Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 12-2008 Analysis of Chemical Bonding in Clusters by Means of The Adaptive Natural Density Partitioning Dmitry Yu Zubarev Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Physical Chemistry Commons Recommended Citation Zubarev, Dmitry Yu, "Analysis of Chemical Bonding in Clusters by Means of The Adaptive Natural Density Partitioning" (2008). All Graduate Theses and Dissertations. 13. https://digitalcommons.usu.edu/etd/13 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]. ANALYSIS OF CHEMICAL BONDING IN CLUSTERS BY MEANS OF THE ADAPTIVE NATURAL DENSITY PARTITIONING by Dmitry Yu. Zubarev A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Chemistry (Physical Chemistry) Approved: _________________________ _________________________ Dr. Alexander I. Boldyrev Dr. Steve Scheiner Major Professor Committee Member _________________________ _________________________ Dr. Stephen E. Bialkowski Dr. Lisa M. Berreau Committee Member Committee Member _________________________ _________________________ Dr. T.-C. Shen Byron R. Burnham Committee Member Dean of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2008 ii Copyright Dmitry Yu. Zubarev 2008 All Rights Reserved iii ABSTRACT Analysis of Chemical Bonding in Clusters by Means of the Adaptive Natural Density Partitioning by Dmitry Yu. Zubarev, Doctor of Philosophy Utah State University, 2008 Major Professor: Dr. Alexander I. Boldyrev Department: Chemistry and Biochemistry Models of chemical bonding are essential for contemporary chemistry. Even the explosive development of the computational resources including, both hardware and software, cannot eliminate necessity of compact, intuitive, and efficient methods of representing chemically relevant information. The Lewis model of chemical bonding, which was proposed eleven years before the formulation of quantum theory and preserves its pivotal role in chemical education and research for more than ninety years, is a vivid example of such a tool. As chemistry shifts to the nanoscale, it is becoming obvious that a certain shift of the paradigms of chemical bonding is inescapable. For example, none of the currently available models of chemical bonding can correctly predict structures and properties of sub-nano and nanoclusters. Clusters of main-group elements and transition metals are of major interest for nanotechnology with potential applications including catalysis, hydrogen storage, molecular conductors, drug development, nanodevices, etc. Thus, the goals of this dissertation were three-fold. Firstly, the dissertation introduces a iv novel approach to the description of chemical bonding and the algorithm of the software performing analysis of chemical bonding, which is called Adaptive Natural Density Partitioning. Secondly, the dissertation presents a series of studies of main-group element and transition-metal clusters in molecular beams, including obtaining their photoelectron spectra, establishing their structures, analyzing chemical bonding, and developing generalized model of chemical bonding. Thirdly, the dissertation clarifies and develops certain methodological aspects of the quantum chemical computations dealing with clusters. This includes appraisal of the performance of several computational methods based on the Density Functional Theory and the development of global optimization software based on the Particle Swarm Optimization algorithm. (431 pages) v CONTENTS Page ABSTRACT............................................................................................................... iii LIST OF TABLES..................................................................................................... xii LIST OF FIGURES................................................................................................... xiv CHAPTER 1. INTRODUCTION.............................................................................................. 1 References.......................................................................................... 4 2. LITERATURE REVIEW.................................................................................... 5 2-1. Introduction........................................................................................ 5 2-2. Chemical Bonding Models for Clusters............................................. 7 2-2.1. Jellium Model......................................................................... 8 2-2.2. Aromaticity/Antiaromaticity.................................................. 10 2-3. Conclusion......................................................................................... 13 References.......................................................................................... 14 3. DEVELOPING PARADIGMS OF CHEMICAL BONDING: ADAPTIVE NATURAL DENSITY PARTITIONING...................................... 20 Abstract.............................................................................................. 20 3-1. Introduction........................................................................................ 20 3-2. Adaptive Natural Density Partitioning (AdNDP) Algorithm............ 24 3-3. Theoretical Methods.......................................................................... 30 3-4. Numerical Application and Discussion............................................. 30 3-4.1. Li4 cluster............................................................................... 31 3-4.2. B4 cluster................................................................................ 31 - 3-4.3. B5 cluster............................................................................... 33 2- 3-4.4. B6 cluster.............................................................................. 36 - 3-4.5. B9 cluster............................................................................... 38 - 3-4.6. B11 cluster.............................................................................. 40 + 3-4.7. B13 cluster............................................................................. 42 vi 3-5. Conclusion......................................................................................... 44 References.......................................................................................... 46 4. COMPREHENSIVE ANALYSIS OF CHEMICAL BONDING IN BORON CLUSTERS..................................................................................... 53 Abstract.............................................................................................. 53 4-1. Introduction........................................................................................ 54 4-2. Theoretical Methods.......................................................................... 56 4-3. Chemical Bonding Analysis............................................................... 57 + - 4-3.1. B3 and B3 Clusters................................................................ 60 2- 4-3.2. B4 and B4 Clusters................................................................ 62 + - 4-3.3. B5 and B5 Clusters................................................................ 65 2+ 2- 4-3.4. B6 , B6 and B6 Clusters....................................................... 68 + - 4-3.5. B7 and B7 Clusters................................................................ 73 2- - 4-3.6. B8, B8 and B9 Clusters......................................................... 76 + - 4-3.7. B10, B11 and B11 Clusters...................................................... 80 + 4-3.8. B12 and B13 Clusters.............................................................. 84 - 4-3.9. B14 and B15 Clusters.............................................................. 87 4-4. Overview............................................................................................ 90 References.......................................................................................... 93 5. AROMATICITY AND ANTIAROMATICITY IN TRANSITION-METAL SYSTEMS................................................................... 101 Abstract.............................................................................................. 101 5-1. Introduction........................................................................................ 102 5-2. s-AO based σ-aromaticity and σ-antiaromaticity in transition metal systems............................................................... 107 5-2.1. s-AO based σ-aromaticity and σ-antiaromaticity in M3 clusters.................................... 107 5-2.2. s-AO based σ-aromaticity 2- in M4 clusters..................................................................... 110 5-2.3. s-AO based σ-aromaticity + in the Au5Zn cluster and Au6.............................................. 111 5-2.4. s-AO based σ-aromaticity in the cyclo-MnHn (M = Cu, Ag, Au; n = 3-6), cyclo- Au3LnH3-n (L = CH3, NH2, OH, and Cl; n = 1-3), cyclo-CunAgk-nHn ( n =1-k, k = 3-5) clusters...................... 113 5-3. p-AO based aromaticity and antiaromaticity vii in transition metal systems............................................................... 117 6- 5-3.1. p-AO based multiple aromaticity in the Hg4 cluster............ 117 2- - 5-3.2.