Ab Initio Search for Novel Bxhy Building Blocks with Potential for Hydrogen Storage

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12-2010

Ab Initio Search for Novel BxHy Building Blocks with Potential for Hydrogen Storage

Jared K. Olson Utah State University

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This Dissertation is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. AB INITIO SEARCH FOR NOVEL BXHY BUILDING BLOCKS WITH POTENTIAL

FOR HYDROGEN STORAGE

Jared K. Olson

A dissertation submitted in partial fulfillment of the requirements for the degree

DOCTOR OF PHILOSOPHY

Chemistry (Physical Chemistry)

Approved:

Dr. Alexander I. Boldyrev Dr. Steve Scheiner Major Professor Committee Member

Dr. David Farrelly Dr. Stephen Bialkowski Committee Member Committee Member

Dr. T.C. Shen Byron Burnham Committee Member Dean of Graduate Studies

UTAH STATE UNIVERSITY Logan, Utah

2010

iii

ABSTRACT

Ab Initio Search for Novel BxHy Building Blocks with Potential for Hydrogen Storage

Jared K. Olson, Doctor of Philosophy

Utah State University, 2010

Major Professor: Dr. Alexander I. Boldyrev Department: Chemistry and Biochemistry

On-board hydrogen storage presents a challenging barrier to the use of hydrogen

as an energy source because the performance of current storage materials falls short of

platform requirements. Because boron is one of the lightest chemical elements that can

form strong covalent bonds with hydrogen, it provides an excellent opportunity to design

new lightweight materials on the basis of novel boron hydride building blocks. Realizing

this potential requires an understanding of the electronic structure, chemical bonding, and

stability of neutral and anionic BxHy clusters with variable stoichiometry. While a large

number of boron hydride compounds are known, there are still entire classes of yet

unknown neutral and anionic BxHy clusters and molecules with various new x/y ratios

which may be good candidates for hydrogen storage or as intermediates of borane de-

hydrogenation. The primary aim of this dissertation was to search for neutral and anionic

BxHy clusters that are thermochemically stable towards hydrogen release and to understand the chemical bonding in these novel clusters. These goals were accomplished

by performing an unbiased search for neutral and anionic global minimum BxHy clusters using ab initio methods.

In addition to finding a rich variety of new neutral and anionic BxHy (x = 3 – 6

and y = 4 – 7) clusters that could be building blocks for novel hydrogen-boron materials

during the course of conducting this research, optical isomerism was discovered in select

neutral and anionic boron-hydride clusters. Furthermore, the transition from planar to 3-

- dimensional geometries in global minimum B6Hx clusters was discovered using ab initio

techniques during this study. Chemical bonding analysis using the AdNDP method was

performed for all global minimum structures and low-lying isomers. The chemical

bonding pattern recovered by the AdNDP method in all cases is consistent with the

geometric structure. The theoretical vertical detachment energies presented in this

dissertation may help interpret future photoelectron spectroscopic studies of the anions presented here.

(106 pages)

DEDICATION

To Shirlene, Olivia, and Aidan.

ACKNOWLEDGMENTS

I express my sincere gratitude to my advisor, Professor Alexander I. Boldyrev, for all I have learned from him throughout my tenure as a graduate student at Utah State

University. He helped me greatly to develop my skills in quantum chemistry, to master the methodology of successful research, and to gain a deep appreciation for the tenacity required to perform such research.

I thank all the members of my supervisory committee: Dr. Steve Scheiner, Dr.

David Farrelly, Dr. Stephen Bialkowski, and Dr. T.C. Shen. I appreciate their support, encouragement, and openness for questions and discussions, which greatly influenced my progress and professional growth. I express my gratitude to Dr. Boldyrev and the

committee for the patience and flexibility they exercised in facilitating my studies here.

I express my deep appreciation for my wife, Shirlene, for her love and patience during the last several years. I thank Brent H. Larsen, Nathan Seidner, Dr. Sarah Hiza,

Dr. Daniel Doll, Dr. James Burns, and Dr. Robert Wardle at ATK Launch Systems for

their encouragement and support during my studies at Utah State University. I also thank my parents for their encouragement.

This theoretical work was supported partially by the National Science Foundation

(CHE-0714851). Computer time from the Center for High Performance Computing at

Utah State University is gratefully acknowledged. The computational resource, the Uinta

cluster supercomputer, was provided through the National Science Foundation under

Grant CTS-0321170 with matching funds provided by Utah State University. An

vii

allocation of computer time from the Center for High Performance Computing at the

University of Utah is also gratefully acknowledged.

Jared K. Olson

viii

CONTENTS

Page

ABSTRACT ...... iii

DEDICATION ...... v

ACKNOWLEDGMENTS ...... vi

LIST OF TABLES ...... x

LIST OF FIGURES ...... xi

CHAPTER

1. INTRODUCTION ...... 1

1-1. Background ...... 1 1-2. Specific Goals ...... 1 1-3. Motivation ...... 2 1-4. Relevant Prior Work ...... 2 1-5. Theoretical Methods ...... 6 1-6. References ...... 9

2. AB INITIO SEARCH FOR GLOBAL MINIMUM STRUCTURES OF THE NOVEL B3HY (Y=4-7) NEUTRAL AND ANIONIC CLUSTERS...... 17

Abstract ...... 17 2-1. Introduction ...... 17 2-2. Computational Details ...... 20 2-3. Computational Results ...... 22 - 2-4. Chemical Bonding in B3Hx and B3Hx (x=4-7) Species ...... 26 2-5. Conclusions ...... 34 2-6. References ...... 34

3. AB INITIO SEARCH FOR GLOBAL MINIMUM STRUCTURES OF NEUTRAL AND ANIONIC B4H4 CLUSTERS ...... 40

Abstract ...... 40 3-1. Introduction ...... 40 3-2. Computational Details ...... 41 3-3. Results and Discussion ...... 43 3-4. Summary and Conclusions ...... 50

3-5. References ...... 50

4. AB INITIO SEARCH FOR GLOBAL MINIMUM STRUCTURES OF NEUTRAL AND ANIONIC B4H5 CLUSTERS ...... 57

Abstract ...... 57 4-1. Computational Details ...... 57 4-2. Results and Discussion ...... 58 4-3. Conclusions ...... 64 4-4. References ...... 65

