VALENCE BOND METHODS
CONTENTS I THEORY AND TWO-ELECTRON SYSTEMS INTRODUCTION HISTORY MATHEMATICAL BACKGROUND SCHR¨ODINGER’S EQUATION THE VARIATION THEOREM GENERAL VARIATION FUNCTIONS LINEAR VARIATION FUNCTIONS A 2 × 2 GENERALIZED EIGENVALUE PROBLEM WEIGHTS OF NONORTHOGONAL FUNCTIONS WEIGHTS WITHOUT ORTHOGONALIZATION WEIGHTS REQUIRING ORTHOGONALIZATION H2 AND LOCALIZED ORBITALS THE SEPARATION OF SPIN AND SPACE VARIABLES THE SPIN FUNCTIONS THE SPATIAL FUNCTIONS THE AO APPROXIMATION ACCURACY OF THE HEITLER–LONDON FUNCTION EXTENSIONS TO THE SIMPLE HEITLER–LONDON TREATMENT WHY IS THE H2 MOLECULE STABLE? ELECTROSTATIC INTERACTIONS KINETIC ENERGY EFFECTS ELECTRON CORRELATION GAUSSIAN AO BASES A FULL MCVB CALCULATION TWO DIFFERENT AO BASES EFFECT OF ELIMINATING VARIOUS STRUCTURES ACCURACY OF FULL MCVB CALCULATION WITH 10 AOS ACCURACY OF FULL MCVB CALCULATION WITH 28 AOS EGSO WEIGHTS FOR 10 AND 28 AO ORTHOGONALIZED BASES H2 AND DELOCALIZED ORBITALS ORTHOGONALIZED AOS OPTIMAL DELOCALIZED ORBITALS THE METHOD OF COULSON AND FISHER[15] COMPLEMENTARY ORBITALS UNSYMMETRIC ORBITALS THREE ELECTRONS IN DOUBLET STATES SPIN EIGENFUNCTIONS REQUIREMENTS OF SPATIAL FUNCTIONS ORBITAL APPROXIMATION ADVANCED METHODS FOR LARGER MOLECULES PERMUTATIONS GROUP ALGEBRAS SOME GENERAL RESULTS FOR ?NITE GROUPS IRREDUCIBLE MATRIX REPRESENTATIONS BASES FOR GROUP ALGEBRAS ALGEBRAS OF SYMMETRIC GROUPS THE UNITARITY OF PERMUTATIONS PARTITIONS YOUNG TABLEAUX AND N AND P OPERATORS STANDARD TABLEAUX THE LINEAR INDEPENDENCE OF NIPI AND PINI VON NEUMANN’S THEOREM TWO HERMITIAN IDEMPOTENTS OF THE GROUP ALGEBRA A MATRIX BASIS FOR GROUP ALGEBRAS OF SYMMETRIC GROUPS SANDWICH REPRESENTATIONS GROUP ALGEBRAIC REPRESENTATION OF THE ANTISYMMETRIZER ANTISYMMETRIC EIGENFUNCTIONS OF THE SPIN TWO SIMPLE EIGENFUNCTIONS OF THE SPIN THE FUNCTION THE INDEPENDENT FUNCTIONS FROM AN ORBITAL PRODUCT TWO SIMPLE SORTS OF VB FUNCTIONS TRANSFORMATIONS BETWEEN STANDARD TABLEAUX AND HLSP FUNCTIONS REPRESENTING ? NPN AS A FUNCTIONAL DETERMINANT CONTENTS SPATIAL SYMMETRY THE AO BASIS BASES FOR SPATIAL GROUP ALGEBRAS CONSTELLATIONS AND CON?GURATIONS EXAMPLE 1 H2O EXAMPLE 3 THE ? SYSTEM OF BENZENE VARIETIES OF VB TREATMENTS LOCAL ORBITALS NONLOCAL ORBITALS THE PHYSICS OF IONIC STRUCTURES A SILLY TWO-ELECTRON EXAMPLE IONIC STRUCTURES AND THE ELECTRIC MOMENT OF LIH COVALENT AND IONIC CURVE CROSSINGS IN LIF II EXAMPLES AND INTERPRETATIONS SELECTION OF STRUCTURES AND ARRANGEMENT OF BASES THE AO BASES STRUCTURE SELECTION N2 AND AN STO3G BASIS N2 AND A 6-31G BASIS N2 AND A 6-31G?BASIS PLANAR AROMATIC AND ? SYSTEMS 10 FOUR SIMPLE THREE-ELECTRON SYSTEMS THE ALLYL RADICAL MCVB TREATMENT EXAMPLE OF TRANSFORMATION TO HLSP FUNCTIONS SCVB TREATMENT WITH CORRESPONDING ORBITALS THE HE+ 2 ION MCVB CALCULATION SCVB WITH CORRESPONDING ORBITALS THE VALENCE ORBITALS OF THE BEH MOLECULE FULL MCVB TREATMENT AN SCVB TREATMENT THE LI ATOM SCVB TREATMENT 11 SECOND ROW HOMONUCLEAR DIATOMICS ATOMIC PROPERTIES ARRANGEMENT OF BASES AND QUANTITATIVE RESULTS QUALITATIVE DISCUSSION GENERAL CONCLUSIONS 12 SECOND ROW HETERONUCLEAR DIATOMICS AN STO3G AO BASIS BENE QUANTITATIVE RESULTS FROM A 6-31G?BASIS DIPOLE MOMENTS OF CO, BF, AND BENE RESULTS FOR 6-31G?BASIS DIF?CULTIES WITH THE STO3G BASIS 13 METHANE, ETHANE AND HYBRIDIZATION STO3G BASIS 6-31G?BASIS ETHANE CONCLUSIONS 14 RINGS OF HYDROGEN ATOMS BASIS SET ENERGY SURFACES 15 AROMATIC COMPOUNDS STO3G CALCULATION SCVB TREATMENT OF ? SYSTEM COMPARISON WITH LINEAR 1,3,5-HEXATRIENE THE 6-31G?BASIS COMPARISON WITH CYCLOBUTADIENE THE RESONANCE ENERGY OF BENZENE NAPHTHALENE WITH AN STO3G BASIS THE MOCI TREATMENT 16 INTERACTION OF MOLECULAR FRAGMENTS METHYLENE, ETHYLENE, AND CYCLOPROPANE 16 1 1 THE METHYLENE BIRADICAL ETHYLENE CYCLOPROPANE WITH A 6-31G?BASIS CYCLOPROPANE WITH AN STO-3G BASIS FORMALDEHYDE, H2CO THE LEAST MOTION PATH THE TRUE SADDLE POINT WAVE FUNCTIONS DURING SEPARATION REFERENCES