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III.B.3.b. (XIII.C.2.)

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.956 ± 0.023 62 258 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
CS2 Carbon disulfide 3 Πu 410 397 0.969 1 1
    2 Σu 1552 1535 0.989 1 2
    1 Σg 676 658 0.974 1 3
HNCO Isocyanic acid 6 A" 641 656 1.024 2 4
    5 A' 569 577 1.014 2 5
    4 A' 832 777 0.933 2 6
    3 A' 1329 1327 0.999 2 7
    2 A' 2328 2269 0.975 2 8
    1 A' 3721 3538 0.951 2 9
HCN Hydrogen cyanide 3 Π 741 712 0.960 3 10
    2 Σ 2162 2089 0.966 3 11
    1 Σ 3467 3312 0.955 3 12
CH3NH2 methyl amine 15 A" 307 268 0.872 4 13
    14 A" 985     4 14
    13 A" 1371 1335 0.974 4 15
    12 A" 1540 1485 0.964 4 16
    11 A" 3129 2985 0.954 4 17
    10 A" 3609 3427 0.950 4 18
    9 A' 883 780 0.884 4 19
    8 A' 1081 1044 0.966 4 20
    7 A' 1198 1130 0.943 4 21
    6 A' 1474 1430 0.970 4 22
    5 A' 1521 1473 0.968 4 23
    4 A' 1684 1623 0.964 4 24
    3 A' 3013 2820 0.936 4 25
    2 A' 3094 2961 0.957 4 26
    1 A' 3530 3361 0.952 4 27
C2H2 Acetylene 5 Πu 766 730 0.954 5 28
    4 Πg 617 612 0.991 5 29
    3 Σu 3429 3289 0.959 5 30
    2 Σg 2040 1974 0.968 5 31
    1 Σg 3533 3374 0.955 5 32
C2H4 Ethylene 12 B3u 986 949 0.963 6 33
    11 B3g 1255 1217 0.970 6 34
    10 B3g 3236 3086 0.954 6 35
    9 B2u 832 826 0.992 6 36
    8 B2u 3262 3105 0.952 6 37
    7 B2g 969 940 0.969 6 38
    6 B1u 1493 1444 0.967 6 39
    5 B1u 3156 2989 0.947 6 40
    4 Au 1063 1023 0.962 6 41
    3 Ag 1386 1342 0.968 6 42
    2 Ag 1700 1623 0.955 6 43
    1 Ag 3176 3026 0.953 6 44
CH4 Methane 4 T2 1356 1306 0.963 7 45
    3 T2 3164 3019 0.954 7 46
    2 E 1581 1534 0.971 7 47
    1 A1 3047 2917 0.957 7 48
CH3OH Methyl alcohol 12 A" 306 200 0.653 8 49
    11 A" 1193 1165 0.977 8 50
    10 A" 1520 1477 0.971 8 51
    9 A" 3080 2960 0.961 8 52
    8 A' 1080 1033 0.956 8 53
    7 A' 1109 1060 0.956 8 54
    6 A' 1405 1345 0.958 8 55
    5 A' 1503 1455 0.968 8 56
    4 A' 1536 1477 0.962 8 57
    3 A' 3027 2844 0.940 8 58
    2 A' 3142 3000 0.955 8 59
    1 A' 3901 3681 0.944 8 60
HCOOH Formic acid 9 A" 676 638 0.944 9 61
    8 A" 1081 1033 0.956 9 62
    7 A' 639 625 0.978 9 63
    6 A' 1156 1105 0.956 9 64
    5 A' 1341 1229 0.917 9 65
    4 A' 1431 1387 0.969 9 66
    3 A' 1851 1770 0.956 9 67
    2 A' 3113 2943 0.945 9 68
    1 A' 3808 3570 0.938 9 69
CCl4 Carbon tetrachloride 4 T2 321 314 0.979 10 70
    3 T2 825 776 0.940 10 71
    2 E 222 217 0.979 10 72
    1 A1 470 459 0.976 10 73
H2CO Formaldehyde 6 B2 1287 1249 0.971 11 74
MgO magnesium oxide 1 Σ 719 785 1.092 12 75
H2CO Formaldehyde 5 B2 3018 2843 0.942 13 76
    4 B1 1213 1167 0.962 13 77
    3 A1 1557 1500 0.963 13 78
    2 A1 1817 1746 0.961 13 79
    1 A1 2953 2782 0.942 13 80
C3H6 Cyclopropane 11 E' 906 866 0.956 14 81
    10 E' 1078 1029 0.954 14 82
CN Cyano radical 1 Σ 2177 2069 0.950 15 83
C3H6 Cyclopropane 9 E' 1493 1438 0.963 16 84
    8 E' 3163 3025 0.956 16 85
    7 A2" 865 854 0.987 16 86
    6 A2" 3264 3103 0.951 16 87
    5 A2' 1109 1070 0.965 16 88
    4 A1" 1174 1126 0.959 16 89
    3 A1' 1230 1188 0.966 16 90
    2 A1' 1547 1479 0.956 16 91