5. AB INITIO DISCOVERY OF THE PLANAR TO 3-DIMENSIONAL - TRANSITION IN B6HX CLUSTERS ...... 68

Abstract ...... 68 5-1. Computational Details ...... 69 5-2. Results and Discussion ...... 70 5-3. Conclusions ...... 77 5-4. References ...... 78

6. SUMMARY ...... 81

6-1. Summary ...... 81 6-2. References ...... 83

APPENDIX ...... 84

CURRICULUM VITAE ...... 91

LIST OF TABLES

Table Page

2-1. Spectroscopic states, electronic configurations, and relative energies of each - isomer for each of the neutral B3Hy and anionic B3Hy (y=4-7) species ...... 25

- 2-2. Stability of B3Hy and B3Hy (y=5-7) species towards H2 release ...... 27

- 2-3. Bonds recovered by the AdNDP analysis for the selected isomers of B3 and - B3H4 ...... 28

2-4. Bonds recovered by the AdNDP analysis for the selected isomers of B3H5 and - B3H5 ...... 29

2-5. Bonds recovered by the AdNDP analysis for the selected isomers of B3H6...... 30

- 2-6. Bonds recovered by the AdNDP analysis for the selected isomers of B3H6 ...... 31

2-7. Bonds recovered by the AdNDP analysis for the selected isomers of B3H7 and - B3H7 ...... 32

- 3-1. Theoretical Photoelectron Spectrum for structures IV and V of B4H4 ...... 45

- 4-1. Theoretical Photoelectron Spectrum for structure IX of B4H5 ...... 61

- 5-1. Theoretical Photoelectron Spectrum for isomers of B6Hx ...... 72

- 6-1. Stability of BxHy and BxHy (x=3, 4, 6; y=2-7) species towards H2 release ...... 82

LIST OF FIGURES

Figure Page

1-1. Schematic view of a laser vaporization magnetic-bottled PES apparatus ...... 5

1-2. Logic flow diagram for ab initio study methodology ...... 7

1-3. Logic flow diagram for the GEGA algorithm ...... 8

1-4. Logic flow diagram for the Coalescence Kick program ...... 8

- 2-1. The lowest energy isomers for neutral B3Hy and anionic B3Hy (y=4-5) species ...... 23

- 2-2. The lowest energy isomers for neutral B3Hy and anionic B3Hy (y=6-7) species ...... 24

- 3-1. Lowest isomers for B4H4 and B4H4 with their symmetry, spectroscopic state and relative energies at the CCSD(T) infinite basis set extrapolation in the square brackets, at the CCSD(T)/6-311++G** in curly brackets, at the MP2/6-311++G** in parentheses, otherwise at B3LYP/6-311++G**...... 44

3-2. Bonds recovered by the AdNDP analysis for B4H4 isomer I ...... 47

3-3. Bonds recovered by the AdNDP analysis for B4H4 isomer I ...... 47

3-4. Bonds recovered by the AdNDP analysis for B4H4 isomer III ...... 47

- 3-5. Bonds recovered by the AdNDP analysis for B4H4 isomer IV. AdNDP analysis 2- was performed for the doubly charged anion B4H4 at the optimal geometry of - isomers IV of B4H4 ...... 49

- 3-6. Bonds recovered by the AdNDP analysis for B4H4 isomer V. AdNDP analysis 2- was performed for the doubly charged anion B4H4 at the optimal geometry of - isomers V of B4H4 ...... 49

4-1. Lowest isomers for B4H5 with their symmetry, spectroscopic state and relative energies at the B3LYP/6-311++G** level of theory ...... 59

- 4-2. Lowest isomers for B4H5 with their symmetry, spectroscopic state and relative energies at the at B3LYP/6-311++G** level of theory...... 60

xii

4-3. Bonds recovered by the AdNDP analysis for B4H5 isomer I. AdNDP analysis was - performed for the B4H5 anion at the optimal geometry of isomer I of B4H5 ...... 62

4-4. Bonds recovered by the AdNDP analysis for B4H5 isomer III. AdNDP - analysis was performed for the B4H5 anion at the optimal geometry of isomer I of B4H5 ...... 63

4-5. Bonds recovered by the AdNDP analysis for B4H5 isomer IX ...... 64

- 5-1. Lowest isomers for B6H2 with their symmetry, spectroscopic state and relative energies at the CCSD(T) infinite basis set extrapolation in curly brackets, at the CCSD(T)/6-311++G** in parentheses, otherwise at B3LYP/6-311++G** ...... 70

- 5-2. Lowest isomers for B6H3 with their symmetry, spectroscopic state and relative energies at the B3LYP/6-311++G** level of theory ...... 71

- 5-3. Lowest isomers for B6H4 with their symmetry, spectroscopic state and relative energies at the CCSD(T)/6-311G++** level of theory in parenthesis, otherwise at the B3LYP/6-311++G** level of theory ...... 71

- 5-4. Bonds recovered by the AdNDP analysis for B6H2 isomer I. AdNDP analysis - was performed for the doubly charged B6H2 anion at the optimal geometry of - isomer I of B6H2 ...... 73

- 5-5. Bonds recovered by the AdNDP analysis for B6H3 isomer III ...... 74

- 5-6. Bonds recovered by the AdNDP analysis for B6H3 isomer V ...... 75

- 5-7. Bonds recovered by the AdNDP analysis for B6H4 isomer VIII. AdNDP analysis 2- was performed for the doubly charged B6H4 anion at the optimal geometry of - isomer VIII of B6H4 ...... 76

CHAPTER 1

INTRODUCTION

1-1. Background

Boron is the lightest atom that can form strong covalent bonds with hydrogen and thus provides excellent opportunities to design new light-weight materials on the basis of

BxHy clusters with a potential for high hydrogen storage capacity needed for

transportation applications. In order to realize this possibility, one needs to first

understand the electronic structure, chemical bonding, and stability of the BxHy clusters.

1 2 3-7 Borohydride compounds such as LiBH4, NH4BH4(NH2)3, NH4BH4 and NH3BH3

have been extensively studied with regard to their potential hydrogen storage properties.

