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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP4/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.969 ± 0.036 69 311 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4442 4161 0.937 1 1
LiH Lithium Hydride 1 Σ 1405 1360 0.968 2 2
NaH sodium hydride 1 Σ 1147 1133 0.988 3 3
N2 Nitrogen diatomic 1 Σg 2191 2330 1.063 4 4
BeO beryllium oxide 1 Σ 994 1435 1.443 5 5
CO Carbon monoxide 1 Σ 2009 2143 1.067 6 6
MgO magnesium oxide 1 Σ 1148 775 0.675 7 7
CS carbon monosulfide 1 Σ 1168 1272 1.090 8 8
HF Hydrogen fluoride 1 Σ 4167 3961 0.951 9 9
CF Fluoromethylidyne 1 Σ 1301 1286 0.989 10 10
F2 Fluorine diatomic 1 Σg 924 894 0.967 11 11
NaF sodium fluoride 1 Σ 543 529 0.974 12 12
HCl Hydrogen chloride 1 Σ 3011 2886 0.958 13 13
LiCl lithium chloride 1 Σ 637 634 0.995 14 14
CCl carbon monochloride 1 Σ 870 866 0.996 15 15
NaCl Sodium Chloride 1 Σ 353 361 1.023 16 16
Cl2 Chlorine diatomic 1 Σg 550 554 1.008 17 17
MgH2 magnesium dihydride 2 Σu 1645 1572 0.956 18 18
    3 Πu 442 440 0.995 18 19
HCN Hydrogen cyanide 1 Σ 3439 3312 0.963 19 20
    2 Σ 2014 2089 1.037 19 21
    3 Π 705 712 1.010 19 22
HNC hydrogen isocyanide 1 Σ 3824 3653 0.955 20 23
    2 Σ 1960 2029 1.035 20 24
    3 Π 452 477 1.055 20 25
HCP HCP 1 Σ 3334 3217 0.965 21 26
    2 Σ 1221 1278 1.047 21 27
    3 Π 673 674 1.003 21 28
H2O Water 1 A1 3834 3657 0.954 22 29
    2 A1 1664 1595 0.959 22 30
    3 B2 3943 3756 0.952 22 31
LiOH lithium hydroxide 1 Σ 3994 3688 0.923 23 32
    2 Σ 956 871 0.911 23 33
    3 Π 318 257 0.807 23 34
HCO Formyl radical 1 A' 2672 2434 0.911 24 35
    2 A' 1862 1868 1.003 24 36
    3 A' 1108 1081 0.976 24 37
HO2 Hydroperoxy radical 1 A' 3671 3436 0.936 25 38
    2 A' 1442 1392 0.965 25 39
    3 A' 1185 1098 0.926 25 40
CO2 Carbon dioxide 1 Σg 1270 1333 1.050 26 41
    2 Σu 2348 2349 1.000 26 42
    3 Πu 634 667 1.051 26 43
NaOH sodium hydroxide 1 Σ 3936 3637 0.924 27 44
    2 Σ 568 540 0.951 27 45
    3 Π 213 300 1.411 27 46
SiO2 silicon dioxide 2 Σu 1358 1416 1.043 28 47
    3 Πu 270 273 1.008 28 48
H2S Hydrogen sulfide 1 A1 2731 2615 0.957 29 49
    2 A1 1204 1183 0.982 29 50
    3 B2 2747 2626 0.956 29 51
OCS Carbonyl sulfide 1 Σ 1998 2062 1.032 30 52
    2 Σ 846 859 1.015 30 53
    3 Π 504 520 1.033 30 54
SO2 Sulfur dioxide 1 A1 1032 1151 1.116 31 55
    2 A1 483 518 1.071 31 56
    3 B2 1252 1362 1.088 31 57
CF2 Difluoromethylene 1 A1 1228 1225 0.997 32 58
    2 A1 664 667 1.005 32 59
    3 B2 1133 1114 0.984 32 60
NF2 Difluoroamino radical 1 A1 1096 1075 0.981 33 61
    2 A1 574 573 0.999 33 62
    3 B2 961 942 0.981 33 63
F2O Difluorine monoxide 1 A1 918 928 1.011 34 64
    2 A1 459 461 1.005 34 65
    3 B2 842 831 0.987 34 66
