Gallup G.A. - Valence Bond Methods, Theory and applications (CUP, 2002)

alternation of saddle points, 193 antisymmetrizer, 66

column, 72 factored, 80

AO bases, 121

ROHF, using, 121

spherical vs. non-spherical environment, 122 AO basis

group representation, 98

AOs

sizes of, 123 atomic charges in CH atomic properties, 145

Rydberg configurations, 145 valence configurations, 145

B 2

qualitative results, 149 quantitative results, 147 VB structure statistics, 147

BeH

dipole moment, 138

full valence MCVB wave function, 137 SCVB wave function, 139

extra variation parameter in, 141

BeNe

quantitative results, 6-31G*, 173 quantitative results, STO3G, 163

BF

quantitative results, 6-31G*, 173 quantitative results, STO3G, 162

binary interchanges, 65

bond distances, see quantitative results under individual molecules

bonding in

B 2 , 152

BeNe, 171

BF, 168

C 2 , 153

C 2 H 4, 216

C 3 H 6 , 220 CO, 166

“cyclohexatriene”, 209

F 2 , 160

N2 , 154, 164

O2 , 157

Born–Oppenheimer approximation, 7 breathing orbital, 108

C 2

qualitative results, 152 quantitative results, 147 VB structure statistics, 147

C 2 H 4, 214

breathing orbitals, 215

C 2 H 6

hybrid vs. Cartesian AOs, 188 ionic structures in, 188

perfect pairing wave function, 188 statistics, 189

C 3 H 5

allyl radical, 125 correlation energy, 126 HLSPs, 128

MCVB wave function, 126

SCVB wave function and corresponding orbitals, 132

small basis, 128

standard tableaux functions, 126

symmetry of standard tableaux functions, 126 transformation to HLSPs, 129

normalization and, 131

C 3 H 6 6-31G*, 218

change in geometry on dissociation, 220 curve crossing on dissociation, 219 hybrid orbital in, 223

reaction barrier and avoided curve crossing, 219 STO3G, 225

triplet–triplet coupling of tableaux, 222

C 4H 4

electronic structure and equilibrium geometry, 208

C 6 H 6 , 197 6-31G*, 205

bonding in distorted benzene, 209

electronic structure and equilibrium geometry, 206

(cont. )

Kekul´e and Dewar structures, 197 resonance energy, 208

SCVB wave function, 200 STO3G, 198

symmetry enhancement of wave function terms, 199

6-31G*, 186 quadrupole moment, 184 STO3G, 178

CH 4 6-31G*, 186

octopole moment, 185 STO3G, 178

charge separation limits,

see VB structure selection

CO

quantitative results, 6-31G*, 173 quantitative results, STO3G, 163

computer program, 8 configuration, 99

confocal ellipsoidal–hyperboloidal coordinates, 26 constellation, 99

core repulsion in fragment interaction, 218, 219 correlation

angular, 38 bond parallel, 38

over-correlation, 29 targeted, 214

Coulomb integral, 32 Coulomb’s law, 5, 6 covalent functions, 27

CRUNCH, xiv, 8, 98, 103, 123, 165

De , see quantitative results under individual molecules dipole moment

anomalous direction, 111, 162 BeNe, 174

BF, 174

CH, 179

CH 2 , 182 CO, 174

covalent function, from, 112 effect of electronegativity, 111 effects of overlap and spin, 111

Index

inadequacy of STO3G basis, 175 ionic structures and, 111

dipole moment function BeNe, 174

BF, 174

CO, 174

direct transformations, 97

EGSO weights, STO3G BeNe, 172

BF, 170

CO, 169

N 2 , 166 eigenvalue problem

generalized, 10 2 ×2, 14 electron correlation

B2 , 151

C2 , 153

H 2 , 29, 40, 50, 52

F 2

qualitative results, 160 quantitative results, 147 VB structure statistics, 148

full MCVB, 39

GAMESS, 121 Gaussian units, 5 GGVB, 108

Gi method, 109 group algebra, 66

general bases, 69 Hermitian idempotents of, 76 matrix basis, 77

spatial symmetry groups, 98 groups

irreducible matrix representations, 68 matrix representations, 68

H 2 , 24 bonding

Coulombic interactions in, 32 kinetic energy in, 37 polarization, 38

resonance in, 37 complementary orbitals, 49 delocalization energy, 37 delocalized orbitals, 47 double- ζ basis, 38 exponential orbitals, 25, 47 Gaussian orbitals, 38

GGVB and SCVB treatments, 51 localized orbitals, 23

optimal delocalized orbitals, 49 optimal unsymmetric orbitals, 51 orthogonalized orbitals, 47

physical significance, 111 isoelectronic series, 162

kinetic energy, 6

Li

MCVB wave function, 144 nodes in SCVB AOs, 143 SCVB wave function, 142

LiF

covalent–ionic curve crossing, 115

dipole moment and covalent–ionic curve crossing, 116

LiH

dipole moment

full valence wave function, 115 three-state wave function, 113

linear variation functions, 9 local orbitals

general, 107

maximum overlap principle, 180 MCVB method, 107

characteristics, 108 metathesis reaction, 191 multi-structure VB, 108

N operator, 71

N 2

qualitative results, 154 quantitative results, 147 quantitative results, 6-31G*, 173

quantitative results, STO3G, 163 VB structure statistics, 147

NH 3

Rumer tableaux, 103 symmetry analysis, 102

nonlocal orbitals characteristics, 110 general, 108

O 2

qualitative results, 157 quantitative results, 147 VB structure statistics, 147

octopole moment CH 4, 185

optimal unsymmetric orbitals

H 2 , 51 orthogonality theorem, 68

orthogonalization, 19 canonical, 11, 19 Schmidt, 19, 20 symmetric, 19, 47 overlap integral, 32

P operator, 71 partitions, 70

conjugate, 74

Pauli exclusion principle, 24 permutation, 64

cycle structure, 64 inverse, 65 signature, 66 unitarity, 70

potential energy surfaces, 191 principal tableaux

B 2 , 151

BeNe, 171

BF, 169

C 2 , 153

C 2 H 4, 217

C 3 H 6 , 221, 223, 224

C 6 H 6 , 198

C 6 H 8 , 210 CH, 178

CH 2 , 180

CH 3 , 183

CH 4, 185 CO, 167

F 2 , 160

H 2 CO, 228

N2 , 155, 164

O2 , 158

quadrupole moment CH 3 , 183

Rayleigh quotient, 9 reaction surfaces, 191 representation

generalized permutation, 98 ROHF, see AO bases, 121

238

three-electron, 53, 55 two-electron, 23

Index

standard tableaux functions, 87 static exchange approximation,

see SEP supercomputers, 4

symgenn, 103, 104, 123, 165 symmetric groups, 63

symmetrizer row, 71

tableau functions

nonintuitive symmetry property, 101, 103, 104

θNPN matrix element evaluation, 91

θPN P matrix element evaluation, 88 three-electron bond

O 2 , 157

united atom limit, 3 units, physical, 5

valence state of C, 186 variation theorem, 9

VB structure selection, 123 orbital excitation, 123 planar molecules, 124 virtual AOs, role of, 122 Von Neumann’s theorem, 76

weights EGSO, 20

Chirgwin and Coulson, 18 inverse overlap, 18 nonorthogonal functions, 18 orthogonal functions, 16 symmetric orthogonalization, 19

Weyl dimension formula, 87 Woodward–Hoffman rules, 192

Young tableau, 71 standard, 72