Boron and hydrogen also form a wide variety of three-dimensional compounds such as

the famous closo-boranes and their numerous derivatives with a lesser degree of

hydrogenation than the borohydrides mentioned above. Even though a large number of

boron-hydrogen compounds are known, there are still entire classes of yet unknown BxHy clusters and molecules with various new x/y ratios which may be good candidates for hydrogen storage.

1-2. Specific Goals

The major goals of this dissertation were to provide a fundamental understanding

0/-1 of the structures and chemical bonding in BxHy clusters and to discover new boron-

hydride-based chemical building blocks for potential hydrogen storage materials. These

goals were accomplished through the theoretical study of neutral and anionic BxHy clusters with systematically varied stoichiometries for x = 3, 4, and 6 and y = 4 – 7.

1-3. Motivation

The Report of DOE’s Basic Energy Sciences Workshop on Hydrogen Production,

Storage, and Use (May 13-15, 2003) states:

On-board hydrogen storage is considered to be one of the most challenging barriers to the widespread use of hydrogen because the performance of current hydrogen storage materials and technologies fall far short of vehicle requirements. Research is needed to develop and examine new materials and obtain an atomic- and molecular-level understanding of the physical and chemical processes involved in hydrogen storage and release. These novel storage materials may fall outside of the hydrogen-storage materials that are currently under investigation. 8

Other systems such as ammonia-borane or metal hydrides do not meet the DOE’s

goals, so the motivation of this dissertation was to discover new boron-hydride compounds or building blocks which are different from known compounds based on

- 2- BH3, BH4 or BnHn species that may be useful for hydrogen storage and release and may

be attractive because of the light weights and high hydrogen storage capacities of boron-

hydrogen systems. This motivation led to the generating a large number of clusters from which hydrogen release energies could be calculated, chemical bonding could be studied, and meaningful conclusions could be drawn about the potential for some of these clusters to be used for hydrogen storage.

1-4. Relevant Prior Work

Very limited works on new BxHy structural units have been carried out previously.

In 2003, Boldyrev and co-workers predicted theoretically a new family of planar

9,10 6- + aromatic and highly charged boranes, such as B6H6 stabilized by six Li cations. An

extended analysis of the chemical bonding in the lowest energy planar and non-planar

6- 9,10 6- isomers involving B6H6 has been performed. The planar B6H6 species can be

viewed as a benzene analog. Boron possesses one less valence electron than carbon.

Thus, a B- anion becomes isoelectronic to a C atom, which underlies the graphite-like

6- network of B in MgB2 and the benzene-like properties of B6H6 . Salts like Li6B6H6 with

6- 11-13 the B6H6 benzene-like unit remain a theoretical prediction. Fehlner and co-workers

have reported synthesis and crystal structures of two remarkable triple-deck

(Cp*ReH2)B5Cl5 and (Cp*)2B6H4Cl2 compounds containing planar B5Cl5 and B6H4Cl2 structural fragments, respectively. It is believed that the planar B5Cl5 and B6H4Cl2 structural fragments in Fehlner’s compounds acquire six electrons from the Re atom formally and thus become six -electron aromatic compounds similar to the predicted

6- 6- B5H5 and B6H6 building blocks in the Li6B5H5 and Li6B6H6 salt molecules. Fehlner

and co-workers also reported synthesis and characterization of a variety of new

11 12 compounds containing novel structural groups such as B3H7, B4H7 and B4H8, and

13 B4H11, with highly unusual B:H stoichiometries, thus showing that there are indeed still

many new undiscovered structural units with almost continuous B:H ratios.

0/-1 There have been few prior experimental studies on BxHy type clusters in the gas

phase with the only relevant work being done by Anderson and co-workers, who studied

+ 14 the dynamics of Bx cluster (x = 1 – 16) reactions with D2. They observed the

+ + + formation of BxD and D2 adducts, Bx ( D2), and estimated the Bx –D bond energies. This

work stimulated a theoretical study by Ricca and Bauschlicher, who calculated the

+ + 15 structures of BxH (x = 1 – 13) and the Hx –D bond energies. They found that the

+ + structures of the BxH clusters are similar to the bare Bx clusters with the H atom

+ bonded to the edge of planar or quasi-planar Bx clusters.

Extensive experimental work has been performed to validate other systems that

were predicted using methods similar to those used in this dissertation and laser

vaporization/photoelectron spectroscopy (PES). A schematic diagram of a laser

vaporization magnetic-bottled PES apparatus is included as Figure 1-1 for reference.

Briefly, anionic clusters can be produced by laser vaporization of target materials of

interest in the presence of a helium carrier gas containing H2. Clusters are formed via the

reaction of the gas and the target material in a laser-induced plasma. Clusters formed in

the nozzle (see Figure 1-1) are entrained in the helium carrier gas, which undergoes a

supersonic expansion to form a cluster beam. After passing a skimmer to form a

collimated beam, negatively charged clusters are extracted perpendicularly into a time-of- flight mass spectrometer for mass separation. Clusters of interest can be selected via a mass gate and decelerated before being crossed by a laser beam in the interaction zone of the magnetic-bottle PES spectrometer for photodetachment. Photoemitted electrons are collected by the magnetic bottle where time-of-flight spectra are collected and converted into kinetic energy (KE) spectra. The electron binding energy (BE) spectra are obtained by subtracting the KE spectra from the photon energy (h) using Einstein’s photoelectric equation: BE = h – KE.

Figure 1-1. Schematic view of a laser vaporization magnetic-bottled PES apparatus.

Using theoretical methods similar to those used in this dissertation and laser vaporization/(PES) method described above, the Boldyrev and Wang groups experimentally produced and confirmed the first 5-atom tetra-coordinated planar carbon molecules,16-18 discovered the first all-metal aromatic and antiaromatic clusters,19-24 and elucidated the structures and chemical bonding of boron clustters.25-34 Recent success in

- generating a series of AlxHy clusters in a molecuular beam and obtaining their

35-40 - photoelectron spectra by Bowen and co-workers opens a possibility of making BxHy under similar conditions. Experimental studies on the decomposition of LLiBH4 and

41-44 44 Mg(BH4)2 byy Orimo and co-workers and Her and co-workers have produced the

2- stable B12H12 cluster. An understanding of the methods used in references 41-44 could lead to synthetic methods for producing the borohydrides presented here in bulk quantities.

