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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCD/TZVP
Scale factor How many Source
Molecules Vibrations
0.948 ± 0.033 49 290 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1408 1360 0.966 1 1
Li2 Lithium diatomic 1 Σg 337 346 1.027 2 2
NaH sodium hydride 1 Σ 1134 1133 1.000 3 3
Na2 Sodium diatomic 1 Σg 143 158 1.104 4 4
BeH beryllium monohydride 1 Σ 2092 1987 0.950 5 5
C2 Carbon diatomic 1 Σg 1920 1827 0.952 6 6
CN Cyano radical 1 Σ 2676 2042 0.763 7 7
N2 Nitrogen diatomic 1 Σg 2419 2330 0.963 8 8
P2 Phosphorus diatomic 1 Σg 802 775 0.967 9 9
OH Hydroxyl radical 1 Σ 3778 3570 0.945 10 10
BeO beryllium oxide 1 Σ 1540 1435 0.932 11 11
CO Carbon monoxide 1 Σ 2265 2143 0.946 12 12
HS Mercapto radical 1 Σ 2720 2599 0.955 13 13
SO Sulfur monoxide 1 Σ 1178 1138 0.966 14 14
HF Hydrogen fluoride 1 Σ 4205 3961 0.942 15 15
F2 Fluorine diatomic 1 Σg 1010 894 0.885 16 16
SF Monosulfur monofluoride 1 Σ 826 829 1.003 17 17
HCl Hydrogen chloride 1 Σ 3034 2886 0.951 18 18
NaCl Sodium Chloride 1 Σ 346 361 1.044 19 19
AlCl Aluminum monochloride 1 Σ 489 478 0.976 20 20
SCl sulfur monochloride 1 Σ 551 577 1.047 21 21
Cl2 Chlorine diatomic 1 Σg 542 554 1.022 22 22
BeH2 beryllium dihydride 2 Σu 2290 2159 0.943 23 23
    3 Πu 747 698 0.934 23 24
SiH2 silicon dihydride 1 A1 2100 1996 0.950 24 25
    2 A1 1058 999 0.945 24 26
    3 B2 2093 1993 0.952 24 27
HCN Hydrogen cyanide 1 Σ 3505 3312 0.945 25 28
    2 Σ 2204 2089 0.948 25 29
    3 Π 754 712 0.944 25 30
CO2 Carbon dioxide 1 Σg 1417 1333 0.940 26 31
    2 Σu 2467 2349 0.952 26 32
    3 Πu 698 667 0.956 26 33
N2O Nitrous oxide 1 Σ 2379 2224 0.935 27 34
    2 Σ 1348 1285 0.954 27 35
    3 Π 560 589 1.052 27 36
SO2 Sulfur dioxide 1 A1 1194 1151 0.964 28 37
    2 A1 520 518 0.995 28 38
    3 B2 1382 1362 0.985 28 39
BH3 boron trihydride 2 A2" 1185 1148 0.969 29 40
    3 E' 2744 2602 0.948 29 41
    4 E' 1246 1197 0.960 29 42
C2H2 Acetylene 1 Σg 3559 3374 0.948 30 43
    2 Σg 2070 1974 0.954 30 44
    3 Σu 3461 3289 0.950 30 45
    4 Πg 380 612 1.613 30 46
    5 Πu 751 730 0.972 30 47
NH3 Ammonia 1 A1 3524 3337 0.947 31 48
    2 A1 1099 950 0.864 31 49
    3 E 3661 3444 0.941 31 50
    4 E 1678 1627 0.970 31 51
H2CO Formaldehyde 1 A1 2990 2782 0.930 32 52
    2 A1 1846 1746 0.946 32 53
    3 A1 1593 1500 0.941 32 54
    4 B1 1222 1167 0.955 32 55
    5 B2 3064 2843 0.928 32 56
    6 B2 1310 1249 0.953 32 57
BF3 Borane, trifluoro- 1 A1' 914 888 0.971 33 58
    2 A2" 712 691 0.971 33 59
    3 E' 1511 1449 0.959 33 60
    4 E' 483 480 0.993 33 61
AlF3 Aluminum trifluoride 1 A1' 693 690 0.996 34 62
    2 A2" 305 297 0.972 34 63
    3 E' 960 935 0.974 34 64
    4 E' 247 263 1.067 34 65
CH4 Methane 1 A1 3069 2917 0.950 35 66
    2 E 1569 1534 0.978 35 67
    3 T2 3192 3019 0.946 35 68
    4 T2 1380 1306 0.947 35 69
C2H4 Ethylene 1 Ag 3198 3026 0.946 36 70
    2 Ag 1716 1623 0.946 36 71
    3 Ag 1401 1342 0.958 36 72
    4 Au 1053 1023 0.972 36 73
    5 B1u 3180 2989 0.940 36 74
    6 B1u 1505 1444 0.959 36 75
    7 B2g 805 940 1.167 36 76
    8 B2u 3287 3105 0.945 36 77
    9 B2u 840 826 0.983 36 78
    10 B3g 3260 3086 0.947 36 79
    11 B3g 1254 1217 0.971 36 80
    12 B3u 961 949 0.987 36 81