    1 A1' 3175 3038 0.957 16 92
    12 E" 3244 3082 0.950 16 93
    13 E" 1231 1188 0.965 16 94
    14 E" 750 739 0.986 16 95
CCl2O Phosgene 1 A1 1883 1827 0.970 17 96
    2 A1 584 567 0.971 17 97
    3 A1 306 285 0.932 17 98
OH Hydroxyl radical 1 Σ 3772 3738 0.991 18 99
CCl2O Phosgene 4 B1 598 580 0.969 19 100
    5 B2 883 849 0.962 19 101
    6 B2 453 440 0.970 19 102
CF2Cl2 difluorodichloromethane 1 A1 1162 1101 0.947 20 103
    2 A1 684 667 0.975 20 104
    3 A1 468 458 0.979 20 105
    4 A1 266 262 0.985 20 106
    5 A2 328 322 0.980 20 107
    6 B1 944 902 0.955 20 108
    7 B1 447 437 0.978 20 109
    8 B2 1234 1159 0.939 20 110
    9 B2 444 446 1.003 20 111
CH2CHCH3 Propene 1 A' 3248 3090 0.951 21 112
C2Cl2 dichloroacetylene 1 Σg 2341 2234 0.954 22 113
    2 Σg 478 477 0.998 22 114
    3 Σu 1004 988 0.984 22 115
    4 Πg 369 333 0.904 22 116
    5 Πu 180 172 0.955 22 117
CH2CHCH3 Propene 2 A' 3171 3013 0.950 23 118
    3 A' 3157 2991 0.947 23 119
    4 A' 3129 2954 0.944 23 120
    5 A' 3047 2871 0.942 23 121
    6 A' 1728 1650 0.955 23 122
    7 A' 1515 1470 0.970 23 123
    8 A' 1472 1420 0.965 23 124
    9 A' 1425 1378 0.967 23 125
CH3Cl Methyl chloride 6 E 1043 1015 0.973 24 126
    5 E 1506 1455 0.966 24 127
    4 E 3197 3042 0.952 24 128
    3 A1 755 732 0.970 24 129
    2 A1 1401 1355 0.967 24 130
    1 A1 3097 2966 0.958 24 131
CH2CHCH3 Propene 10 A' 1337 1297 0.970 25 132
    11 A' 1205 1171 0.972 25 133
    12 A' 953 963 1.010 25 134
    13 A' 940 920 0.979 25 135
    14 A' 424 428 1.011 25 136
    15 A" 3105 2954 0.951 25 137
    16 A" 1502 1443 0.961 25 138
    17 A" 1084 1045 0.964 25 139
    18 A" 1032 991 0.960 25 140
    19 A" 950 912 0.960 25 141
    20 A" 594 578 0.974 25 142
    21 A" 202 174 0.863 25 143
CO2 Carbon dioxide 1 Σg 1372 1333 0.971 26 144
    2 Σu 2414 2349 0.973 26 145
    3 Πu 678 667 0.984 26 146
CF2O Carbonic difluoride 1 A1 2007 1928 0.961 27 147
    2 A1 1000 965 0.965 27 148
    3 A1 596 584 0.980 27 149
    4 B1 801 774 0.966 27 150
    5 B2 1318 1249 0.948 27 151
    6 B2 635 626 0.985 27 152
CH2CCH2 allene 1 A1 3166 3015 0.952 28 153
    2 A1 1507 1443 0.958 28 154
    3 A1 1100 1073 0.975 28 155
    4 B1 884 865 0.978 28 156
    5 B2 3165 3007 0.950 28 157
    6 B2 2050 1957 0.954 28 158
    7 B2 1453 1398 0.962 28 159
    8 E 3247 3086 0.950 28 160
    9 E 1031 999 0.969 28 161
    10 E 882 841 0.954 28 162
    11 E 361 355 0.985 28 163
CO Carbon monoxide 1 Σ 2187 2170 0.992 29 164
H2 Hydrogen diatomic 1 Σg 4409 4401 0.998 30 165
CF2 Difluoromethylene 1 A1 1271 1225 0.964 31 166
    2 A1 682 667 0.978 31 167
    3 B2 1181 1114 0.944 31 168
HCO Formyl radical 1 A' 2725 2434 0.893 32 169
    2 A' 1911 1868 0.978 32 170
    3 A' 1141 1081 0.947 32 171
ClNO Nitrosyl chloride 1 A' 1845 1800 0.975 33 172
    2 A' 630 596 0.946 33 173
    3 A' 356 332 0.932 33 174
CS carbon monosulfide 1 Σ 1288 1285 0.998 34 175
HO2 Hydroperoxy radical 1 A' 3719 3436 0.924 35 176
    2 A' 1451 1392 0.959 35 177
    3 A' 1130 1098 0.971 35 178
CH Methylidyne 1 Σ 2852 2861 1.003 36 179
    1 Σ 3134 3145 1.004 36 180
CF Fluoromethylidyne 1 Σ 1328 1308 0.985 37 181
CCl carbon monochloride 1 Σ 869 877 1.009 38 182