1-5. Theoretical Methods

A logic flow diagram for the ab initio study methodology employed here is

included as Figure 1-2. For each given neutral or anionic BxHy species, an unbiased

search was performed for the global minima of that species using the hybrid density

functional method known as B3LYP45-47 with small split-valence basis sets (3-21G) for energy, gradient, and force calculations. Geometries were then re-optimized and frequencies were calculated for the lowest energy structures using B3LYP with polarized split-valence basis sets (6-311++G**).48-50 Following this re-optimization, for the few

lowest structures found at the B3LYP/6-311++G** level of theory, we re-optimized

geometries and calculated harmonic frequencies at the second order Moller-Plesset

perturbation theory (MP2)51-53 and coupled-cluster with single, double, and non-iterative

triple excitations method [CCSD(T)]54-56 using the 6-311++G** basis set for both

calculations. A detailed discussion of these methods can be found in references 57-61.

Energies of these lowest energy isomers were also recalculated by extrapolating to the

infinite basis set at the CCSD(T) level of theory as proposed by Truhlar and co-

workers.62-63 Following these energy calculations, chemical bonding was analyzed for all

global minimum and low lying isomers, and vertical detachment energies were calculated

for the lowest isomers. All ab initio calculations were performed using the Gaussian 03

pacakge.64 Molecular visualization was performed using the MOLDEN3.4 program,65

and chemical bonding visualization was completed using the MOLEKEL 4.3 program.66

The gradient embedded genetic algorithm (GEGA) program written by A. N.

Alexandrova67,68 and the coalescence kick (CK) program written by B. B. Averkiev69,70

7 were used to conduct the unbiased search for global minimum structures. Logic flow diagrams for these methods are included as Figures 1-3 and 1-4.

Chemical bonding analysis for structures studied in this dissertation was completed using the Adaptive Natural Density Partitioning (AdNDP) method developed byy Zubarev and Boldyrev.71-73 The AdNDP analysis is based on the concept of electron pairs as the main elements of chemical bonding, is an extension of NBO analysis,74-75 and provides is unbiased as no preliminary concept of the bonding pattern is required to perform the analysis. Where NBO represents electronic structure in terms of 2-centeer-2- electron (2c-2e) and 3-center-3-electron (3c-2e) bonds, AdNDP represents the electronic structure in terms of n-center–two-electron (nc-2e) bonds with n ranging from one to the total number of atoms in the whole cluster. AdNDP recovers both Lewis bonding elements (1c-2e or 2c-2e objects, i.e., lone pairs or two-center two-electron bonds) and delocalized bonding elements, which are associated with the concepts of aromaticity.

Figure 1-2. Logic flow diagram for ab initio study methodology.

Figure 1-3. Logic flow diagram for the GEGA algorithm.

Figure 1-4. Logic flow diagram for the Coalescennce Kick program

- Chapter 2 presents B3Hx and B3Hx (x = 4-7) structures identified using the GEGA

algorithm, discusses their stability towards hydrogen release, and discusses chemical

bonding in these structures by discussing bonds recovered by AdNDP analysis.

Chapter 3 presents the global and lowest local minimum structures for neutral and anionic B4H4 identified using the Coalescence Kick method. Bonds recovered by

AdNDP analysis are discussed, and theoretical VDEs are presented with the goal of

- helping to interpret future photoelectron spectroscopic studies of the B4H4 anion.

Chapter 4 presents similar data for neutral and anionic B4H5 clusters identified

using the Coalescence Kick method.

- Chapter 5 presents the discovery of the 2D-3D transition in B6Hx clusters

identified using the Coalescence Kick method, discusses chemical bonding through

bonds recovered by AdNDP analysis, presents theoretical VDEs to help interpret future

- photoelectron spectroscopic studies of the B6Hx clusters, and discloses the theoretical

discovery of optical isomerism in these inorganic clusters.

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CHAPTER 2

AB INITIO SEARCH FOR GLOBAL MINIMUM STRUCTURES OF THE NOVEL

B3HY (Y=4-7) NEUTRAL AND ANIONIC CLUSTERS*

Abstract

We sampled potential energy surfaces of neutral and anionic B3Hy clusters using

the Gradient Embedded Genetic Algorithm (GEGA) program at the B3LYP/3-21G level

of theory. The lowest energy isomers were recalculated at the B3LYP/6-311++G**,

MP2/6-311++G**, and CCSD(T)/6-311++G** levels of theory. We found a diverse set

of global minimum structures and low-lying isomers for the studied clusters. The

Adaptive Natural Density Partitioning (AdNDP) method was then used for chemical

bonding analysis for all global minimum structures and low-lying isomers. The chemical

bonding patterns revealed by the AdNDP analysis can easily explain the geometric

structure of even very exotic isomers and global minima.

2-1. Introduction

Boron is one of the lightest chemical elements that can form strong covalent

bonds with hydrogen, and thus provides excellent opportunities to design new light-

weight materials on the basis of novel boron hydride building blocks, in the form of

0/n+/n– BxHy clusters with a potential for high hydrogen storage capacity. To realize this

potential requires an understanding of the electronic structure, chemical bonding, and

0/n+/n– stability of the BxHy clusters with variable stoichiometry. Boron hydride

compounds such as LiBH4, Li4BH4(NH2)3, NH4BH4, NH3BH3, NH2BH2, and NH3B3H7

have been studied extensively with regard to their potential hydrogen storage

properties.1-11 Boron and hydrogen also form a wide variety of three-dimensional compounds such as the well known deltahedral boranes and their numerous derivatives with a lesser degree of hydrogenation than the above mentioned borohydrides.12-16 While

a large number of boron hydride compounds are known, there are still entire classes of

0/n+/n– yet unknown BxHy clusters and molecules with various new x/y ratios which may be

good candidates for hydrogen storage or as intermediates of borane de-hydrogenation.

Very limited work on new BxHy structural units has been carried out previously.

