of interest is inferred based on the pKas of similar molecules in the available databases. For this prediction, techniques such as interpolation or triangulation can be used. In order to cover all chemical space, it is necessary to have large databases.

Decision tree methods [27, 28]: This is a method which groups molecules into different categories according to various properties. The prediction has two steps: ﬁrst, the unknown molecule is assigned to some group, and then the property of interest (in this case pKa) is computed based on the other molecules in this group. For example, the pKa of the molecule of interest can be calculated as an average of the pKas of the rest of the molecules in the group.

Ab initio quantum mechanical calculations [29, 30]: Such methods calculate the change in Gibbs energy for the reaction, and then use equation 1.3 for calculating pKa. However, there is no universal approach, and a speciﬁc con- ﬁguration of the calculation needs to be setup for every type of molecule. Moreover, this prediction is very time-consuming and the calculation of the solvation energy is still complicated. On the other hand, this method can be very accurate if provided with the correct parameters. This method is imple- mented as a module of Jaguar [31], a quantum chemical software package provided by Schro¨dinger.

1Source: Inorganic chemistry[18], except phenol, for this was used Physprop [20] Chapter 1. Acid dissociation constant 7

QSPR2methods [32–34]: These methods construct most commonly linear, but also nonlinear models for predicting a molecular property. The QSPR models describe the relations between the property of interest, and various indicators calculated based on the structure of the molecule. These indicators are referred to as descriptors (more in chapter 3). pKa correlates well with polarizability, HOMO energy [35], proton-transfer energy [35], partial atomic charges [12–15], the electrostatic potential of the molecule [36] etc..

However, pKa values remain one of the most challenging physicochemical properties to predict. A promising approach for pKa prediction is to use QSPR models which employ partial atomic charges as descriptors [12–15].

2Quantitave Structure-Property Relationship 2

Atomic charges

Partial atomic charges [37] are conceptual quantities assigned to every atom in a molecule to describe the electron density around any given atom. Partial charges result due to an asymmetric distribution of electrons in chemical bonds. When a neutral atom bonds chemically to a second neutral atom, but which is more electronegative (able to attract electrons), the electrons of the first atom tend to spend more time in the vicinity of the second atom. This leads to less electron density around the nucleus of the first (less electronegative) atom, creating a partial positive charge on this atom, while the second nucleus will be surrounded by more electron density, and thus the second atom will be assigned a partial negative charge. The molecular electron density can be determined by experiment or calculation, as it is related to many chemical properties, such as molecular dipole [16], electrostatic potential [16], chemical shift [16] in NMR (Nuclear magnetic resonance spectroscopy), X-ray diffraction [16] or EPR [16] (Electron paramagnetic resonance) etc.. The visualization of the molecular electron density and electrostatic potential is given in Figure 2.1. Since there is no unique (universally valid) way to define the boundaries of an atom which is part of a molecule, there is no unique way to measure the amount of electron density which belongs to each atom, and subsequently calculate its partial charge. Many different approaches have been developed to calculate partial atomic charges.

2.1 QM approaches for charge calculation

The most common approach for charge calculation is to apply quantum mechanics (QM) [16, 37], and subsequently employ a selected charge distribution scheme [37]. A disadvantage of this method is that it is very time-consuming. Its time complexity is at least θ(B4), where B is the number of basis functions used during the QM calculation. Therefore, B is greater than the number of electrons in the molecule.

– 8 – Chapter 2. Atomic charges 9

Figure 2.1: Examples of electron density visualization using electrostatic potential (left) and electron density map from X-ray (right).

2.1.1 Quantum mechanics

Systems having the size of a particle, an atom or a molecule (i.e., the microworld) cannot be described by classical Newtonian mechanics. The reason is Newtonian mechanics cannot handle special aspects of the microworld, speciﬁcally: quanti- zation of microparticle energy, Heisenberg’s uncertainty principle, wave-particle duality etc.. Therefore, the quantum theory [16, 37, 38] was developed to characterize the microworld. Quantum mechanics [16, 37, 38] provides a computational approach which describes molecular systems using the quantum theory. Quantum theory is based on the following principles [16]: Each physical system can be represented using a Hilbert space3. Each state of a system in a Hilbert space is fully described by a wavefunction ψ, which is a vector of this space. The wavefunction is the function ψ : R3 → R, whose domain is made up of coordinates of particles in a space. The range of ψ are real numbers whose squares describe the probability of occurrence of a particle in some point of space. The wavefunction can be obtained by solving the Schro¨dinger equation:

Hψ = Eψ (2.1) where E is the energy and H is the Hamiltonian operator. The Schro¨dinger equation is a second-order differential equation, whose solutions are pairs (ψ, E) ful- ﬁlling this equation.