CH3OH Methyl alcohol 1 A' 3914 3681 0.940 37 82
    2 A' 3177 3000 0.944 37 83
    3 A' 3052 2844 0.932 37 84
    4 A' 1545 1477 0.956 37 85
    5 A' 1530 1455 0.951 37 86
    6 A' 1408 1345 0.955 37 87
    7 A' 1111 1060 0.954 37 88
    8 A' 1089 1033 0.949 37 89
    9 A" 3110 2960 0.952 37 90
    10 A" 1520 1477 0.972 37 91
    11 A" 1210 1165 0.963 37 92
    12 A" 331 200 0.604 37 93
CHONH2 formamide 1 A' 3801 3564 0.937 38 94
    2 A' 3660 3439 0.940 38 95
    3 A' 3037 2854 0.940 38 96
    4 A' 1859 1754 0.944 38 97
    5 A' 1656 1577 0.952 38 98
    6 A' 1473 1390 0.943 38 99
    7 A' 1290 1258 0.975 38 100
    8 A' 1077 1046 0.971 38 101
    9 A' 583 581 0.997 38 102
    10 A" 1057 1021 0.966 38 103
    11 A" 612 603 0.985 38 104
    12 A" 337i 289 -0.856 38 105
B2Cl4 Diboron tetrachloride 1 A1 1167 1122 0.962 39 106
    2 A1 415 401 0.967 39 107
    3 A1 180 176 0.980 39 108
    5 B2 752 728 0.968 39 109
    6 B2 304 289 0.950 39 110
    7 E 952 917 0.963 39 111
    8 E 512 512 1.001 39 112
    9 E 102 104 1.016 39 113
CH2N4 1H-Tetrazole 1 A' 3726 3447 0.925 40 114
    2 A' 3343 3102 0.928 40 115
    3 A' 1562 1441 0.923 40 116
    4 A' 1516 1384 0.913 40 117
    5 A' 1340 1259 0.940 40 118
    6 A' 1314 1159 0.882 40 119
    7 A' 1178 1084 0.921 40 120
    8 A' 1117 1015 0.909 40 121
    9 A' 1082 1002 0.926 40 122
    10 A' 1027 969 0.944 40 123
    11 A' 988 925 0.936 40 124
    12 A" 838 906 1.081 40 125
    13 A" 726 663 0.914 40 126
    14 A" 687 658 0.958 40 127
    15 A" 480 578 1.205 40 128
H2SO4 Sulfuric acid 1 A 3856 3563 0.924 41 129
    2 A 1220 1216 0.997 41 130
    3 A 1192 1136 0.953 41 131
    4 A 840 831 0.989 41 132
    5 A 536 548 1.023 41 133
    6 A 433 422 0.973 41 134
    7 A 380 379 0.997 41 135
    8 A 259 224 0.866 41 136
    9 B 3852 3567 0.926 41 137
    10 B 1479 1452 0.982 41 138
    11 B 1204 1157 0.961 41 139
    12 B 891 882 0.990 41 140
    13 B 551 558 1.012 41 141
    14 B 496 506 1.021 41 142
    15 B 319 288 0.901 41 143
C2H6 Ethane 1 A1g 3076 2954 0.960 42 144
    2 A1g 1468 1388 0.945 42 145
    3 A1g 1024 995 0.972 42 146
    4 A1u 325 289 0.889 42 147
    5 A2u 3074 2896 0.942 42 148
    6 A2u 1441 1379 0.957 42 149
    7 Eg 3137 2969 0.946 42 150
    8 Eg 1524 1468 0.963 42 151
    9 Eg 1252 1190 0.951 42 152
    10 Eu 3160 2985 0.945 42 153
    11 Eu 1528 1469 0.961 42 154
    12 Eu 837 822 0.982 42 155
C3H5 Allyl radical 1 A1 3304 3114 0.943 43 156
    2 A1 3206 3048 0.951 43 157
    4 A1 1564 1488 0.952 43 158
    5 A1 1310 1245 0.950 43 159
    6 A1 1064 1066 1.002 43 160
    7 A1 438 427 0.974 43 161
    9 A2 552 549 0.995 43 162
    10 B1 988 968 0.979 43 163
    11 B1 682 802 1.175 43 164
    12 B1 513 518 1.010 43 165
    13 B2 3301 3105 0.941 43 166
    14 B2 3197 3016 0.943 43 167
    15 B2 1529 1463 0.957 43 168
    16 B2 1443 1389 0.962 43 169
    17 B2 1153 1182 1.025 43 170
C3H3NO Oxazole 1 A' 3355 3170 0.945 44 171
    2 A' 3330 3144 0.944 44 172
    3 A' 3321 3141 0.946 44 173
    4 A' 1630 1537 0.943 44 174
    5 A' 1584 1504 0.950 44 175
    6 A' 1400 1324 0.945 44 176
    7 A' 1317 1252 0.950 44 177
    8 A' 1223 1139 0.932 44 178
    9 A' 1147 1086 0.947 44 179
    10 A' 1131 1078 0.953 44 180
    11 A' 1108 1046 0.944 44 181