ClCN chlorocyanogen 1 Σ 2114 2216 1.048 35 67
    2 Σ 730 744 1.019 35 68
    3 Π 376 378 1.006 35 69
ClNO Nitrosyl chloride 1 A' 1758 1800 1.024 36 70
    2 A' 582 596 1.024 36 71
    3 A' 325 332 1.023 36 72
CCl2 dichloromethylene 1 A1 726 730 1.006 37 73
    2 A1 333 335 1.007 37 74
    3 B2 749 758 1.012 37 75
C2H2 Acetylene 1 Σg 3512 3374 0.961 38 76
    2 Σg 1961 1974 1.006 38 77
    3 Σu 3415 3289 0.963 38 78
    4 Πg 566 612 1.081 38 79
    5 Πu 743 730 0.982 38 80
NH3 Ammonia 1 A1 3470 3337 0.962 39 81
    2 A1 1108 950 0.857 39 82
    3 E 3601 3444 0.956 39 83
    4 E 1687 1627 0.964 39 84
C2N2 Cyanogen 1 Σg 2234 2330 1.043 40 85
    2 Σg 840 846 1.007 40 86
    3 Σu 2043 2158 1.056 40 87
    4 Πg 500 503 1.007 40 88
    5 Πu 233 234 1.005 40 89
H2CO Formaldehyde 1 A1 2919 2782 0.953 41 90
    2 A1 1745 1746 1.001 41 91
    3 A1 1532 1500 0.979 41 92
    4 B1 1188 1167 0.982 41 93
    5 B2 2983 2843 0.953 41 94
    6 B2 1266 1249 0.987 41 95
H2O2 Hydrogen peroxide 1 A 3800 3599 0.947 42 96
    2 A 1426 1402 0.983 42 97
    3 A 898 877 0.977 42 98
    4 A 357 371 1.038 42 99
    5 B 3798 3608 0.950 42 100
    6 B 1313 1266 0.964 42 101
HNCO Isocyanic acid 1 A' 3679 3538 0.962 43 102
    2 A' 2270 2269 0.999 43 103
    3 A' 1250 1327 1.061 43 104
    4 A' 819 777 0.948 43 105
    5 A' 554 577 1.042 43 106
    6 A" 608 656 1.079 43 107
HNO2 Nitrous acid 1 A' 3765 3591 0.954 44 108
    2 A' 1641 1700 1.036 44 109
    3 A' 1273 1263 0.992 44 110
    4 A' 796 790 0.992 44 111
    5 A' 569 596 1.046 44 112
    6 A" 582 543 0.933 44 113
H2CS Thioformaldehyde 1 A1 3073 2971 0.967 45 114
    2 A1 1494 1456 0.974 45 115
    3 A1 1061 1059 0.998 45 116
    4 B1 1006 990 0.984 45 117
    5 B2 3165 3025 0.956 45 118
    6 B2 1002 991 0.989 45 119
SO3 Sulfur trioxide 1 A1' 987 1065 1.080 46 120
    2 A2" 469 498 1.063 46 121
    3 E' 1349 1391 1.031 46 122
    4 E' 497 530 1.066 46 123
CF2O Carbonic difluoride 1 A1 1937 1928 0.995 47 124
    2 A1 956 965 1.009 47 125
    3 A1 581 584 1.005 47 126
    4 B1 772 774 1.002 47 127
    5 B2 1259 1249 0.992 47 128
    6 B2 614 626 1.019 47 129
BF3 Borane, trifluoro- 1 A1' 888 888 1.000 48 130
    2 A2" 694 691 0.996 48 131
    3 E' 1479 1449 0.980 48 132
    4 E' 479 480 1.002 48 133
CF3 Trifluoromethyl radical 1 A1 1100 1089 0.990 49 134
    2 A1 706 701 0.993 49 135
    3 E 1282 1260 0.983 49 136
    4 E 509 509 0.998 49 137
NF3 Nitrogen trifluoride 1 A1 1026 1032 1.006 50 138
    2 A1 648 647 0.999 50 139
    3 E 905 907 1.002 50 140
    4 E 491 492 1.003 50 141
PF3 Phosphorus trifluoride 1 A1 889 892 1.004 51 142
    2 A1 478 487 1.020 51 143
    3 E 864 860 0.995 51 144
    4 E 340 344 1.011 51 145
PCl3 Phosphorus trichloride 1 A1 516 504 0.977 52 146
