268
Index
Pseudo-scalar representation, 152
Pythagorean tradition, 35
Q
Qiu, ix, 218, 261
Quantum chemistry, vii, 8, 103, 104, 106, 108,
110, 112, 149
Quartet spin state, 184, 188
Quinn, 211, 261
R
Rank, 168, 259
Reciprocity theorem, 72, 93, 148
Reduced matrix element, 127, 128, 142, 173
Representation
determinantal, 126
faithful, 23, 175
ground, 72–74, 126
irreducible, 55–59, 62, 63, 65, 68, 106, 107
mechanical, 148, 149, 154, 155, 211
positional, 73, 74, 148–150, 211
pseudoscalar, 152, 153, 156
Reversal, 11, 16–18, 63, 91, 109, 110, 129,
180–184
space, 18, 63, 109, 110, 181–183
time, 11, 16–18, 63, 91, 110, 129, 180–184
Rhombohedral, 168, 169, 189
Right-thumb rule, 90
Ring closure, 136, 137
Rodger, 138, 161
Rodrigues, 174
Rosenfeld equation, 254
Rotation, 1–10, 16, 22, 23, 32, 34, 40–45, 48,
52, 53, 61, 78, 83, 86, 87, 90, 95, 107,
109, 111, 112, 133, 134, 139, 151–154,
163, 164, 167, 172, 175, 176, 179, 180,
189, 197, 235, 245, 246, 248, 249, 251,
255
bodily, 52, 61, 111, 112
matrix, 3, 6, 7, 10, 16, 23, 45, 52, 53, 83,
163–165, 167, 172, 175, 179, 180, 245,
251
operator, 2, 8–10, 16, 23, 53, 86, 112, 133,
134, 176, 180, 245, 246, 251
optical, 36
pole, 2, 3, 164, 175, 176
Rotatory strength, 148, 254
Rouvray, 97, 102
Ru(bipy) 3 , 144
Ruthenocene, 40, 41
S
Sachs, 84
SALC, 53, 55, 59, 65, 67, 76, 77, 86, 152
Salem, 84, 101
Samuel, 93, 102
Sanders, 139
Satten, 189, 190
Schäffer, 39
Schrödinger
stationary equation, 17, 106
time-dependent equation, 17
Schulman, 93, 102
Schur, 56, 61, 63, 107
Secular equation, 54, 81, 132, 186
see Zeeman
Selection rule, 65, 115, 128–130, 135, 137,
142
Shapere, 5, 134
Shimanouchi, 81, 101
Similarity transformation, 32, 72
Singleton, 40, 62
Site symmetry, 75, 76, 93, 94, 148, 149, 249
Smalley, 38, 49
sp 3 -hybridization, 76, 77, 150
Spherical harmonics, 165–168, 218
Spin, spinor, 170, 171, 173–175, 177, 180,
183–185, 259
Spin-orbit coupling, 175, 186, 235, 261
Splitting scheme, 71, 121
Stabilizer, 30, 33, 39, 72
Standard fibre, 149
Stanger, 93, 102
Stark effect, 46
Stereo-isomers, 70
Stone, 261
Stretching modes, 82, 83
Subduction, 29, 51, 69–73, 75, 87, 165, 167,
168, 184, 207–210, 212, 214, 218, 237,
249
Subelement, 73–75
Subgroup, 29–34, 36–40, 43, 45–48, 69–72,
101, 128, 164, 176, 248, 251, 252
Subporphyrin, 44
Subrepresentation, 65, 68, 126
Sum rule, 75, 136, 148
Symmetry
see operators
see point groups
active definition, 1, 7, 10, 22, 46, 130, 132
breaking, 30, 34, 41, 69, 70, 128, 136, 205,
206
dynamic, 41, 111, 112
hidden, 95, 98, 106
spherical, 34, 35, 40, 117, 149, 163–166,
168, 170, 172, 174, 176, 178, 180, 182,
184, 186, 188, 190, 204, 205