HNC hydrogen isocyanide 1 Σ 3857 3653 0.947 39 183
    2 Σ 2087 2029 0.972 39 184
    3 Π 484 477 0.985 39 185
SO2 Sulfur dioxide 1 A1 1195 1151 0.963 40 186
    2 A1 530 518 0.978 40 187
    3 B2 1394 1362 0.977 40 188
SO3 Sulfur trioxide 1 A1' 1096 1065 0.972 41 189
    2 A2" 506 498 0.984 41 190
    3 E' 1428 1391 0.974 41 191
    4 E' 532 530 0.995 41 192
LiCl lithium chloride 1 Σ 639 643 1.006 42 193
LiH Lithium Hydride 1 Σ 1395 1405 1.008 43 194
SiO2 silicon dioxide 2 Σu 1449 1416 0.977 44 195
    3 Πu 300 273 0.907 44 196
NaH sodium hydride 1 Σ 1132 1172 1.036 45 197
HCl Hydrogen chloride 1 Σ 3019 2991 0.991 46 198
NaCl Sodium Chloride 1 Σ 354 365 1.031 47 199
HF Hydrogen fluoride 1 Σ 4202 4138 0.985 48 200
NaF sodium fluoride 1 Σ 550 536 0.975 49 201
MgH2 magnesium dihydride 2 Σu 1636 1572 0.961 50 202
    3 Πu 441 440 0.998 50 203
N2 Nitrogen diatomic 1 Σg 2409 2359 0.979 51 204
F2 Fluorine diatomic 1 Σg 1009 917 0.909 52 205
Cl2 Chlorine diatomic 1 Σg 562 560 0.996 53 206
H2S Hydrogen sulfide 1 A1 2734 2615 0.957 54 207
    2 A1 1219 1183 0.970 54 208
    3 B2 2748 2626 0.956 54 209
F2O Difluorine monoxide 1 A1 1008 928 0.920 55 210
    2 A1 494 461 0.933 55 211
    3 B2 952 831 0.873 55 212
OCS Carbonyl sulfide 1 Σ 2117 2062 0.974 56 213
    2 Σ 870 859 0.988 56 214
    3 Π 534 520 0.975 56 215
ClCN chlorocyanogen 1 Σ 2304 2216 0.962 57 216
    2 Σ 747 744 0.996 57 217
    3 Π 395 378 0.956 57 218
H2CS Thioformaldehyde 1 A1 3107 2971 0.956 58 219
    2 A1 1517 1456 0.959 58 220
    3 A1 1089 1059 0.973 58 221
    4 B1 1030 990 0.961 58 222
    5 B2 3196 3025 0.946 58 223
    6 B2 1014 991 0.977 58 224
BeO beryllium oxide 1 Σ 1434 1457 1.016 59 225
LiOH lithium hydroxide 1 Σ 4050 3688 0.910 60 226
    2 Σ 959 871 0.907 60 227
    3 Π 323 257 0.793 60 228
NaOH sodium hydroxide 1 Σ 3995 3637 0.910 61 229
    2 Σ 572 540 0.945 61 230
    3 Π 227 300 1.319 61 231
BF3 Borane, trifluoro- 1 A1' 905 888 0.981 62 232
    2 A2" 704 691 0.981 62 233
    3 E' 1503 1449 0.964 62 234
    4 E' 487 480 0.986 62 235
H2O2 Hydrogen peroxide 1 A 3846 3599 0.936 63 236
    2 A 1465 1402 0.957 63 237
    3 A 968 877 0.906 63 238
    4 A 383 371 0.968 63 239
    5 B 3845 3608 0.938 63 240
    6 B 1354 1266 0.935 63 241
H2O Water 1 A1 3873 3657 0.944 64 242
    2 A1 1677 1595 0.951 64 243
    3 B2 3976 3756 0.945 64 244
HNO2 Nitrous acid 1 A' 3834 3591 0.937 65 245
    2 A' 1782 1700 0.954 65 246
    3 A' 1348 1263 0.937 65 247
    4 A' 877 790 0.901 65 248
    5 A' 662 596 0.899 65 249
    6 A" 573 543 0.948 65 250
NF3 Nitrogen trifluoride 4 E 519 492 0.949 66 251
    3 E 1003 907 0.905 66 252
    2 A1 681 647 0.951 66 253
    1 A1 1089 1032 0.948 66 254
NH3 Ammonia 1 A1 3499 3337 0.954 67 255
    2 A1 1110 950 0.856 67 256
    3 E 3623 3444 0.951 67 257
    4 E 1700 1627 0.957 67 258

How do we calculate the scaling factor?


Histogram of vibrational frequency ratios

Ratios greater than 1.35 are in the 1.35 bin. Ratios less than 0.7 are in the 0.7 bin.

180
160
140
120
100
80
60
40
20
0
0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35
Ratio of experimental frequency to calculated frequency