    2 A1 257 252 0.981 52 147
    3 E 508 482 0.949 52 148
    4 E 185 198 1.068 52 149
CH4 Methane 1 A1 3039 2917 0.960 53 150
    2 E 1572 1534 0.976 53 151
    3 T2 3163 3019 0.955 53 152
    4 T2 1343 1306 0.972 53 153
CH2NH Methanimine 1 A' 3439 3263 0.949 54 154
    2 A' 3152 3024 0.959 54 155
    3 A' 3049 2914 0.956 54 156
    4 A' 1660 1638 0.987 54 157
    5 A' 1477 1452 0.983 54 158
    6 A' 1379 1344 0.975 54 159
    7 A' 1069 1058 0.990 54 160
    8 A" 1165 1127 0.968 54 161
    9 A" 1081 1061 0.982 54 162
HNO3 Nitric acid 1 A' 3730 3550 0.952 55 163
    2 A' 1771 1708 0.965 55 164
    3 A' 1328 1331 1.002 55 165
    4 A' 1286 1325 1.030 55 166
    5 A' 857 879 1.025 55 167
    6 A' 631 647 1.025 55 168
    7 A' 569 579 1.017 55 169
    8 A" 759 762 1.004 55 170
    9 A" 486 456 0.938 55 171
C3O2 Carbon suboxide 1 Σg 2123 2196 1.034 56 172
    2 Σg 742 786 1.060 56 173
    3 Σu 2367 2258 0.954 56 174
    4 Σu 1527 1573 1.030 56 175
    5 Πg 557 573 1.029 56 176
    6 Πu 508 550 1.083 56 177
    7 Πu 53 61 1.150 56 178
CH3F Methyl fluoride 1 A1 3047 2930 0.962 57 179
    2 A1 1498 1464 0.977 57 180
    3 A1 1081 1049 0.970 57 181
    4 E 3138 3006 0.958 57 182
    5 E 1507 1467 0.973 57 183
    6 E 1205 1182 0.981 57 184
CHF3 Methane, trifluoro- 1 A1 3162 3036 0.960 58 185
    2 A1 1148 1117 0.973 58 186
    3 A1 702 700 0.997 58 187
    4 E 1414 1372 0.970 58 188
    5 E 1185 1152 0.972 58 189
    6 E 509 507 0.995 58 190
CF4 Carbon tetrafluoride 1 A1 908 909 1.001 59 191
    2 E 435 435 1.000 59 192
    3 T2 1302 1283 0.986 59 193
    4 T2 632 631 0.998 59 194
SiF4 Silicon tetrafluoride 1 A1 783 800 1.021 60 195
    2 E 257 268 1.041 60 196
    3 T2 1026 1032 1.006 60 197
    4 T2 381 389 1.022 60 198
C2H4 Ethylene 1 Ag 3162 3026 0.957 61 199
    2 Ag 1666 1623 0.974 61 200
    3 Ag 1368 1342 0.981 61 201
    4 Au 1054 1023 0.970 61 202
    5 B1u 3143 2989 0.951 61 203
    6 B1u 1477 1444 0.978 61 204
    7 B2g 942 940 0.997 61 205
    8 B2u 3253 3105 0.954 61 206
    9 B2u 819 826 1.008 61 207
    10 B3g 3226 3086 0.957 61 208
    11 B3g 1240 1217 0.982 61 209
    12 B3u 969 949 0.980 61 210
C4H2 Diacetylene 6 Πg 609 627 1.030 62 211
    7 Πg 475 482 1.016 62 212
    8 Πu 616 630 1.023 62 213
    9 Πu 227 231 1.018 62 214
N2H4 Hydrazine 1 A 3574 3398 0.951 63 215
    2 A 3474 3329 0.958 63 216
    3 A 1687 1642 0.973 63 217
    4 A 1346 1275 0.948 63 218
    5 A 1125 1076 0.957 63 219
    6 A 852 780 0.915 63 220
    7 A 400 377 0.943 63 221
    8 B 3579 3350 0.936 63 222
    9 B 3464 3314 0.957 63 223
    10 B 1674 1628 0.973 63 224
    11 B 1311 1275 0.972 63 225
    12 B 1046 966 0.924 63 226
C4N2 2-Butynedinitrile 1 Σg 2229 2290 1.027 64 227