3A Hilbert space is a full unitary vector space. Chapter 2. Atomic charges 10

An exact (analytical) solution of the Schro¨dinger equation is possible only for the hydrogen atom (a system with two particles). For the molecule, it is necessary to introduce approximations into this equation. Two types of approximation can be used – an approximation of the Hamiltonian operator and an approximation of the wavefunction. Well-known approximations of the Hamiltonian are the Born-Oppenheimer approximation, effective Hamiltonian approximation etc. A set of approximations used together as an approach for solving of the Schro¨dinger equation is called a theory level. Several theory levels were published, the most common are: Hartree-Fock (HF) method [16, 37, 38]: In this method, the Schro¨dinger equation is approximated via the system of Hartree-Fock equations:

Fiψi = εiψi (2.2) where Fi is the Fock operator of the electron i and represents an effective Hamil- tonian. ψi is the wavefunction of the electron i and εi is the Lagrangian multiplier of the electron i. The Hartree-Fock method is based on the following iterative process: First, a set of input solutions ψi of the Hartree-Fock equations is obtained. Afterwards, the Fock operators are calculated from these values. The Hartree-Fock equations with these Fock operators are solved and the new set of ψi values is obtained. These ψi values are used in the next iteration. HF method this way step by step refines the wavefunctions that correspond to lower and lower total energies. The process is repeated, until the energy values remain unchanged (self-consistent). Density functional theory (DFT) [37, 38]: Theory levels based on DFT oper- ate with electrons in terms of the electronic density distribution. DFT replaces the problem of solving the many electron Schro¨dinger equation by the problem of find- ing sufficiently accurate approximations to a universal functional of the electronic density. Particular examples of DFT theory levels are BLYP (named according its authors Becke, Lee, Yang and Parr), its extension B3LYP (BLYP combined with HF) and BP86 (gradient-corrected functional). The wavefunction is approximated by its representation using a basis set – a set of simple mathematical functions (i.e., Gaussian functions, Slater functions etc.). A lot of basis sets were published [39] and they differ in the type and number of basis functions. Examples of well-known basis sets are the following: STO-3G: This basis set approximates the wave function of each orbital by a set of three Gaussians4 and it is the simplest possible basis set. An analogous case is STO-nG. 6-31G: This notation means that each valence orbital5 is expressed by two sets of Gaussians (one with 3 Gaussians and the second with one Gaussian), while the other orbitals are expressed by one set of six Gaussians. Analogous cases are 3-21G, 6-311G, etc.. 6-31G*: The basis set is an extension of 6-31G, which has one more Gaussian

2 4Gaussian type functions - functions having the form e−α·r 5An orbital in an upper layer of an electronic shell. Chapter 2. Atomic charges 11

(called polarization function) to all atoms other than hydrogens (analogously all basis sets with *).

2.1.2 Charge distribution schemes

QM based charge calculation approaches can be divided in two main groups [37]: calculated directly from the wave function and calculated from the wave function and based on some physical observation. The first group uses some orbital-based scheme (population analysis, PA) for calculating the atomic charge from the wave function. The first scheme was proposed by Mulliken [40, 41], and this population analysis now bears his name. Within the Mulliken Population Analysis (MPA), the atomic charge for each atom is computed from the electron density in the single AO (atomic orbital) basis functions, together with half of the electron density shared with other atoms. Mulliken partial charges prove to be very sensitive to basis-set size, and thus a comparison among MPA charges calculated at different theory levels is impossible. Moreover, Mulliken charges have a tendency to become unphysically large as basis sets become larger. Another population analysis is Lo¨wdin PA [42]. This scheme requires the tranformation of AO basis functions into an orthonormal set of basis functions using a symmetric orthogonalization scheme. Then, it follows the same procedure as MPA. These partial atomic charges have higher basis-set stability than MPA. Nevertheless, even Lo¨wdin charges can become unstable with large basis sets. Natural population analysis (NPA) [43] is very similar to Lo¨wdin PA, but this PA uses more complicated orthogonalization. The electron density around each atom is initially rendered as compact as possible, and futher diagonalization is carried out to preserve the shape of the strongly occupied atomic orbitals to as large an extent as possible. Atomic charges produced by NPA effectively converge to a stable value with increasing basis-set size. AIM (atoms-in-molecules) [44] belongs to the second type of QM approaches, where the calculation is based also on some physical observation. This approach was developed by Bader and his co-workers, and it is based on the idea that electron density measured by X-ray can be used directly in the calculation of partial charges. In particular, an atomic volume is defined as that region of space including the nucleus, that lies within all zero-flux surfaces surrounding the nucleus (as can be seen in Figure 2.2). Then partial atomic charges are defined as the nuclear charge minus the total number of electrons residing within the atomic basin. In the Hirshfeld charge analysis [45], the total electron density is divided between the different atoms of a system according to a scheme which preserves the proportional contribution of each atom in its neutral state to the molecular electron density. One last group of QM-based charge calculation approaches is made up of MK [46] (Merz-Kollman, CHELP) and CHELPG [47] schemes based on fitting the partial charges to the molecular ESP (electrostatic potential). There is only a small Chapter 2. Atomic charges 12