Fehlner and co-workers17-19 have reported synthesis and crystal structures of two

remarkable triple-deck (Cp*ReH2)B5Cl5 and (Cp*)2B6H4Cl2 compounds containing

planar B5Cl5 and B6H4Cl2 structural fragments, respectively. It is believed that the planar

B5Cl5 and B6H4Cl2 structural fragments in Fehlner’s compounds acquire six electrons

from the Re atom formally and thus become six p-electron aromatic compounds similar

6– 6– to the predicted B5H5 and B6H6 building blocks in the Li6B5H5 and Li6B6H6 salt

molecules.20,21 Fehlner and co-workers also reported the synthesis and characterization

17 of a variety of new compounds containing novel structural groups such as B3H7, B4H7

18 19 and B4H8, and B4H11, with highly unusual B:H stoichiometries. Surprisingly, there

0/n+/n– have been few prior experimental works on BxHy type clusters in the gas phase. To the best of our knowledge, the only relevant work is by Anderson et al., who studied the

+ 22 dynamics of Bx cluster (x = 1–16) reactions with D2. Among the various reaction

+ + channels, they observed the formation of BxD and D2 adducts, Bx (D2), and estimated

+ the Bx –D bond energies. Interactions of the B3 cluster with H atoms and H2 molecules

have been studied by Hernandez and Simons.23 This work stimulated a theoretical study

+ by Ricca and Bauschlicher, who calculated the structures of BxH (x = 1–13) and the

+ 24 + Bx –H bond energies. Interestingly, they found that the structures of the BxH clusters

+ are similar to the bare Bx clusters with the H atom bonded to the edge of planar or quasi-

+ 25 planar Bx clusters. Alexandrova et al. performed a global minimum structure search

- and rationalized chemical bonding in terms of aromaticity/antiaromaticity in the B7H2 cluster anion. Alexandrova et al.26 also studied series of boron-hydrogen anions

analogous to planar aromatic hydrocarbons. A few groups have previously studied the

27-30 B3H7 cluster. Five different isomers were found in early theoretical studies with

geometry optimization at the Hartree-Fock level with small basis sets.27 In follow up

studies,28-30 high-level calculations were performed for one,28 two,29 or three30 isomers of

B3H7.

There are still many new undiscovered structural units with almost continuous

B:H ratios. The non-stoichiometric and non-conventional boron hydride clusters with

0/-1 three boron atoms and variable number of hydrogen atoms B3Hy will be the main focus of the research presented in this paper. Counter cations may affect the relative stability of

- the corresponding anionic B3Hy isomers. In this article, however, we will concentrate on

the intrinsic properties of these anions free of such influence. We believe that

- understanding the structure, stability and bonding of bare B3Hy anions is an important

first step in predicting novel boron-hydrogen species. We plan to study the influence on

- B3Hy from counter cations in our future works.

2-2. Computational Details

- We initially performed searches for the global minimum of B3Hy and B3Hy

(y=4-7) using our gradient embedded genetic algorithm (GEGA) program written by A.

N. Alexandrova.31,32 Briefly, within the GEGA procedure, the initial geometries of

individuals in a population are randomly generated and optimized to the nearest local

minima on the potential energy surface using the Gaussian 03 package. If a saddle point is encountered, the normal mode of the first imaginary frequency is followed until a local minimum is found. Further, the population, composed of the thus selected good individuals, undergoes breeding and mutations. Probabilities to be bred are assigned according to the best-fit (lowest-energy) criterion. Based on the probabilities, couples of parents are randomly selected. The geometries of parents are cut by a random cutting plane, and the newly obtained halves (genes) are then recombined either in a simple or head-to-tail manner forming a child. The number of atoms in the newly generated geometry is checked, and the child is optimized to the nearest local minimum. After the number of individuals in the population is doubled within the breeding process, the best-

fit group is selected and convergence of the algorithm is checked. GEGA is considered

as converged if the current lowest energy species (global minimum or at least very stable

local minimum) remains leading for 20 iterations. If the convergence is not yet met, the

highest energy species in the population undergo mutations. The mutation rate is set to

33.33%. Mutations are shifts of random atoms of a species in random directions, with the

purpose of changing the initial geometry so as to push the structure out of the current

local minimum to another well on the potential energy surface. Mutants are then

optimized to the nearest local minima. After this optimization, the algorithm proceeds

with the new cycle of breeding. All low-lying isomers are detected and stored throughout the execution of the GEGA algorithm and are reported to the user at the end of the run. A

few runs of GEGA are done on the system of interest in order to confirm the global

minimum structure which is discovered. A more complete description of the GEGA algorithm is contained in reference 31.

For the global minimum search, we used a hybrid method known as B3LYP33-35

with small split-valence basis sets (3-21G) for energy, gradient, and force calculations.

Geometries were then re-optimized and frequencies were calculated for the lowest energy structures using B3LYP with polarized split-valence basis sets (6-311++G**).36-38

Following this re-optimization, for the few lowest structures found at the

B3LYP/6-311++G** level of theory, we re-optimized geometries and calculated harmonic frequencies at the second order Moller-Plesset perturbation theory (MP2)39-41 and coupled-cluster with single, double, and non-iterative triple excitations method

[CCSD(T)]42-44 using the 6-311++G** basis set for both calculations. Relative energies

reported in this work were corrected for zero-point energies (ZPE) at the corresponding

level of theory.

To understand the relationship between chemical bonding and structure in

0/-1 B3Hy clusters, we performed chemical bonding analysis for the lowest energy isomers using the recently developed Adaptive Natural Density Partitioning (AdNDP)

method.45-47 AdNDP performs analysis of the first-order reduced density matrix with the

purpose of obtaining its local block eigenfunctions with optimal convergence properties

for describing the electron density. The local blocks of the first-order reduced density

matrix correspond to the sets of n atoms (from one to all the atoms of the molecule) that

are tested for the presence of a two-electron object (nc-2e bonds, including core electrons

and lone pairs as a special case of n=1) associated with this particular set of n atoms. The

n-atomic sets are formed and checked in an exhaustive manner, so that the recovered

nc-2e bonding elements always correspond to the point-group symmetry of the system after these bonding elements are superimposed onto the molecular frame. For the given

n-atomic block those eigenvectors are accepted whose occupation numbers (eigenvalues)

exceed the established threshold value, usually close to 2.00 |e|. Thus Lewis's idea of an

electronic pair as the essential element of bonding is preserved. The AdNDP procedure is

numerically efficient since it involves only a series of diagonalizations of density matrix

blocks. It is unbiased in the sense that no preliminary ideas of the bonding pattern are

required to perform the analysis.

