Doctoral Thesis: Quantum Chemical Research on Boron Cluster Structure and Aromaticity

MINISTRY OF EDUCATION AND TRAINING QUY NHON UNIVERSITY DUONG VAN LONG A QUANTUM CHEMICAL RESEACH OF STRUCTURE AND AROMATICITY OF SOME BORON CLUSTERS DOCTORAL DISSERTATION: Theoretical and Physical Chemistry MINISTRY OF EDUCATION AND TRAINING QUY NHON UNIVERSITY DUONG VAN LONG A QUANTUM CHEMICAL RESEACH OF STRUCTURE AND AROMATICITY OF SOME BORON CLUSTERS Major: Theoretical and Physical Chemistry Code No: 9440119 Reviewer 1: Prof. Nguyen Ngoc Ha Reviewer 2: Prof. Tran Thai Hoa Reviewer 3: Prof. Duong Tuan Quang Supervisors: 1.

Nguyen Phi Hung 2. Nguyen Minh Tho BINH DINH – 2023 DECLARATION This dissertation was written on the basis of research work carried out at Quy Nhon University, Binh Dinh province, under the supervision of Professor Nguyen Minh Tho and Associate Professor Nguyen Phi Hung. I hereby declare that the results presented are original from my own research work. Most of them were already published in peer-reviewed international journals.

For the use of the results from joint papers, I received permissions from my co- authors. Quy Nhon Binh Dinh 06 November 2023 Author Duong Van Long ACKNOWLEDGEMENTS I would like to express my sincere gratitude to professors and colleagues at Quy Nhon University, my family and friends who have accompanied me throughout the long years of pursuing a doctoral program. In particular, I would like to express sincere thanks to the professors and faculty staffs of the Department of Chemistry, Faculty of Natural Sciences and Postgraduate Training Office of Quy Nhon University for their support, understanding and for creating conditions for me to overcome obstacles caused by the COVID-19 pandemic. I would like to express my deepest gratitude to my supervisors, Profs.

Nguyen Minh Tho and Nguyen Phi Hung, for their invaluable guidance and support throughout my academic journey. Tho and Prof. Hung have been my scientific mentor since the beginning of my academic career, and I am truly grateful for their unwavering support and encouragement. They provided me with the foundation and skills necessary to succeed in my academic pursuits.

Their expertise and mentorship have been instrumental in shaping my research and helping me achieve my academic goals. I am honoured to have the opportunity to work under the guidance of both Professors Tho and Hung and I am forever grateful for their constant support. Thank you, Nguyen Ngoc Tri, Phan Dang Cam Tu, My Phuong Pham Ho and Nguyen Minh Tam, for sharing and accompanying me on my academic path. I would like to express my debt to my parents for their unconditional love and support.

Their guidance sacrifices and encouragement have been instrumental in shaping me into the person I am today. Thank you, Mom and Dad, for everything. I would also like to thank my wife and my little son for their love and encouragement. My wife has been a constant source of inspiration and support.

She has stood by my side through thick and thin, even during long nights when she had/has to listen to the sound of clattering keyboards while I was, and I am, working on my academic projects. I cannot thank her enough for her patience, understanding and foremost love. And my little son, you are the driving force for me to move forward, to achieve what we have now and in the future. I dedicate this thesis, my great achievement, to my family, and hope to continue making them proud.

Table of Contents List of symbols and notations. i List of Figures. iii List of Tables. ix GENERAL INTRODUCTION.

Objectives and scope of the research. Novelty and scientific significance. Overview of the research. Objectives of the research.

Search for lower-lying isomers. ELF – The electron localization function. Ring current maps. Bond order and net atomic charge.

THEORETICAL BACKGROUNDS AND COMPUTATIONAL METHODS. Theoretical backgrounds of computational quantum chemistry. Schrödinger equation. The Born–Oppenheimer Approximation.

Ab initio computational method. The Hartree-Fock Method. Density Functional Theory. Benchmarking the functional and basis set in DFT.

Post-Hartree-Fock methods. Aromaticity models in boron clusters. The Hückel and Baird rules. Hollow cylinder model.