Figure 2.2: Electron density gradient paths in a plane containing atoms of the HCN molecule. The solid lines are the intersections of the zero-ﬂux surface with the plane. The large black points are the bond critical points.

difference between these two methods. Such atomic charges have been found useful especially in modeling short to long range molecule-molecule interactions in molecular mechanics simulations [48].

2.2 Empirical approaches for charge calculation

Empirical approaches determine partial atomic charges without calculating a quantum mechanical wave function for the given molecule. Therefore they are markedly faster than QM approaches. One of the ﬁrst empirical approaches developed, CHARGE [49], performs a breakdown of the charge transmission by polar atoms into one-bond, two-bond, and three-bond additive contributions. Most of the other empirical approaches have been derived on the basis of the electronegativity equalization principle. One group of these empirical approaches invoke the Laplacian matrix formalism, and result in a redistribution of electronegativity. Such methods are PEOE (partial equalization of orbital electronegativity) [50], GDAC (geometry-dependent atomic charge) [51], KCM (Kirchhoff charge model) [52], DENR (dynamic electronegativity relaxation) [53] or TSEF (topologically symmetric energy function) [53]. The second group of approaches use full equalization of orbital electronegativity, and such approaches are, for example, EEM (electronegativity equalization method) [17], QEq (charge equilibration) [54] or SQE (split charge equilibration) [55]. The empirical atomic charge calculation approaches can also be divided into ’topological’ and ’geometrical’. Topological charges are calculated using the 2D structure of the molecule, and they are conformationally independent (i.e., CHARGE, PEOE, KCM, DENR, and Chapter 2. Atomic charges 13

TSEF). Geometrical charges are computed from the 3D structure of the molecule and they consider the inﬂuence of conformation (i.e., GDAC, EEM, Qeq, and SQE).

2.2.1 Electronegativity equalization method

EEM is very popular, and despite the fact that it was developed more than twenty years ago, new parameterizations [17, 56–62] and modiﬁcations [59, 63, 64] of EEM are still under development. The EEM method is a geometrical empirical charge calculation approach, and therefore EEM charges consider the inﬂuence of the molecule’s conformation on the atomic charges. For this reason, EEM charges are often used as chemoinformatics descriptors [65] and they are also promissing inputs for QSPR models. EEM is based on three principles: 1. Sanderson’s electronegativity equalization principle. According to this principle, the efective electronegativity of each atom in the molecule is considered to be equal to the molecular electronegativity χ¯:

χ1 = χ2 = ... = χN = χ¯ (2.3)

where χx is the efective electronegativity of the atom x. 2. The principle of the charge balance. The total charge Q of the molecule is equal to the sum of all atomic charges:

∑ qx = Q (2.4) x=1

where qx is the charge of the atom x. 3. The principle of the charge dependent electronegativity. This principle is the deﬁnition of the atomic electronegativity, and states that the electronegativity of each atom can be expressed as a function of its charge:

N qy χx = Ax + Bxqx + κ ∑ (2.5) y=1 x6=y Rxy

where Rxy is the distance between atoms x and y, and the coeﬁcients Ax, Bx and κ are empirical parameters. The previously described principles can be used to derivate a system of equations of the form