The B3LYP, R(U)MP2, R(U)CCSD(T) calculations were performed using the

Gaussian 03 program.48 Molecular visualization was performed using the MOLDEN3.4

program,49 and molecular orbital visualization was completed using the MOLEKEL 4.3 program.50

2-3. Computational Results

We initially performed GEGA searches for the global minimum of the neutral

- B3Hy and anionic B3Hy (y=4-7) isomers at the B3LYP/3-21G level of theory. The lowest

energy isomers were then recalculated at the B3LYP/6-311++G**, MP2/6-311++G**,

and CCSD(T)/6-311++G** levels of theory. Figures 2-1 and 2-2 show the lowest energy

structures identified in our scanning of the potential energy surfaces for the neutral B3Hy

- and anionic B3Hy (y=4-7) species.

- Figure 2-1. The lowest energy isomers for neutral B3Hy and anionic B3Hy (y=4-5) species.

- Figure 2-2. The lowest energy isomers for neutral B3Hy and anionic B3Hy (y=6-7) species.

The corresponding spectroscopic states, electronic configurations, and relative energies of each isomer (at the B3LYP/6-311++G**, MP2/6-311++G**, and

- CCSD(T)/6-311++G** levels of theory) for each of the neutral B3Hy and anionic B3Hy

(y=4-7) species are summarized in Table 2-1.

Table 2-1. Spectroscopic states, electronic configurations, and relative energies of each - isomer for each of the neutral B3Hy and anionic B3Hy (y=4-7) species.

Relative Energy1) Cluster Isomer State B3LYP2) MP22) CCSD(T) 2) 2 2 2 2 2 2 2 1 B3H4 I C2v, B2, 1a1 2a1 1b2 3a1 4a1 1b1 2b2 0 0 0 2 2 2 2 2 2 2 1 II D2h, B3u,1ag 1b1u 2ag 1b2u 1b3g 2b1u 1b3u 7.9 16.7 12.5 - 1 2 2 2 2 2 2 2 B3H4 III C2v, A1, 1a1 2a1 1b2 3a1 4a1 1b1 2b2 0 0 0 1 2 2 2 2 2 2 2 IV C2v, A1, 1a1 1b2 2a1 3a1 2b2 4a1 1b1 2.0 2.3 2.4 1 2 2 2 2 2 2 2 V D2h, Ag, 1ag 1b1u 2ag 1b2u 1b3g 2b1u 1b3u 6.4 17.6 10.7 1 2 2 2 2 2 2 2 B3H5 VI C2v, A1, 1a1 1b2 2a1 3a1 2b2 4a1 1b1 0 0 0 1 2 2 2 2 2 2 2 VII C2v, A1, 1a1 2a1 1b2 3a1 2b2 4a1 1b1 0.4 0.7 0.3 1 2 2 2 2 2 2 2 VIII C2v, A1, 1a1 1b2 2a1 1b1 1a2 3a1 2b2 14.1 23.3 17.6 1 2 2 2 2 2 2 2 IX Cs, A, 1a’ 2a’ 3a’ 1a” 4a’ 5a’ 2a” 18.9 23.0 19.5 1 2 2 2 2 2 2 2 X C2v, A1, 1a1 2a1 1b2 3a1 1b1 4a1 2b2 27.3 29.9 26.8 - 2 2 2 2 2 2 2 2 1 B3H5 XI Cs, A”, 1a’ 2a’ 3a’ 4a’ 1a” 5a’ 6a’ 2a” 0 0 0 1 2 2 2 2 1 2 1 1 XII Cs, A’, 1a’ 1a” 2a’ 3a’ 2a” 4a’ 3a” 5a’ 6.5 7.0 4.6 1 2 2 2 2 1 2 1 1 XIII Cs, A”, 1a’ 1a” 2a’ 3a’ 2a” 4a’ 3a” 5a’ 8.9 6.8 7.8 2 2 2 2 2 2 2 2 1 B3H6 XIV C2v, B2, 1a1 2a1 1b2 1b1 3a1 4a1 1a2 2b2 0 0 0 2 2 2 2 2 2 2 2 1 XV C2v, B2, 1a1 2a1 1b2 1b1 3a1 4a1 2b1 2b2 3.7 1.2 2.6 - 1 2 2 2 2 2 2 2 2 B3H6 XVI C1, A, 1a 2a 3a 4a 5a 6a 7a 8a 0 0 0 1 2 2 2 4 4 2 XVII D3d, A1g, 1a1g 1a2u 2a1g 1eu 1eg 2au -0.2 6.7 3.7 1 2 2 2 2 2 2 2 2 B3H7 XVIII Cs, A”, 1a’ 1a” 2a’ 3a’ 2a” 4a’ 3a” 5a’ 0 0 0 1 2 2 2 2 2 2 2 2 XIX C2v, A1, 1a1 2a1 1b2 1b1 2b2 3a1 4a1 1a2 1.8 3.7 3.2 1 2 2 2 2 2 2 2 2 XX Cs, A’, a’ 2a’ 3a’ 1a” 4a’ 5a’ 2a” 6a’ 6.8 9.1 7.7 - 2 2 2 2 2 2 2 2 2 1 B3H7 XXI C2v, B2, 1a1 2a1 1b2 1b1 3a1 4a1 1a2 2b1 2b2 0 0 0 2 2 2 2 2 2 2 2 2 1 XXII Cs, A”, 1a’ 1a” 2a’ 3a’ 2a” 4a’ 5a’ 3a” 6a’ 21.7 24.3 30.4 2 2 2 2 2 2 2 2 2 1 XXIII C2, A, 1a 1b 2a 2b 3a 3b 4a 4b 5a 25.9 28.6 30.4 1) Relative energy was corrected by zero-point vibrational energies at the corresponding level of theory. 2) Calculations were performed with the 6-311++G** basis set.

