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

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