 κ κ  B1 ··· −1     R1,2 R1,N q1 −A1 κ κ  B2 ··· −1  −  R2,1 R2,N   q2   A2     .   .   ......  ·  .  =  .  (2.6)  . . . . .   .   .  κ κ      ··· B −1   qN   −AN   RN,1 RN,2 N  1 1 ··· 1 0 χ¯ Q Chapter 2. Atomic charges 14

This system of equations contains N + 1 equations with N + 1 unknowns: q1, q2,..., qN and χ¯. The values of parameters Ai, Bi and κ can be obtained from literature [17, 56–62] or by a new parametrization. The accuracy of EEM is comparable to the accuracy of the QM charge calculation approach for which it was parameterized. Additionally, EEM is very fast, as its computational complexity is θ(N3), where N is the number of atoms in the molecule. 3

QSPR

QSPR (Quantitative Structure-Property Relationship) [66, 67] models describe the relation between a property of interest and a structure, respectively, between the property and descriptors, which are indicators calculated from the structure. In other words, QSPR is a multidimensional function which quantiﬁes the relationship between the physicochemical property of interest and the characteristics of molecular structure. The main application of the QSPR models is the prediction of various properties. Nowadays, a huge amount of experimental and calculated data is available about the structure of small organic molecules and big biomolecules. Advanced computational methods and large clusters or clouds of high performance comput- ers allow to obtain huge sets of descriptors [66, 67]. Therefore, the QSPR models provide a fast and effective approach to estimate physicochemical properties of compounds. The best feature of these models is that they can be used for predicting sophisticated properties which can be obtained only by performing very demanding experiments or complicated calculations. The QSPR models are derived from the Quantitative Structure-Activity Relationship (QSAR) models [66], which are focused on estimating one speciﬁc property of a molecule – its biological activity. QSPR models are very often used in virtual screening, e.g. for designing new drugs [4].

3.1 Descriptors

Molecular descriptors [65, 66] are numerical values that are calculated from a structure of a molecule. They are frequently used in chemoinformatics, bioinformatics, chemistry, pharmaceutical research and quality control. The reason is, these values characterize the properties of molecules. Therefore they provide a straightforward approach on how to represent these properties in an algorithmically processable way.

– 15 – Chapter 3. Quantitative Structure-Property Relationship (QSPR) 16

Thousands of molecular descriptors have been developed for various applica- tions [65, 66]. The descriptors are frequently divided into 1D, 2D, or 3D descriptors, depending on the dimensionality of the molecular structure from which they were calculated [65, 66]. 1D descriptors. These descriptors are based on 1D structure of a molecule (i.e., the type of atoms which the molecule contains). An example of a 1D descriptor is a number of carbons, molecular weight, etc. 2D descriptors. The 2D descriptors incorporate the topology of the molecule. Such descriptors can be obtained using counting (e.g., count of some type of bonds) or graph algoritms (e.g., number of rings), or using some empirical approach (e.g., Gasteiger-Marsilli charges, logP, etc.). 3D descriptors. These descriptors include information about a location of atoms in 3D space. For their calculation one can use some measurement (e.g., length of some speciﬁc bond, distance between two atoms, some angles or dihedral angles, etc.), QM calculations (e.g., atomic charges, energy, etc.), or empirical calculations (e.g., EEM charges, etc.). A very important application of the descriptors is, they are inputs of QSPR models.

3.2 Parametrization of models

Before using QSPR to predict the value of a physicochemical property of interest, it is necessary to build a QSPR model. For creating the classical QSPR model, two conditions must be met. First, the physicochemical property of the molecule must be a function of its structure, and therefore also a function of the descriptors. Second, the relationship between the property and the descriptors must be linear. The ﬁrst condition is generally valid, although not all effects that are relevant for the molecular properties are directly related to the structure. The second premise clearly represents an approximation. Many structure-property relationships can be very well approximated by linear modeling, while others require the application of non-linear methods such as neural network (NN) simulations [68]. A QSPR model is a multidimensional function described by the equation:

P = c1D1 + c2D2 + ··· + cnDn + c (3.1) where P is the molecular property in linear relation with various descriptors Dx, with coefficients cx weighting their relative importance. Descriptors are often chosen based on knowledge or intuition. After the selection of the descriptors it is necessary to calculate the relevant coefficients. The coefficients are also called parameters, and the process of their calculation is denoted as the parameterization of the QSPR model. The parameters are calculated using training sets containing different molecules with known experimental values of the analyzed property. The multiple linear regression (MLR) [69] is a popular method to obtain applicable coefficients. Chapter 3. Quantitative Structure-Property Relationship (QSPR) 17

Table 3.1: Examples of descriptors classiﬁed according to dimensionality, demon- strated on the saccharin molecule.