RESULTS AND DISCUSSION. The Hückel rule and the ribbon model: The cases of B2Si3 and p B3Si2 clusters. Motivation for the study. The benchmarking tests.

Ribbon aromaticity model versus the Hückel electron count. 72 The disk aromaticity on the quasi-planar boron cluster B700/2- 3. Motivation of the study. 74 The quasi-planar B700/2- 3.

Disk model and electron count rule. Binary boron lithium clusters B12Lin with n = 1–14: the disk-cone model for the B12Li4 cluster. Motivation of the study. The growth pattern of B12Lin with n = 0 – 14.

Relative stabilities of clusters. A mixed cone-disk model .B14FeLi2 and the hollow cylinder model. Motivation of the study. Stability of B14FeLi2 and its potential applications.

GENERAL CONCLUSIONS AND FUTURE DIRECTIONS. 114 LIST OF PUBLICATIONS CONTRIBUTING TO THE DISSERTATION. 133 List of symbols and notations 2D Two dimensional 3D Three dimensional ACID Anisotropy of the induced current density ADE Adiabatic detachment energy AdNDP Adaptive Natural Density Partitioning AO Atomic orbital ASBO Average of the sum of the bond orders CASSCF Complete Active Space Self-Consistent Field CBS Complete basis set CC Coupled cluster CCSD Coupled cluster including singles and doubles CCSD(T) CCSD with a perturbative triples correction CI Configuration Interaction CMO Canonical Molecular Orbital CTOCD-DZ2 Continuous transformation of the origin of the current density - diamagnetic zero, with shifting the origin toward the nearest nucleus DFT Density functional theory DM Disk model DR Double ring ELF Electron localization function GA Genetic algorithm GGA Generalized gradient approximation GTO Gaussian-type orbitals HCM Hollow cylinder model HF Hartree-Fock HLG Frontier orbital (HOMO – LUMO) energy gap HOMO Highest Occupied Molecular Orbital i IEv Vertical ionization energy IR-UV2CI Resonant infrared-ultraviolet two-color ionization spectroscopy LCAO Linear combination of atomic orbitals LDA Local density approximation LUMO Lowest Unoccupied Molecular Orbital MBPT Many-body perturbation theory MEGA Mexican Enhanced Genetic Algorithm meta-GGA Meta-generalized gradient approximation MO Molecular orbital MPn n-order Møller-Plesset perturbation method MRCI Multireference Configuration Interaction NAC Calculated net atomic charged NICS Nuclear independent chemical shift PES Photoelectron spectroscopy PSM Phenomenological shell model QP Quasi-planar RMS Root mean square RSS Residual sum of squares SBO Sum of bond orders SOMO Singly Occupied Molecular Orbital SPION Superparamagnetic iron oxide nanoparticles STO Slater-type orbitals TD-DFT Time dependent density functional theory method TEAv Vertical two-electron affinity UV Ultraviolet UV-Vis Ultraviolet-Visible VASP Vienna ab initio simulation package (VASP) VDE Vertical detachment energy ii List of Figures Figure 1. Illustration of a genetic algorithm (GA) procedure ([31]).

The current density maps of π electron contribution of a) C4H4 and b) C6H6 plotted by both SYSMOIC and ACID packages. The π molecular orbitals of benzene according to the Hückel theory. The dashed line represent the energy of an isolated p orbital, and all orbitals below this line are bonding. All orbitals above it are antibonding.

MO energy diagrams of C4H4 (in both singlet and triplet states), C6H6, C8H8 (in both singlet and triplet states), and C10H8. The blue/red labels indicate the aromatic/antiaromatic species. Calculated curves as a function of size n for (a) adiabatic detachment - energies of Li2BnH2 (n = 6–22) ribbon clusters, and (b) Ionization energies of Li2BnH2 (n = 6–22) ([88]). The electron configuration π σ of the ribbons B10H2 and B11H2.

