Index
267
Multiplication table, 22–29, 31, 47, 177, 189,
247, 257, 258
Mys, 188, 190
N
Neumann principle, 104
Nordén, 138
Normal modes, 81, 100, 129, 250
O
O’Brien, 38, 49
OCAMS, 161
Octahedron, 35, 37, 70, 95, 96, 107, 138, 148,
149, 154, 159, 168, 170, 187–189, 216
Octupole, 186
Odaba¸ si, 174
Ojha, 95, 102
O’Leary, 84, 101
Omnicapping, 101, 157
Opechowski, 178
Opechowski theorem, 178
Operator
action on a function, 4, 51, 52, 181
action on a point, 1
action on an operator, 1, 66
anti-linear, 11
congruence, 46
idempotent, 69
inverse, 18, 23, 171
inversion, 2, 17, 18, 109, 110, 112
ladder, 65, 67, 108, 112
linear, 11–13, 16–18, 53, 105, 114, 133,
146, 147, 180, 188, 253
projection, 65, 67, 86, 100
proper and improper, vii, 163, 165
rotation, 2, 8–10, 16, 23, 53, 86, 112, 133,
134, 176, 180, 245, 246, 251
rotation-reflection, 40
spin, 125, 134, 170, 173, 180, 181,
184–186, 188–190, 259, 260
Orbitals, 4–7, 11, 23, 41, 51–53, 55, 59, 60,
63, 76–78, 84–89, 94, 95, 98–101, 107,
108, 115, 117, 123, 136–145, 149,
155–157, 159–161, 165, 168, 169, 204,
211, 249, 250, 253, 256
d, 78, 95, 107, 108, 165, 168, 204
f, 78, 149
molecular, 4, 51, 77, 84, 85, 95, 98, 99,
101, 149, 156, 161, 211, 249
Order of a group, 32, 33, 59, 114
Organo–transition–metal complexes, 78, 107,
138
Orgel, 138, 161
Orthonormality, 15, 16, 116, 118, 135
Orthorhombic, 34, 40, 71, 131–133
P
Paquette, 38, 49
Parity
permutational, 28, 36, 110, 118
space, 167, 182
Parker, 215, 218, 261
Partial derivative, 129
Partitioning, 30, 31
Pauli exclusion principle, 125
Pauling, 77
Pekker, 134, 161
Permutation group, 126, 165
Perturbation theory, 135
Phase convention, 108, 167
Phillips, 191, 261
Platonic solids, 34–36, 153, 154, 170
Point groups, 34–37, 39, 41–45, 47, 62, 117,
121, 181, 192
C 2 , C i , C s , 27, 29, 30, 34, 39, 45–47, 72,
75, 94, 104, 192, 205, 206, 211–214,
247, 249, 251–253
C 3v , 44, 62
C n , C nh , C nv , 27, 41, 43, 44, 62, 72, 76,
90, 95, 151, 192, 195, 196, 206
D 2 , 27, 176, 208, 211, 217, 218, 247
D 2h , 34, 38, 39
D 6h , 41, 42, 87, 100, 199, 212, 249, 251
D n , D nd , D nh , 40, 45, 90, 194, 198, 199,
206
I , I h , 35, 36, 39, 40, 93, 99, 120, 205, 209,
210, 214, 218, 237, 248–250
O, O h , 35–37, 39, 70–72, 78, 93–98, 116,
118, 122, 149, 184, 185, 205, 209, 210,
214
S 2n , 42, 62
T , T d , T h , 35–40, 45, 47, 62, 76, 99,
150–152, 181, 205, 208, 209, 213, 220,
249
Polarization function, 149
Polyhedrane, 155
Polyhedron, 48, 93, 99, 148, 150–154, 248
Potential energy, 80, 89, 110
Prisms, 40, 43
Product
antisymmetrized, 119, 121, 125, 219
direct group, 45, 46, 176
direct representation, 125
multiplicity, 121, 128, 184
scalar, 10–12, 14, 58, 59, 63, 80, 115, 118,
127, 128, 154, 174, 245
symmetrized, 120, 121, 125, 177, 184, 219,
252, 253, 259, 260
Pseudo Jahn–Teller effect (PJT), 134, 136, 137
Pseudo-doublet, 188