Structure Representation of the molecule Descriptors

Number of nitrogen atoms 1D C H NO S 7 5 3 Molecular weight

Number of double and triple bonds

Number of rings 2D Gasteiger-Marsilli charges

logP

Distance between sulphur and nitrogen

Angles or dihedral angles 3D QM partial atomic charges

EEM charges Chapter 3. Quantitative Structure-Property Relationship (QSPR) 18 3.3 Validation of models

After a model has been obtained, it needs to be validated before its use for prediction, and the quality of the prediction needs to be evaluated. For this purpose of evaluating the quality of the model, the following indicators can be used: Pearson correlation coefficient (R) [69, 70] is widely used in science as a measure of the strength of the linear dependence between two variables. It’s defined as the covariance of the two variables divided by the product of their standard deviations: s N calc calc exp exp ∑ (P − P¯ ) · (Px − P¯x ) R = x=1 x x (3.2) N calc ¯calc 2 N exp ¯exp 2 ∑x=1(Px − Px ) · ∑x=1(Px − Px ) calc exp where Px is the calculated value of the property, and Px is the experimental ¯calc ¯exp calc exp value. Px , Px are average values of Px , respectively Px . The squared Pearson correlation coefficient, also called coefficient of determi- nation (R2) [69, 70], describes how well the regression line fits the data. If the regression line fits the data well, the value is close to 1, while if the fit is bad, the value is close to 0. Root mean square error (RMSE) [69, 70] is the normalized sum of squared errors, and provides us with an independent measure of the model’s reliability. RMSE can be calculated the following way: s epx ∑N (Pcalc − P )2 RMSE = x=1 x x (3.3) N

With respect to pKa prediction, the accuracy of a model is considered excellent if RMSE is smaller than about 0.5, and respectively sufﬁcient if RMSE is smaller than about 0.8 to 1. Average absolute error (∆¯ ) [69] is a quantity used to measure how close the predictions are to the possible outcomes. It is given by:

epx ∑N |Pcalc − P | ∆¯ = x=1 x x (3.4) N Standard deviation of the estimation (s) [69] evaluates the extent of the vari- ation of the predicted value from the expected value. A low standard deviation indicates that the data points tend to be very close to the expected value; high standard deviation indicates that the data points are spread out over a large range of values. s N · RMSE2 s = (3.5) N − k − 1 where N is the number of molecules in the set, and k is the number of descriptors in the model. Fisher’s statistics of the regression (F) [69, 70] is a statistical test in which the probability distribution is under the null hypothesis, and is meant to check Chapter 3. Quantitative Structure-Property Relationship (QSPR) 19 whether there is indeed a relationship between the sets of predicted values and the set of expected values. R2(N − k − 1) F = (3.6) k(1 − R2) This quality measurement (validation) can be performed on the training set, i.e., the set of molecules, corresponding descriptors and values for the property of interest, which have been used for creating the QSPR model. The validation step is used to obtain information about the suitability of the model, descriptors or potential outliers. However, if a model appears to be highly accurate in predicting correct values for the training set, it doesn’t necessarily mean that this model will be as accurate when used for predictions of the same property for molecules outside the training set. From this reason, it is necessary to perform a validation also on a testing set, i.e., an additional set of molecules (not included in the training set), along with the corresponding descriptors and experimentally determined values of the property of interest. Alternatively, it is possible do a cross-validation.

3.3.1 Cross-validation

Cross-validation [71, 72] is a validation technique used to analyze if and how the results from the validation step could be generalized to an independent data set. It can give an estimate regarding how accurately a predictive model will perform in practice. One round of cross-validation involves dividing a sample data set into several similar subsets. Then, the QSPR model is parameterized and validated on one subset (training set), and subsequent validations are done for all other subsets (validation sets). Multiple rounds of cross-validation are performed using different combinations of subsets, and the validation results are averaged over the rounds. k-fold cross-validation [71, 72] is a common cross-validation method where the original sample is randomly partitioned into k, equal sized, subsamples. One single subsample is chosen as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times (the folds), with each of the k subsamples being used exactly once as validation data. The k results from the folds are then averaged (or otherwise combined) to produce a single estimation. The advantage of this method over repeated random sub-sampling is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold or 5-fold cross-validation is commonly used, but in general k remains an unﬁxed parameter. Part III

Methods

– 20 – 4

Tools

4.1 NCI database

NCI database [73] is a database of molecules collected within the Developmental Therapeutics Program (DTP) of the National Cancer Institute. This database contains 260,071 structures in SDF format, with their 3D structure calculated by the program Corina [74], unique SMILES calculated by CACTVS according to Daylight’s original (1989) canonicalization rules, the IUPAC/NIST InChI chemical identiﬁer, IUPAC names generated with ACD/Name Batch, and additional helpful properties.