The potential-energy function of the one-dimensional model. A comparison between the , and the distance of between the two 2- most distant B atoms of B14H2. a) The ribbon structure of B14H2. b) ELFσl plot for B14H2 , and c) ELFπ 2- (yellow basins) and ELFσd (green basins) are plotted simultaneously for B14H2 .8 a) The ribbon structure of the singlet B12H2 ; b) ELFσl plot for the 2- singlet B12H2 , and c) ELFπ (yellow basins) and ELFσd (green basins) are plotted 2- simultaneously for the singlet B12H2.

a) The ribbon structure of the triplet B12H2. b) ELFσl plot for the triplet 2- B12H2. c) ELFπ (yellow basins) and ELFσd (green basins) are plotted 2- simultaneously for the triplet B12H2. d) and e) are the ELFπ and ELFσd plotted 2- simultaneously for the triplet B12H2 from and electrons, respectively.

The Bessel functions with 44 = 0, 1, and 2. Symmetries of some wavefunctions in the disk model. The two colours red and blue indicate the opposite signs of the wave functions. Hollow cylinder model.

The hollow cylinder's height is L, radius is R, inner radius is R0, and outer radius is R1. Particle's movement is limited from R0 to R1, with R0 = R – r, R1 = R + r where r is called the active radius of the hollow cylinder. The variation of function in equation (2.85) according to with = 0. Photoelectron spectra of B2Si3 clusters recorded with 266 nm photons [93].

(a) Comparison of IR-UV2CI spectrum of B 2Si3 with IR absorption spectra calculated for the low-energy structures 3.a isomer was obtained using the CCSD method or different DFT functionals [95]. An illustration of clusters with 2 π electrons and 2 σ delocalized electrons. Shapes of low-lying isomers of B 2Si3 clusters with q going from -2 to +2. Geometry optimizations are carried out using the TPSSh/6-311+G(d) level of theory.

Relative energies (kcal/mol) are computed using three different methods and will be elucidated in the text. Shapes of low-lying isomers of B 3Si2 clusters with p going from -3 to +1. Geometry optimizations are carried out using the TPSSh/6-311+G(d) level of theory. Relative energies (kcal/mol) are computed using three different methods and will be elucidated in the text.

A pathway illustrating the evolution leading to the B 2Si3 from the 3- - trianionic ribbon II.B3Si2 in which a B unit is replaced by an isovalent Si atom at two different positions leading to two isomeric types, namely ribbon (R) and Hückel (H). Delocalized π and delocalized σ CMOs of a) II.B2Si3 and 2- c) II. The atom positions are labelled by a, b, c, d and e. a-f) Ribbon structures of B3Si2.

i) Bond lengths (Å) and bond order (given in brackets) by blue numbers and net atomic charges are given by red numbers. ELF isosurfaces of ELF = 0.8 under ii) top view and iii) side view. iv) Electron configurations. Energy levels with green arrow(s) belong to π and σ delocalized CMOs whereas energy levels with grey arrows point out localized CMOs.

The representation of the self-locking phenomenon in the ribbon - 3- - - structures of B7H2 , B8H2, B9H2 , B9H2Li2 , and B10H2. B-B bond lengths are assigned by colour range from red to blue: 1. Nimag indicates the number of negative frequencies of the structure. The lowest-lying isomers of B3Si2Li2 shares the same B3Si2 ribbon + frame and two decorative Li ions in different positions.

Relative energies are calculated at TPSSh/6-311+G(d) + ZPE level of theory. ELFπ maps for II. a-f) Nanoribbon structures of B2Si3. i) Bond lengths (Å) and bond order (given in braces) are given by blue numbers and net charges are given by red numbers.

ELF isosurfaces of ELF = 0.8 under ii) top view and iii) side view. iv) Electron configurations. Energy levels with green arrow(s) belong to π and σ delocalized CMOs while energy levels with grey arrows point out localized CMOs. a-e) The Hückel type of B2Si3 i) Bond lengths (Å) and bond order (given in braces) are given by blue numbers and net charges are given by red numbers.

ELF isosurfaces of ELF = 0.8 under ii) top view and iii) side view. iv) Electron configurations. Energy levels with green arrow(s) belong to π and σ delocalized CMOs while energy levels with grey arrows point out localized CMOs. A quasi-planar structure consisting of 70 boron atoms was generated using the topological leapfrog algorithm starting from an initial B16 form with 13 vertices (the atom with yellow glow).

The selection of energetically favourable isomers of B70.