From our calculations we found that isomers with the lowest possible

multiplicities were found to be the lowest energy states for all clusters studied here.

- Several of the neutral B3Hy and anionic B3Hy (y=4-7) species have two or more

structures competing for the global minimum isomer. The low-lying isomers were found

to be structures with the triangular and linear core B3 units. There is no clear pattern why

for some species, isomers with the triangular B3 core are more stable, while for others

27-30 isomers with the linear B3 core are more stable. Previously reported results on B3H7 clusters showing that isomer XVIII is the most stable structure with isomers XIX and XX being the second and third most stable structures are in excellent agreement with our results.

- Table 2-2 summarizes the dissociation energies for B3Hy and B3Hy (y=5-7)

- - species for H2 release. All of the B3Hy and B3Hy (y=5-7) species, except for the B3H5 ,

are thermochemically stable towards spontaneous hydrogen release.

- 2-4. Chemical Bonding in B3Hx and B3Hx (x=4-7) Species

In order to facilitate the understanding between bonding and structure for B3Hy

- and B3Hy (y=4-7) species we performed chemical bonding analysis for the lowest

isomers of each species using our newly developed AdNDP analysis. We briefly

discussed this method in the Computational Details. A more extensive discussion on this

method and its application to boron clusters, aromatic organic molecules and golden

clusters can be found in references 45-48. The bonding pattern recovered in a particular

chemical species by the AdNDP analysis depends on how close the recovered bonds are

to the ideal 2.00 |e| the occupation numbers (ON). Therefore we report ON for a

27 particular bond for each isomer discussed in this section. We found that in all isomers

ONs are indeed very close to the ideal values, thus providing us with confidence in our chemical bonding pattern. The results of the AdNDP analysis, including pictorial representations of the recovered “bond,” are presented and summarized in Tables 2-3 through 2-7.

- Table 2-2. Stability of B3Hy and B3Hy (y=5-7) species towards H2 release.

Dissociation channel Dissociation energy1) 1 2 B3H5 VI (C2v, A1)  B3H4 I (C2v, B2) + 1/2H2 + 31.2 kcal/mol

- 2 - 1 B3H5 XI (Cs, A”)  B3H4 III (C2v, A1) + 1/2H2 - 6.5 kcal/mol

2 1 B3H6 XIV (C2v, B2)  B3H5 VI (C2v, A1) + 1/2H2 - 15.6 kcal/mol

2 2 B3H6 XIV (C2v, B2)  B3H4 I (C2v, B2) + H2 + 15.6 kcal/mol

- 1 - 2 B3H6 XVI (C1, A)  B3H5 XI (Cs, A”) + 1/2H2 + 25.8 kcal/mol

- 1 - 1 B3H6 XVI (C1, A)  B3H4 III (C2v, A1) + H2 + 19.3 kcal/mol

1 2 B3H7 XVIII (Cs, A’)  B3H6 XIV (C2v, B2) + 1/2H2 + 34.3 kcal/mol

1 1 B3H7 XVIII (Cs, A’)  B3H5 VI (C2v, A1) + H2 + 18.7 kcal/mol

- 2 - 1 B3H7 XXI (C2v, B2)  B3H6 XVI (C1, A) + 1/2H2 + 11.2 kcal/mol

- 2 - 2 B3H7 XXI (C2v, B2)  B3H5 XI (Cs, A”) + H2 + 37.0 kcal/mol 1) E calculated at the CCSD(T)/6-311++G**+ZPE/CCSD(T)/6-311++G** level of theory.

- Table 2-3. Bonds recovered by the AdNDP analysis for the selected isomers of B3 and - B3H4 .

Cluster, Occupation Isomer Structure Number ( |e| ) - B3 (B1–B2)=2.00 (B1–B3)=2.00 (B2–B3)=2.00 (B1–B2–B3)=2.00 (B1–B2–B3)=2.00

- B3H4 , (B3–H5)=1.98 III (B1–H2)=1.99 (B4–H6)=1.99 (B1–B3)=1.89 (B1–B4)=1.89 (B3–B4–H7)=2.00 (B1–B3–B4)=1.96

- 45,51-53 Bonding in the bare B3 cluster was studied previously, and it was shown that this cluster has three 2c-2e -B-B bonds, one 3c-2e -boond and one 3c-2e -bonds.

Thus, this cluster is a doubly (- and -) aromatic system. This double aromaticity explains its high symmetry cyclic structure and high atomizattion energy. The addition of

- - four hydrogen atoms to B3 results in the global minimum strruucture III of the B3H4 anion.

Table 2-4. Bonds recovered by the AdNDP analysis for the selected isomers of B3H5 and - B3H5 .

Cluster, Occupation Isomer Structure Number ( |e| )

B3H5, (B4–H8)=1.97 VI (B1–H2)=1.97 (B3–H7)=1.97 (B1–B4–H6)=1.99 (B1–B3–H5)=1.99 (B1–B3–B4)=1.88 (B1–B3–B4)=2.00

B3H5, (B2–H7)=2.00 VII (B2–H8)=2.00 (B3–H5)=2.00 (B4–H6)=2.00 (B2–B3–B4)=1.92 (B2–B3–B4)=1.99 (B3–B4–H1)=2.00

-,1) B3H5 , (B1–B2)=2.00 XI (B1–B3)=2.00 (B1–B2)=1.96 (B2–H5)=1.97 (B2–H4)=1.97 (B3–H6)=1.97 (B3–H7)=1.97 (B3–H8)=1.97

1) The AdNDP analysis for this isomer was performed for tthe doubly charged anion by adding one extra electron to the singly occupied MO (SOMO).

Table 2-5. Bonds recovered by the AdNDP analysis for the selected isomers of B3H6.

Cluster, Occupation Isomer Structure Number ( |e| ) 1) B3H6 , (B1–B4)=1.93 XIV (B1–B5)=1.93 (B4–H7)=1.97 (B1–H2)=1.97 (B5–H9)=1.97 (B4–H6)=1.97 (B5–H8)=1.97 (B4–B5–H3)=1.97

1) B3H6 , (B1–B4)=1.89 XV (B1–B5)=1.89 (B1–H3)=1.99 (B1–H2)=1.99 (B4–H8)=1.99 (B5–H9)=1.99 (B4–B5–H7)=1.98 (B4–B5–H6)=1.98

1) The AdNDP analysis for this isomer was performed for the anionic state by adding one extra electron to the SOMO.