4.2 Physprop

The Physical Properties Database (PHYSPROP) [20] contains chemical structures, names, and physical properties (melting point, boiling point, water solubility, octanol-water partition coefﬁcient, vapor pressure, pKa, Henry’s Law Constant, and atmospheric OH rate constant) for over 41,000 chemicals. Physical properties are collected from experiment, or they were extrapolated or estimated.

4.3 Gaussian

Gaussian [75] is a software package for electronic structure modeling. Starting from the fundamental laws of quantum mechanics, Gaussian 09 predicts the energies, molecular structures, vibrational frequencies and molecular properties of molecules and reactions. Gaussian can be used for predicting spectra (NMR, op- tical or hyperﬁne spectra) or the calculation of thermochemistry, photochemistry or solvent effects.

– 21 – Chapter 4. Tools 22 4.4 AIMAll

AIMAll [76] is a software package for performing quantitative and visual QTAIM (Quantum Theory of Atoms in Molecules) analyses of molecular systems - starting from molecular wavefunction data.

4.5 EEM solver

EEM solver [77] is a software tool for the calculation of empirical atomic charges using the EEM approach. The program is able to read EEM parameters from an input ﬁle and therefore it can be used with any EEM parameter set. The program includes a serial version applicable for calculation of charges in organic molecules, and a parallel version which is able to calculate charges for proteins.

4.6 QSPR designer

This sophisticated web application [78] is dedicated for QSPR modeling. It is easy to use, and thus allows for a quick design and validation of QSPR models. This software was used for selecting descriptors and validation data.

4.7R

R[79] is a language and a software environment for statistical calculation and visualization. R provides a wide variety of statistical (linear and nonlinear mod- elling, classical statistical tests, time-series analysis, classiﬁcation, clustering, etc.) and graphical techniques, and is highly extensible. R was used for the calculation of all QSPR models and their cross-validation. Part IV

Results and discussion

– 23 – 5

Preparation of input data

5.1 Data sets

5.1.1 Data set for phenols

There are two main ways to create a QSPR model for a feature to be predicted. The first is to create as general a model as possible, with the risk that the accuracy of such a model may not be high. The second approach is to develop more models, each of them being dedicated to a certain class of compounds. Here we took the second approach, following a similar methodology as in previous studies [12–15]. Specifically, we focus on substituted phenols, because they are the most common test molecules employed in the evaluation of novel pKa prediction approaches [12– 15, 80–82]. Our data set contains the 3D structures of 74 distinct phenol molecules. This data set is of high structural diversity and it covers molecules with pKa values from 0.38 to 11.1. The molecules were obtained from the NCI Open Database Compounds [73] and their 3D structures were generated by CORINA 2.6 [74], without any further geometry optimization. Our data set is a subset of the phenol data set used in our previous work related to pKa prediction from QM atomic charges [15]. The subset is made up of phenols which contain only C, O, N and H, and none of the molecules contain triple bonds. This limitation is necessary, because the EEM parameters of all 18 studied EEM parameter sets are available only for such molecules (see Table 5.1). For each phenol molecule from our data set, we also prepared the structure of the dissociated form, where the hydrogen is missing from the phenolic OH group. This dissociated molecule was created by removing the hydrogen from the original structure without subsequent geometry optimization. The list of the molecules, including their NCS numbers, CAS numbers and experimental pKa values, can be found in the AppendixC (Table C.1). The SDF files with the 3D structures of molecules and their dissociated forms are on the attached CD.

– 24 – Chapter 5. Preparation of input data 25

5.1.2 Data set for carboxylic acids

An aspect which is very important for the applicability of the pKa prediction approach is its transferability to other chemical classes. In this work, we provide a case study showing the performance of the approach on carboxylic acids, which are also very common testing molecules for pKa prediction approaches [12, 33, 34, 83]. The data set contains 71 distinct molecules of carboxylic acids and their dissociated forms. The 3D structures of these molecules were obtained in the same way as for the phenols. The list of the molecules, including their NCS numbers, CAS numbers and experimental pKa values can be found in the AppendixC (Table C.2). The SDF ﬁles with the 3D structures of the molecules and their dissociated forms are included on the CD.

