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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at HSEh1PBE/6-31G**
Scale factor How many Source
Molecules Vibrations
0.954 ± 0.019 51 303 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4460 4161 0.933 1 1
LiH Lithium Hydride 1 Σ 1390 1360 0.978 2 2
Li2 Lithium diatomic 1 Σg 338 346 1.024 3 3
NaH sodium hydride 1 Σ 1175 1133 0.964 4 4
Na2 Sodium diatomic 1 Σg 158 158 0.996 5 5
BeH beryllium monohydride 1 Σ 2051 1987 0.969 6 6
C2 Carbon diatomic 1 Σg 1920 1827 0.952 7 7
CN Cyano radical 1 Σ 2195 2042 0.931 8 8
N2 Nitrogen diatomic 1 Σg 2496 2330 0.933 9 9
    1 Σg 1895 1733 0.915 9 10
P2 Phosphorus diatomic 1 Σg 817 775 0.949 10 11
OH Hydroxyl radical 1 Σ 3767 3570 0.948 11 12
BeO beryllium oxide 1 Σ 1563 1435 0.918 12 13
CO Carbon monoxide 1 Σ 2239 2143 0.957 13 14
    1 Σ 1848     13 15
HS Mercapto radical 1 Σ 2733 2599 0.951 14 16
SO Sulfur monoxide 1 Σ 1163 1138 0.979 15 17
    1 Σ 1161 1054 0.908 15 18
HF Hydrogen fluoride 1 Σ 4155 3961 0.954 16 19
F2 Fluorine diatomic 1 Σg 1095 894 0.816 17 20
SF Monosulfur monofluoride 1 Σ 865 829 0.958 18 21
HCl Hydrogen chloride 1 Σ 3013 2886 0.958 19 22
NaCl Sodium Chloride 1 Σ 359 361 1.005 20 23
AlCl Aluminum monochloride 1 Σ 468 478 1.021 21 24
SCl sulfur monochloride 1 Σ 579 577 0.997 22 25
Cl2 Chlorine diatomic 1 Σg 549 554 1.010 23 26
BeH2 beryllium dihydride 2 Σu 2262 2159 0.954 24 27
    3 Πu 729 698 0.957 24 28
SiH2 silicon dihydride 1 A1 2059 1996 0.970 25 29
    2 A1 1026 999 0.974 25 30
    3 B2 2065 1993 0.965 25 31
HCN Hydrogen cyanide 1 Σ 3495 3312 0.948 26 32
    2 Σ 2237 2089 0.934 26 33
    3 Π 779 712 0.914 26 34
H2O Water 1 A1 3868 3657 0.945 27 35
    2 A1 1670 1595 0.955 27 36
    3 B2 3987 3756 0.942 27 37
CO2 Carbon dioxide 1 Σg 1396 1333 0.955 28 38
    2 Σu 2480 2349 0.947 28 39
    3 Πu 655 667 1.019 28 40
N2O Nitrous oxide 1 Σ 2437 2224 0.913 29 41
    2 Σ 1389 1285 0.925 29 42
    3 Π 625 589 0.942 29 43
SO2 Sulfur dioxide 1 A1 1178 1151 0.977 30 44
    2 A1 513 518 1.010 30 45
    3 B2 1381 1362 0.986 30 46
BH3 boron trihydride 2 A2" 1151 1148 0.997 31 47
    3 E' 2717 2602 0.958 31 48
    4 E' 1201 1197 0.996 31 49
C2H2 Acetylene 1 Σg 3555 3374 0.949 32 50
    2 Σg 2100 1974 0.940 32 51
    3 Σu 3453 3289 0.953 32 52
    4 Πg 598 612 1.024 32 53
    5 Πu 779 730 0.937 32 54
NH3 Ammonia 1 A1 3510 3337 0.951 33 55
    2 A1 1079 950 0.881 33 56
    3 E 3651 3444 0.943 33 57
    4 E 1695 1627 0.960 33 58
H2CO Formaldehyde 1 A1 2920 2782 0.953 34 59
    2 A1 1876 1746 0.931 34 60
    3 A1 1556 1500 0.964 34 61
    4 B1 1207 1167 0.967 34 62
    5 B2 2980 2843 0.954 34 63
    6 B2 1277 1249 0.978 34 64
BF3 Borane, trifluoro- 1 A1' 896 888 0.991 35 65
    2 A2" 686 691 1.007 35 66
    3 E' 1503 1449 0.964 35 67
    4 E' 479 480 1.001 35 68
AlF3 Aluminum trifluoride 1 A1' 710 690 0.971 36 69
    2 A2" 293 297 1.013 36 70
    3 E' 995 935 0.940 36 71
    4 E' 257 263 1.024 36 72
CH4 Methane 1 A1 3065 2917 0.952 37 73
    2 E 1576 1534 0.973 37 74