    2 Σg 2022 2119 1.048 64 228
    3 Σg 590 692 1.172 64 229
    4 Σu 2141 2241 1.047 64 230
    5 Σu 1136 1154 1.016 64 231
    6 Πg 501 504 1.005 64 232
    7 Πg 266 263 0.990 64 233
    8 Πu 476 472 0.992 64 234
    9 Πu 110 107 0.977 64 235
C2H6 Ethane 1 A1g 3042 2954 0.971 65 236
    2 A1g 1425 1388 0.974 65 237
    3 A1g 1014 995 0.981 65 238
    4 A1u 310 289 0.932 65 239
    5 A2u 3042 2896 0.952 65 240
    6 A2u 1405 1379 0.981 65 241
    7 Eg 3105 2969 0.956 65 242
    8 Eg 1512 1468 0.971 65 243
    9 Eg 1224 1190 0.972 65 244
    10 Eu 3128 2985 0.954 65 245
    11 Eu 1513 1469 0.971 65 246
    12 Eu 820 822 1.002 65 247
C3H6 Cyclopropane 1 A1' 3159 3038 0.962 66 248
    2 A1' 1525 1479 0.970 66 249
    3 A1' 1214 1188 0.979 66 250
    4 A1" 1161 1126 0.970 66 251
    5 A2' 1085 1070 0.986 66 252
    6 A2" 3254 3103 0.954 66 253
    7 A2" 856 854 0.997 66 254
    8 E' 3149 3025 0.961 66 255
    9 E' 1476 1438 0.974 66 256
    10 E' 1057 1029 0.974 66 257
    11 E' 891 866 0.972 66 258
    12 E" 3235 3082 0.953 66 259
    13 E" 1216 1188 0.977 66 260
    14 E" 739 739 1.000 66 261
CH3CH2OH Ethanol 1 A' 3843 3653 0.951 67 262
    2 A' 3130 2984 0.953 67 263
    3 A' 3047 2939 0.965 67 264
    4 A' 3002 2900 0.966 67 265
    5 A' 1536 1490 0.970 67 266
    6 A' 1508 1464 0.971 67 267
    7 A' 1464 1412 0.965 67 268
    8 A' 1401 1371 0.979 67 269
    9 A' 1280 1256 0.981 67 270
    10 A' 1115 1091 0.978 67 271
    11 A' 1048 1028 0.980 67 272
    12 A' 906 888 0.980 67 273
    13 A' 411 417 1.012 67 274
    14 A" 3135 2991 0.954 67 275
    15 A" 3038 2910 0.958 67 276
    16 A" 1490 1446 0.971 67 277
    17 A" 1304 1275 0.978 67 278
    18 A" 1184 1161 0.980 67 279
    19 A" 818 812 0.993 67 280
    20 A" 283 251 0.887 67 281
    21 A" 237 200 0.844 67 282
CH3CH2SH ethanethiol 1 A' 3124 2966 0.949 68 283
    2 A' 3070 2872 0.936 68 284
    3 A' 3043 2872 0.944 68 285
    4 A' 2717 2580 0.950 68 286
    5 A' 1509 1453 0.963 68 287
    6 A' 1495 1453 0.972 68 288
    7 A' 1411 1385 0.982 68 289
    8 A' 1299 1309 1.008 68 290
    9 A' 1114 1097 0.985 68 291
    10 A' 1001 978 0.977 68 292
    11 A' 859 870 1.013 68 293
    12 A' 686 660 0.962 68 294
    13 A' 301 332 1.103 68 295
    14 A" 3135 2966 0.946 68 296
    15 A" 3113 2930 0.941 68 297
    16 A" 1500 1453 0.969 68 298
    17 A" 1271 1269 0.999 68 299
    18 A" 1045 1049 1.004 68 300
    19 A" 788 745 0.945 68 301

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.

40 140 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 80 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 60 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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