    12 A' 950 899 0.946 44 182
    13 A' 932 854 0.917 44 183
    14 A" 834 907 1.088 44 184
    15 A" 795 830 1.044 44 185
    16 A" 728 750 1.030 44 186
    17 A" 648 647 0.998 44 187
    18 A" 592 607 1.025 44 188
C3H6 Cyclopropane 1 A1' 3190 3038 0.952 45 189
    2 A1' 1561 1479 0.947 45 190
    3 A1' 1235 1188 0.962 45 191
    4 A1" 1196 1126 0.941 45 192
    5 A2' 1134 1070 0.943 45 193
    6 A2" 3284 3103 0.945 45 194
    7 A2" 879 854 0.972 45 195
    8 E' 3180 3025 0.951 45 196
    9 E' 1507 1438 0.954 45 197
    10 E' 1117 1029 0.921 45 198
    11 E' 908 866 0.954 45 199
    12 E" 3264 3082 0.944 45 200
    13 E" 1247 1188 0.953 45 201
    14 E" 773 739 0.956 45 202
CH2CHCH3 Propene 1 A' 3271 3090 0.945 46 203
    2 A' 3190 3013 0.945 46 204
    3 A' 3179 2991 0.941 46 205
    4 A' 3150 2954 0.938 46 206
    5 A' 3065 2871 0.937 46 207
    6 A' 1742 1650 0.947 46 208
    7 A' 1528 1470 0.962 46 209
    8 A' 1486 1420 0.956 46 210
    9 A' 1446 1378 0.953 46 211
    10 A' 1347 1297 0.963 46 212
    11 A' 1213 1171 0.966 46 213
    12 A' 964 963 0.999 46 214
    13 A' 941 920 0.978 46 215
    14 A' 431 428 0.994 46 216
    15 A" 3128 2954 0.944 46 217
    16 A" 1499 1443 0.963 46 218
    17 A" 1086 1045 0.962 46 219
    18 A" 1013 991 0.979 46 220
    19 A" 868 912 1.051 46 221
    20 A" 569 578 1.016 46 222
    21 A" 193 174 0.902 46 223
CHCCH2CH3 1-Butyne 1 A' 3514 3332 0.948 47 224
    2 A' 3160 2988 0.945 47 225
    3 A' 3086     47 226
    4 A' 3080     47 227
    5 A' 2240 2116 0.945 47 228
    6 A' 1531 1470 0.960 47 229
    7 A' 1514 1446 0.955 47 230
    8 A' 1452 1385 0.954 47 231
    9 A' 1391 1322 0.950 47 232
    10 A' 1117 1070 0.958 47 233
    11 A' 1045 1008 0.965 47 234
    12 A' 861 840 0.976 47 235
    13 A' 629 634 1.009 47 236
    14 A' 508 509 1.001 47 237
    15 A' 182 197 1.078 47 238
    16 A" 3167 2988 0.944 47 239
    17 A" 3122 2939 0.941 47 240
    18 A" 1524 1462 0.959 47 241
    19 A" 1311 1261 0.962 47 242
    20 A" 1133 1090 0.962 47 243
    21 A" 804 782 0.973 47 244
    22 A" 600 630 1.049 47 245
    23 A" 319 344 1.077 47 246
    24 A" 202 213 1.053 47 247
CH3CHClCH3 Propane, 2-chloro- 1 A' 3176 3005 0.946 48 248
    2 A' 3158 2955 0.936 48 249
    3 A' 3136 2927 0.933 48 250
    4 A' 3077 2878 0.935 48 251
    5 A' 1530 1472 0.962 48 252
    6 A' 1524 1454 0.954 48 253
    7 A' 1466 1390 0.948 48 254
    8 A' 1344 1270 0.945 48 255
    9 A' 1225 1163 0.950 48 256
    10 A' 1115 1065 0.955 48 257
    11 A' 929 888 0.956 48 258
    12 A' 666 633 0.950 48 259
    13 A' 432 418 0.968 48 260
    14 A' 346 336 0.970 48 261
    15 A' 290 253 0.874 48 262
    16 A" 3170 2997 0.945 48 263
    17 A" 3149 2985 0.948 48 264
    18 A" 3072 2947 0.959 48 265
    19 A" 1510 1472 0.975 48 266
    20 A" 1510 1454 0.963 48 267
    21 A" 1450 1377 0.950 48 268
    22 A" 1390 1334 0.960 48 269
    23 A" 1179 1123 0.953 48 270
    24 A" 981 972 0.991 48 271
    25 A" 965 936 0.970 48 272
    26 A" 333 317 0.952 48 273
    27 A" 247 276 1.118 48 274

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.

40 200 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 150 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 50 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