    3 T2 3197 3019 0.944 37 75
    4 T2 1346 1306 0.970 37 76
C2H4 Ethylene 1 Ag 3185 3026 0.950 38 77
    2 Ag 1727 1623 0.940 38 78
    3 Ag 1391 1342 0.965 38 79
    4 Au 1074 1023 0.952 38 80
    5 B1u 3167 2989 0.944 38 81
    6 B1u 1476 1444 0.978 38 82
    7 B2g 969 940 0.970 38 83
    8 B2u 3275 3105 0.948 38 84
    9 B2u 828 826 0.997 38 85
    10 B3g 3249 3086 0.950 38 86
    11 B3g 1238 1217 0.983 38 87
    12 B3u 980 949 0.968 38 88
CH3OH Methyl alcohol 1 A' 3894 3681 0.945 39 89
    2 A' 3148 3000 0.953 39 90
    3 A' 3009 2844 0.945 39 91
    4 A' 1526 1477 0.968 39 92
    5 A' 1498 1455 0.971 39 93
    6 A' 1390 1345 0.967 39 94
    7 A' 1124 1060 0.943 39 95
    8 A' 1076 1033 0.960 39 96
    9 A" 3063 2960 0.967 39 97
    10 A" 1508 1477 0.980 39 98
    11 A" 1184 1165 0.984 39 99
    12 A" 340 200 0.589 39 100
CHONH2 formamide 1 A' 3788 3564 0.941 40 101
    2 A' 3639 3439 0.945 40 102
    3 A' 2974 2854 0.960 40 103
    4 A' 1869 1754 0.938 40 104
    5 A' 1628 1577 0.969 40 105
    6 A' 1435 1390 0.969 40 106
    7 A' 1295 1258 0.972 40 107
    8 A' 1065 1046 0.982 40 108
    9 A' 565 581 1.028 40 109
    10 A" 1055 1021 0.968 40 110
    11 A" 656 603 0.918 40 111
    12 A" 203 289 1.419 40 112
B2Cl4 Diboron tetrachloride 1 A1 1149 1122 0.976 41 113
    2 A1 411 401 0.976 41 114
    3 A1 175 176 1.005 41 115
    5 B2 742 728 0.981 41 116
    6 B2 298 289 0.971 41 117
    7 E 939 917 0.977 41 118
    8 E 495 512 1.035 41 119
    9 E 97 104 1.074 41 120
CH2N4 1H-Tetrazole 1 A' 3706 3447 0.930 42 121
    2 A' 3324 3102 0.933 42 122
    3 A' 1541 1441 0.935 42 123
    4 A' 1494 1384 0.926 42 124
    5 A' 1343 1259 0.938 42 125
    6 A' 1295 1159 0.895 42 126
    7 A' 1167 1084 0.929 42 127
    8 A' 1112 1015 0.913 42 128
    9 A' 1095 1002 0.915 42 129
    10 A' 1028 969 0.943 42 130
    11 A' 994 925 0.930 42 131
    12 A" 862 906 1.050 42 132
    13 A" 752 663 0.881 42 133
    14 A" 702 658 0.937 42 134
    15 A" 607 578 0.952 42 135
C2H6 Ethane 1 A1g 3065 2954 0.964 43 136
    2 A1g 1440 1388 0.964 43 137
    3 A1g 1031 995 0.965 43 138
    4 A1u 315 289 0.917 43 139
    5 A2u 3066 2896 0.945 43 140
    6 A2u 1411 1379 0.977 43 141
    7 Eg 3132 2969 0.948 43 142
    8 Eg 1514 1468 0.969 43 143
    9 Eg 1224 1190 0.973 43 144
    10 Eu 3156 2985 0.946 43 145
    11 Eu 1517 1469 0.969 43 146
    12 Eu 827 822 0.994 43 147
C3H5 Allyl radical 1 A1 3287 3114 0.947 44 148
    2 A1 3187 3048 0.957 44 149
    4 A1 1532 1488 0.971 44 150
    5 A1 1282 1245 0.971 44 151
    6 A1 1047 1066 1.018 44 152
    7 A1 423 427 1.009 44 153
    9 A2 556 549 0.987 44 154
    10 B1 1014 968 0.955 44 155
    11 B1 804 802 0.997 44 156
    12 B1 533 518 0.971 44 157
    13 B2 3285 3105 0.945 44 158
    14 B2 3180 3016 0.948 44 159
    15 B2 1530 1463 0.956 44 160
    16 B2 1425 1389 0.975 44 161
    17 B2 1222 1182 0.968 44 162
C3H3NO Oxazole 1 A' 3340 3170 0.949 45 163
    2 A' 3314 3144 0.949 45 164
    3 A' 3300 3141 0.952 45 165
    4 A' 1618 1537 0.950 45 166