5.2p Ka values

The experimental pKa values were taken from the Physprop database [20].

5.3 Charge calculation

We calculated QM atomic charges for all the combinations of QM theory level, basis set and population analysis for which we have EEM parameters (see Ta- ble 5.1). Speciﬁcally, atomic charges were calculated for these eight QM approaches: HF/STO-3G/MPA, HF/6-31G*/MK, and B3LYP/6-31G* with MPA, NPA, Hirshfeld, MK, CHELPG and AIM). The QM charge calculations were carried out using Gaussian09 [75]. In the case of AIM population analysis, the output from Gaussian09 was further processed by the software package AIMAll [76]. The EEM charges were calculated by the program EEM SOLVER [77] using each of the 18 EEM parameter sets.

5.3.1 EEM parameter sets

In our study, we used all EEM parameters published till now. Speciﬁcally, we found 18 different EEM parameters sets, published in 8 different articles [17, 56–62]. The parameters cover two QM theory levels (HF and B3LYP), two basis sets (STO- 3G and 6-31G*) and six population analyses (MPA, NPA, Hirshfeld, MK, CHELPG, AIM). Unfortunately, only some combinations of QM theory levels, basis sets and population analyses are available. On the other hand, more parameter sets were published for some combinations (i.e., 6 parameter sets for HF/STO-3G/MPA). All the parameter sets include parameters for C, O, N and H. Some sets include also parameters for S, P, halogens and metals. Most of the sets do not include parameters for C and N bonded by triple bond. Summary information about all these parameter sets is given in Table 5.1. Chapter 5. Preparation of input data 26

Table 5.1: Summary information about the parameter sets used in the present study.

QM theory level PA Parameter set Published by Year of Elements + basis set name publication included HF/STO-3G MPA Svob2007 cbeg2 Svobodova et al. [56] 2007 C, O, N, H, S Svob2007 cmet2 Svobodova et al. [56] 2007 C, O, N, H, S, Fe, Zn Svob2007 chal2 Svobodova et al. [56] 2007 C, O, N, H, S, Br, Cl, I Svob2007 hm2 Svobodova et al. [56] 2007 C, O, N, H, S, F, Cl, Br, I, Fe, Zn Baek1991 Baekelandt et al. [57] 1991 C, O, N, H, P Al, Si Mort1986 Mortier et al. [17] 1986 C, O, N, H HF/6-31G* MK Jir2008 hf Jirouskova et al. [58] 2008 C, O, N, H, S, F, Cl, Br, I, Zn B3LYP/6-31G* MPA Chaves2006 Chaves et al. [59] 2006 C, O, N, H, F Bult2002 mul Bultinck et al. [60] 2002 C, O, N, H, F NPA Ouy2009 Ouyang et al. [61] 2009 C, O, N, H, F Ouy2009 elem Ouyang et al. [61] 2009 C, O, N, H, F Ouy2009 elemF Ouyang et al. [61] 2009 C, O, N, H, F Bult2002 npa Bultinck et al. [60] 2002 C, O, N, H, F Hir. Bult2002 hir Bultinck et al. [60] 2002 C, O, N, H, F MK Jir2008 mk Jirouskova et al. [58] 2008 C, O, N, H, S, F, Cl, Br, I, Zn Bult2002 mk Bultinck et al. [60] 2002 C, O, N, H, F CHELPG Bult2002 che Bultinck et al. [60] 2002 C, O, N, H, F AIM Bult2004 aim Bultinck et al. [62] 2004 C, O, N, H, F

5.3.2 QSPR model parameterization

The parameterization of the QSPR models was done by multiple linear regression (MLR). 6

