Bonding through code : theoretical models for molecules and materials /: theoretical models for molecules and materials. (2020)

• Record Type: Book
• Further Information: Note: Daniel C. Fredrickson.
• Authors: Fredrickson, Daniel C
• Contents: Contents Acknowledgments, xi About the Author, xiii C hapter 1 ◾ The Postulates of Quantum Mechanics 1 C hapter 2 ◾ Atoms and Atomic Orbitals 23 INTRODUCTION 23 THE RADIAL WAVEFUNCTION 24 VISUALIZING ATOMIC ORBITALS WITH MATLAB: THE ANGULAR WAVEFUNCTIONS 28 COMBINING THE RADIAL AND ANGULAR FUNCTIONS 35 FOCUSING ON THE VALENCE ELECTRONS: SLATER-TYPE ORBITALS 38 C hapter 3 ◾ Overlap between Atomic Orbitals 41 INTRODUCTION 41 PARAMETERS FOR SLATER-TYPE ORBITALS 41 COMBINING THE RADIAL AND ANGULAR FUNCTIONS 42 VISUALIZING ISOSURFACES OF SLATER-TYPE ORBITALS 44 PROGRAMMING OVERLAP INTEGRALS IN MATLAB 47 EXERCISES FOR EXPLORING OVERLAP INTEGRALS 49 REFERENCES 53 C hapter 4 ◾ Introduction to Molecular Orbital Theory 55 INTRODUCTION 55 CONSTRUCTION OF THE HAMILTONIAN MATRIX 58 SOLVING FOR THE MOLECULAR ORBITALS 61 VISUALIZING ISOSURFACES OF MOS IN MATLAB 63 EXTENDED HÜCKEL VS. SIMPLE HÜCKEL 69 A SIMPLIFIED REPRESENTATION OF MOs IN MATLAB 72 REFERENCES 76 C hapter 5 ◾ The Molecular Orbitals of N2 77 INTRODUCTION 77 SOLVING THE GENERAL PROBLEM OF BUILDING THE HAMILTONIAN 77 THE BRUTE FORCE SOLUTION OF THE MOs OF N2 84 SYMMETRIZED BASIS FUNCTIONS 85 C hapter 6 ◾ Heteronuclear Diatomic Molecules 93 INTRODUCTION 93 DRAWING MOLECULAR STRUCTURES 93 HeH: ELECTRONEGATIVITY PERTURBATION 97 HeH: INTERATOMIC INTERACTIONS AS A PERTURBATION 103 THE MOs OF CO AND CN− 106 C hapter 7 ◾ Symmetry Operations 109 INTRODUCTION 109 APPLYING SYMMETRY OPERATIONS IN MATLAB 109 THE IDENTITY OPERATION 112 INVERSION THROUGH A CENTRAL POINT 113 REFLECTIONS THROUGH A PLANE 114 ROTATIONS ABOUT AN AXIS 115 IMPROPER ROTATIONS 117 CREATING MORE COMPLICATED OPERATIONS 118 C hapter 8 ◾ Symmetry Groups 123 INTRODUCTION 123 PROPERTIES OF MATHEMATICAL GROUPS 123 DEMONSTRATION OF MATHEMATICAL GROUPS WITH MATLAB 124 GENERATING OPERATIONS 128 APPLYING GROUP OPERATIONS 132 BUILDING THE MOLECULAR SYMMETRY GROUPS 135 C hapter 9 ◾ Group Theory and Basis Sets 139 INTRODUCTION 139 sp3 HYBRID ORBITALS OF H2O AS A BASIS FOR REPRESENTING POINT GROUP SYMMETRY 139 BASIS SETS AS REPRESENTATIONS OF POINT GROUP SYMMETRY 143 CHARACTERS OF A MATRIX REPRESENTATION 146 REDUCIBLE AND IRREDUCIBLE REPRESENTATIONS 147 REDUCTION OF REDUCIBLE REPRESENTATIONS 148 TRANSFORMATION OF BASIS SET TO IRREDUCIBLE REPRESENTATIONS 151 C hapter 10 ◾ The MOs of H2O 153 INTRODUCTION 153 THE MOs OF H2 O BY BRUTE FORCE 155 THE MOs OF H2 O FROM SP3 HYBRID SYMMETRY ADAPTED LINEAR COMBINATIONS (SALCs) 157 PERCEIVING LOCALIZED BONDING IN H2 O 165 BONUS CODE: BETTER BALL-AND-STICK MODELS 166 C hapter 11 ◾ MOs of the Trigonal Planar Geometry 171 INTRODUCTION 171 CONSTRUCTION OF NH3 GEOMETRIES 171 MOs AT SPECIFIC GEOMETRIES 173 SALCs FOR THE TRIGONAL PLANAR GEOMETRY 175 BUILDING THE MO DIAGRAM FROM THE SALCs 182 C hapter 12 ◾ Walsh Diagrams and Molecular Shapes 185 INTRODUCTION 185 GEOMETRIES OF THE AL3 MOLECULE 185 CONSTRUCTING WALSH DIAGRAMS 186 C hapter 13 ◾ Getting Started with Transition Metals 191 INTRODUCTION 191 NORMALIZATION OF DOUBLE-ZETA FUNCTIONS 192 INCLUSION OF D ORBITALS INTO MATLAB FUNCTIONS 193 THE MOs OF AN OCTAHEDRAL COMPLEX WITH σ-LIGANDS; THE 18-ELECTRON RULE 200 C hapter 14 ◾ Translational Symmetry and Band Structures 205 INTRODUCTION 205 TRANSLATIONAL SYMMETRY AND BLOCH’S THEOREM 205 CONSTRUCTING SALCs 208 HAMILTONIAN MATRICES 209 A SIMPLE EXAMPLE: THE CHAIN OF H ATOMS 210 UNIQUE VALUES OF K: THE 1ST BRILLOUIN ZONE 212 BUILDING THE HAMILTONIAN MATRICES FOR PERIODIC STRUCTURES 213 EXAMPLE: THE BAND STRUCTURE OF GRAPHENE 220 DETERMINING THE FERMI ENERGY FOR GRAPHENE 223 INDEX, 227
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2020
• Extent: 1 online resource, illustrations (black and white, and colour)
• Subjects: 541.2240151; Chemical bonds -- Mathematical models; Molecular structure -- Mathematical models
• Languages: English
• ISBNs: 9780429531873; 9781498762229; 9780429546570; 9780429154010
• Related ISBNs: 9781498762212
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.