- According to the AdNDP analysis the global minimum structure of B3H4 has three 2c-2e -B-H bonds, one 3c-2e BHB -bond, two 2c-2e -B-B bonds and one 3c-2e

- -bond. Thus, this anion is only a -aromatic systtem. Compared to the B3 anion, in the

- B3H4 anion, the addition of four hydrogen atoms led to the formation of three new B-H

-bonds, the substitution of a 3c-2e BHB bridged -bond for a 2c-2e B-B -bond, and

- the removal of the delocalized 3c-2e BBB -bond responsible for aromaticity of B3 .

- Table 2-6. Bonds recovered by the AdNDP analysis for the selected isomers of B3H6 .

Cluster, Occupation Isomer Structure Number ( |e| ) - B3H6 , (B2–B3)=1.99 XVI (B3–H6)=1.98 (B3–H4)=1.98 (B1–H7)=1.98 (B1–H5)=1.98 (B2–H8)=1.98 (B1–B2–H9)=1.99 (B3–B2– B1)=1.94

- B3H6 , (B1–B2)=1.93 XVII (B1–B3)=1.93 (B2–H6)=2.00 (B2–H4)=2.00 (B2–H5)=2.00 (B3–H8)=2.00 (B3–H7)=2.00 (B3–H9)=2.00

+ - Addition of a H to B3H4 with the formation of B3H5 led to the substitution of one

2c-2e B-B -bond by the 3c-2e BHB bridged -bond. The B3H5 cluster is still a - aromatic system. The second lowest energy B3H5 isomer VI has three 2c-2e B-H - bonds, two 3c-2e BHB -bonds, one delocalized 3c-2e -bond and one delocalized 3c-2e

-bond. Thus, isomer VI regains double (- and -) aromaticity. When an extra electron

2- is added to the B3H5 cluster, chemical bonding (performed for the B3H5 dianion at the

- - optimal geometry of the B3H5 anion) in the global minimum structure XI of the B3H5 species can be rationalized in terms of the classical structure with five 2c-2e B-H bonds, a

single -bond between H3B and the central boron atom, and a double (- and -) bond

between the central atom and the BH2 fragment.

Table 2-7. Bonds recovered by the AdNDP analysis for the selected isomers of B3H7 and - B3H7 .

Cluster, Occupation Isomer Structure Number ( |e| )

B3H7, (B1–B2–H5)=2.00 XVIII (B1–B3–H4)=2.00 (B1–B2–B3)=1.90 (B2–H9)=1.97 (B3–H8)=1.97 (B2–H7)=1.97 (B3–H6)=1.97 (B1–H10)=1.97

B3H7, (B1–B2–B3)=1.96 XIX (B2–B3–H10)=2.00 (B1–H5)=1.94 (B1–H4)=1.94 (B2–H6)=1.94 (B3–H8)=1.94 (B2–H7)=1.94 (B3–H9)=1.94

-1) B3H7 , (B1–B2)=1.94 XXI (B1–B3)=1.94 (B1–H4)=1.99 (B1–H5)=1.99 (B2–H6)=1.99 (B3–H8)=1.99 (B2–H7)=1.99 (B3–H9)=1.99 (B2–B3–H10)=1.97 1) The AdNDP analysis for this isomer was performed for tthe doubly charged anion by adding one extra electron to the singly occupied MO (SOMO).

The B3H6 cluster has two low-lying isomers XIV and XV. Chemical bonding analysis was performed for the closed shell anionic isomer XIV and XV at the optimal

geometries of the neutral clusters. In the global minimum structure XIV, we found five

2c-2e B-H -bonds, two 2c-2e B-B -bonds and one bridged 3c-2e BHB bond. In the

second isomer XV we found four 2c-2e B-H -bonds, two 2c-2e B-B -bonds, and two

3c-2e BHB bonds. The transition of one of the terminal hydrogen atoms to a bridged

position does not cost much energy, apparently. The two lowest isomers XVI and XVII

- of the B3H6 species are truly remarkable structures. In isomer XVI we found three types

on bonding: the 2c-2e B-B -bond between B2 and B3, 3c-2e BHB -bond between B1

and B2, and the 3c-2e -bond responsible for bonding between B1 and B3. That chemical

bonding pattern can easily explain the unusual geometric structure of the isomer XVI.

The classical type structure of the isomer XVII can also be easily understood from the

AdNDP analysis. Two BH3 groups are attached to the central boron atom through two

dative 2c-2e B-B -bonds. The two lowest isomers XVIII and XIX of the B3H7 species

have similar bonding patterns with the exception that one hydrogen atom migrates from

the bridged position in isomer XVII to the terminal position in isomer XVIII. We noticed

that such migrations do not cost much energy in the hydrogen-boron clusters discussed

here. Finally, in isomer XXI we found that it has two classical 2c-2e B-B sbonds, one 3c-

2e BHB bond which keep the boron kernel together, with all other electron pairs used for

the 2c-2e B-H -bonds.

The overall chemical bonding patterns revealed by the AdNDP analysis can easily

explain the geometric structure of even very exotic isomers and global minima.

2-5. Conclusions

We found global minimum structures and low-lying isomers for a series of B3Hy

- and B3Hy species using the GEGA method. We refined the relative energies at the

CCSD(T)/6-311++G** level of theory, and found a very diverse set of structures for global minimum and low-lying isomers of the studied species.

- - All of the B3Hy and B3Hy (y=5-7) species, except for the B3H5 , are thermochemically

stable towards hydrogen release. Chemical bonding in the global minimum and low-

lying isomers was analyzed using the AdNDP method; from this analysis we found the

chemical bonding patterns in all cases were consistent with the geometric structures of the studied clusters.

We hope that predictions made in our work will be tested in follow-up photoelectron studies of the anionic species studied in this work. We also hope that the bonding patterns presented here recovered by the AdNDP analysis will be useful for the future rational design of novel boron-hydrogen compounds. This is our first step in the

n+/0/n- probing of non-stoichiometric BxHy species.

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