Building QSPR models for phenols

6.1 Selection of descriptors

Our descriptors were atomic charges. We analyzed two types of QSPR models, namely QSPR models with three descriptors (3d QSPR models) and QSPR models with ﬁve descriptors (5d QSPR models). The 3d QSPR models used those descriptors which proved to be the most relevant for pKa prediction in our previous study [15]. Therefore these descriptors were the atomic charge of the hydrogen atom from the phenolic OH group (qH), the charge on the oxygen atom from the phenolic OH group (qO), and the charge on the carbon atom binding the phenolic OH group (qC1). These descriptors were used to establish the QSPR models by the general equation:

pKa = pH · qH + pO · qO + pC1 · qC1 + p (6.1)

where pH, pO, pC1 and p are parameters of the QSPR model (i.e., constants derived by multiple linear regression). The 5d QSPR models employ the above mentioned descriptors qH, qO and qC1 and additionally also the charge on the − phenoxide O from the dissociated molecule (qOD), and the charge on the carbon atom binding this oxygen (qC1D). Using the charges from the dissociated molecules for pKa prediction was inspired by the work of Dixon et al. [33]. The equation of the 5d QSPR models is therefore:

0 0 0 0 0 0 pKa = pH · qH + pO · qO + pC1 · qC1 + pOD · qOD + pC1D · qC1D + p (6.2) 0 0 0 0 0 0 where pH, pO, pC1, pOD, pC1D and p are parameters of the QSPR model. 6.2 Models

We prepared one 3d QSPR model and one 5d QSPR model using atomic charges calculated by each of the above mentioned 18 EEM parameter sets. These models

– 27 – Chapter 6. Building QSPR models for phenols 28 are denoted 3d or 5d EEM QSPR models. Additionally, we created one 3d and one 5d QSPR model using atomic charges calculated by each of the corresponding 8 QM charge calculation approaches (denoted as 3d or 5d QM QSPR models). The data set of 74 phenol molecules was used for the parameterization of the QSPR models, and the obtained models were validated for all molecules in the data set. The parameterization of the 3d EEM QSPR models showed that several molecules in the data set perform as outliers. For this reason, we created also EEM QSPR models without outliers (i.e., EEM QSPR models for which parameterization was done using a data set that excluded the previously observed outliers). These models are denoted 3d EEM QSPR WO models. We classified as outliers 10% of the molecules from our data set, which had the highest Cook’s square distance [84, 85]. Therefore the 3d EEM QSPR WO models were parameterized using 67 molecules, and their validation was also done on the data set excluding outliers. The quality of the QSPR models, i.e. the correlation between experimental pKa and the pKa calculated by each model, was evaluated using the squared Pearson correlation coefficient (R2), root mean square error (RMSE), and average absolute pKa error (∆), while the statistical criteria were the standard deviation of the estimation (s) and Fisher’s statistics of the regression (F). Table 6.1 contains the quality criteria (R2, RMSE, ∆) and statistical criteria (s and F) for all the QSPR models analyzed. All these models are statistically significant at p = 0.01. Since our data sets contained 74 and 67 molecules, respectively, the appropriate F value to consider was that for 60 samples. Thus, the 3d QSPR models are statistically significant (at p = 0.01) when F > 4.126 and the 5d QSPR models when F > 3.339. Table 6.2 summarizes the R2 of all QSPR models for ease of visual comparison, and Tables 6.3 and 6.4 provide a comparison of the models from specific points of view. The parameters of the QSPR models are summarized on the CD. The most relevant graphs of correlation between experimental and calculated pKa are visualized in Figure 6.1.

6.2.1 Prediction of pKa using EEM charges The key question we wanted to answer is whether EEM QSPR models are applicable for pKa prediction. For this purpose we selected a set of phenol molecules and generated QSPR models which used EEM atomic charges as descriptors. We then evaluated the accuracy of these models by comparing the predicted pKa values with the experimental ones. The results (see Tables 6.1, 6.2 and 6.3) clearly show that QSPR models based on EEM charges are indeed able to predict the pKa of phenols with very good accuracy. Namely, 63% of the EEM QSPR models evaluated 2 2 in this study were able to predict pKa with R > 0.9. The average R for all 54 EEM QSPR models considered was 0.9, while the best EEM QSPR model reached R2 = 0.924. Our ﬁndings thus suggest that EEM atomic charges may prove as efﬁcient QSPR descriptors for pKa prediction. The only drawback of EEM is that EEM parameters are currently not available for some types of atoms. Nevertheless, EEM parameterization is still a topic of research, therefore more general parameter sets are being developed. Chapter 6. Building QSPR models for phenols 29

Figure 6.1: Correlation graphs. Graphs showing the correlation between experimental and calculated pKa for selected QSPR models.

HF/STO-3G/MPA/3d B3LYP/6-31G*/MPA/3d B3LYP/6-31G*/NPA/3d B3LYP/6-31G*/MK/3d 12 12 12 12

10 10 10 10

8 8 8 8

6 6 6 6