Index
Pseudo-scalar representation, 152
Pythagorean tradition, 35
Q
Qiu, ix, 218, 261
Quantum chemistry, vii, 8, 103, 104, 106, 108,
110, 112, 149
Quartet spin state, 184, 188
Quinn, 211, 261
R
Rank, 168, 259
Reciprocity theorem, 72, 93, 148
Reduced matrix element, 127, 128, 142, 173
Representation
determinantal, 126
faithful, 23, 175
ground, 72–74, 126
irreducible, 55–59, 62, 63, 65, 68, 106, 107
mechanical, 148, 149, 154, 155, 211
positional, 73, 74, 148–150, 211
pseudoscalar, 152, 153, 156
Reversal, 11, 16–18, 63, 91, 109, 110, 129,
180–184
space, 18, 63, 109, 110, 181–183
time, 11, 16–18, 63, 91, 110, 129, 180–184
Rhombohedral, 168, 169, 189
Right-thumb rule, 90
Ring closure, 136, 137
Rodger, 138, 161
Rodrigues, 174
Rosenfeld equation, 254
Rotation, 1–10, 16, 22, 23, 32, 34, 40–45, 48,
52, 53, 61, 78, 83, 86, 87, 90, 95, 107,
109, 111, 112, 133, 134, 139, 151–154,
163, 164, 167, 172, 175, 176, 179, 180,
189, 197, 235, 245, 246, 248, 249, 251,
255
bodily, 52, 61, 111, 112
matrix, 3, 6, 7, 10, 16, 23, 45, 52, 53, 83,
163–165, 167, 172, 175, 179, 180, 245,
251
operator, 2, 8–10, 16, 23, 53, 86, 112, 133,
134, 176, 180, 245, 246, 251
optical, 36
pole, 2, 3, 164, 175, 176
Rotatory strength, 148, 254
Rouvray, 97, 102
Ru(bipy) 3 , 144
Ruthenocene, 40, 41
S
Sachs, 84
SALC, 53, 55, 59, 65, 67, 76, 77, 86, 152
Salem, 84, 101
Samuel, 93, 102
Sanders, 139
Satten, 189, 190
Schäffer, 39
Schrödinger
stationary equation, 17, 106
time-dependent equation, 17
Schulman, 93, 102
Schur, 56, 61, 63, 107
Secular equation, 54, 81, 132, 186
see Zeeman
Selection rule, 65, 115, 128–130, 135, 137,
142
Shapere, 5, 134
Shimanouchi, 81, 101
Similarity transformation, 32, 72
Singleton, 40, 62
Site symmetry, 75, 76, 93, 94, 148, 149, 249
Smalley, 38, 49
sp 3 -hybridization, 76, 77, 150
Spherical harmonics, 165–168, 218
Spin, spinor, 170, 171, 173–175, 177, 180,
183–185, 259
Spin-orbit coupling, 175, 186, 235, 261
Splitting scheme, 71, 121
Stabilizer, 30, 33, 39, 72
Standard fibre, 149
Stanger, 93, 102
Stark effect, 46
Stereo-isomers, 70
Stone, 261
Stretching modes, 82, 83
Subduction, 29, 51, 69–73, 75, 87, 165, 167,
168, 184, 207–210, 212, 214, 218, 237,
249
Subelement, 73–75
Subgroup, 29–34, 36–40, 43, 45–48, 69–72,
101, 128, 164, 176, 248, 251, 252
Subporphyrin, 44
Subrepresentation, 65, 68, 126
Sum rule, 75, 136, 148
Symmetry
see operators
see point groups
active definition, 1, 7, 10, 22, 46, 130, 132
breaking, 30, 34, 41, 69, 70, 128, 136, 205,
206
dynamic, 41, 111, 112
hidden, 95, 98, 106
spherical, 34, 35, 40, 117, 149, 163–166,
168, 170, 172, 174, 176, 178, 180, 182,
184, 186, 188, 190, 204, 205