267
Multiplication table, 22–29, 31, 47, 177, 189,
247, 257, 258
Mys, 188, 190
N
Neumann principle, 104
Nordén, 138
Normal modes, 81, 100, 129, 250
O
O’Brien, 38, 49
OCAMS, 161
Octahedron, 35, 37, 70, 95, 96, 107, 138, 148,
149, 154, 159, 168, 170, 187–189, 216
Octupole, 186
Odaba¸ si, 174
Ojha, 95, 102
O’Leary, 84, 101
Omnicapping, 101, 157
Opechowski, 178
Opechowski theorem, 178
Operator
action on a function, 4, 51, 52, 181
action on a point, 1
action on an operator, 1, 66
anti-linear, 11
congruence, 46
idempotent, 69
inverse, 18, 23, 171
inversion, 2, 17, 18, 109, 110, 112
ladder, 65, 67, 108, 112
linear, 11–13, 16–18, 53, 105, 114, 133,
146, 147, 180, 188, 253
projection, 65, 67, 86, 100
proper and improper, vii, 163, 165
rotation, 2, 8–10, 16, 23, 53, 86, 112, 133,
134, 176, 180, 245, 246, 251
rotation-reflection, 40
spin, 125, 134, 170, 173, 180, 181,
184–186, 188–190, 259, 260
Orbitals, 4–7, 11, 23, 41, 51–53, 55, 59, 60,
63, 76–78, 84–89, 94, 95, 98–101, 107,
108, 115, 117, 123, 136–145, 149,
155–157, 159–161, 165, 168, 169, 204,
211, 249, 250, 253, 256
d, 78, 95, 107, 108, 165, 168, 204
f, 78, 149
molecular, 4, 51, 77, 84, 85, 95, 98, 99,
101, 149, 156, 161, 211, 249
Order of a group, 32, 33, 59, 114
Organo–transition–metal complexes, 78, 107,
138
Orgel, 138, 161
Orthonormality, 15, 16, 116, 118, 135
Orthorhombic, 34, 40, 71, 131–133
P
Paquette, 38, 49
Parity
permutational, 28, 36, 110, 118
space, 167, 182
Parker, 215, 218, 261
Partial derivative, 129
Partitioning, 30, 31
Pauli exclusion principle, 125
Pauling, 77
Pekker, 134, 161
Permutation group, 126, 165
Perturbation theory, 135
Phase convention, 108, 167
Phillips, 191, 261
Platonic solids, 34–36, 153, 154, 170
Point groups, 34–37, 39, 41–45, 47, 62, 117,
121, 181, 192
C 2 , C i , C s , 27, 29, 30, 34, 39, 45–47, 72,
75, 94, 104, 192, 205, 206, 211–214,
247, 249, 251–253
C 3v , 44, 62
C n , C nh , C nv , 27, 41, 43, 44, 62, 72, 76,
90, 95, 151, 192, 195, 196, 206
D 2 , 27, 176, 208, 211, 217, 218, 247
D 2h , 34, 38, 39
D 6h , 41, 42, 87, 100, 199, 212, 249, 251
D n , D nd , D nh , 40, 45, 90, 194, 198, 199,
206
I , I h , 35, 36, 39, 40, 93, 99, 120, 205, 209,
210, 214, 218, 237, 248–250
O, O h , 35–37, 39, 70–72, 78, 93–98, 116,
118, 122, 149, 184, 185, 205, 209, 210,
214
S 2n , 42, 62
T , T d , T h , 35–40, 45, 47, 62, 76, 99,
150–152, 181, 205, 208, 209, 213, 220,
249
Polarization function, 149
Polyhedrane, 155
Polyhedron, 48, 93, 99, 148, 150–154, 248
Potential energy, 80, 89, 110
Prisms, 40, 43
Product
antisymmetrized, 119, 121, 125, 219
direct group, 45, 46, 176
direct representation, 125
multiplicity, 121, 128, 184
scalar, 10–12, 14, 58, 59, 63, 80, 115, 118,
127, 128, 154, 174, 245
symmetrized, 120, 121, 125, 177, 184, 219,
252, 253, 259, 260
Pseudo Jahn–Teller effect (PJT), 134, 136, 137
Pseudo-doublet, 188