    5 A' 1569 1504 0.959 45 167
    6 A' 1391 1324 0.952 45 168
    7 A' 1284 1252 0.975 45 169
    8 A' 1204 1139 0.946 45 170
    9 A' 1164 1086 0.933 45 171
    10 A' 1127 1078 0.957 45 172
    11 A' 1103 1046 0.948 45 173
    12 A' 936 899 0.960 45 174
    13 A' 920 854 0.928 45 175
    14 A" 882 907 1.028 45 176
    15 A" 845 830 0.983 45 177
    16 A" 770 750 0.974 45 178
    17 A" 673 647 0.962 45 179
    18 A" 635 607 0.956 45 180
C3H6 Cyclopropane 1 A1' 3173 3038 0.957 46 181
    2 A1' 1540 1479 0.961 46 182
    3 A1' 1249 1188 0.952 46 183
    4 A1" 1160 1126 0.971 46 184
    5 A2' 1088 1070 0.983 46 185
    6 A2" 3266 3103 0.950 46 186
    7 A2" 863 854 0.990 46 187
    8 E' 3165 3025 0.956 46 188
    9 E' 1481 1438 0.971 46 189
    10 E' 1069 1029 0.963 46 190
    11 E' 924 866 0.937 46 191
    12 E" 3247 3082 0.949 46 192
    13 E" 1219 1188 0.975 46 193
    14 E" 741 739 0.997 46 194
CH2CHCH3 Propene 1 A' 3262 3090 0.947 47 195
    2 A' 3175 3013 0.949 47 196
    3 A' 3166 2991 0.945 47 197
    4 A' 3147 2954 0.939 47 198
    5 A' 3050 2871 0.941 47 199
    6 A' 1752 1650 0.942 47 200
    7 A' 1503 1470 0.978 47 201
    8 A' 1457 1420 0.974 47 202
    9 A' 1413 1378 0.975 47 203
    10 A' 1330 1297 0.975 47 204
    11 A' 1199 1171 0.977 47 205
    12 A' 947 963 1.016 47 206
    13 A' 944 920 0.975 47 207
    14 A' 425 428 1.008 47 208
    15 A" 3114 2954 0.949 47 209
    16 A" 1488 1443 0.970 47 210
    17 A" 1071 1045 0.975 47 211
    18 A" 1036 991 0.956 47 212
    19 A" 942 912 0.969 47 213
    20 A" 591 578 0.977 47 214
    21 A" 211 174 0.825 47 215
CHCCH2CH3 1-Butyne 1 A' 3509 3332 0.950 48 216
    2 A' 3163 2988 0.945 48 217
    3 A' 3076     48 218
    4 A' 3059     48 219
    5 A' 2258 2116 0.937 48 220
    6 A' 1515 1470 0.970 48 221
    7 A' 1482 1446 0.975 48 222
    8 A' 1421 1385 0.975 48 223
    9 A' 1357 1322 0.974 48 224
    10 A' 1098 1070 0.974 48 225
    11 A' 1047 1008 0.963 48 226
    12 A' 866 840 0.970 48 227
    13 A' 643 634 0.987 48 228
    14 A' 526 509 0.968 48 229
    15 A' 203 197 0.966 48 230
    16 A" 3168 2988 0.943 48 231
    17 A" 3097 2939 0.949 48 232
    18 A" 1506 1462 0.971 48 233
    19 A" 1292 1261 0.976 48 234
    20 A" 1108 1090 0.983 48 235
    21 A" 790 782 0.990 48 236
    22 A" 630 630 1.000 48 237
    23 A" 370 344 0.928 48 238
    24 A" 224 213 0.949 48 239
C4H6 Bicyclo[1.1.0]butane 1 A1 3289 3131 0.952 49 240
    2 A1 3202 3044 0.951 49 241
    3 A1 3089 2935 0.950 49 242
    4 A1 1549 1501 0.969 49 243
    5 A1 1331 1266 0.951 49 244
    6 A1 1122 1081 0.963 49 245
    7 A1 912 839 0.920 49 246
    8 A1 710 657 0.925 49 247
    9 A1 431 423 0.980 49 248
    10 A2 1192 1172 0.983 49 249
    11 A2 1090 1063 0.975 49 250
    12 A2 948 909 0.959 49 251
    13 A2 875 838 0.957 49 252
    14 B1 3275 3120 0.953 49 253
    15 B1 1192 1110 0.931 49 254
    16 B1 1145 1092 0.954 49 255
    17 B1 1017 980 0.964 49 256
    18 B1 784 737 0.940 49 257
    19 B2 3204 3044 0.950 49 258
    20 B2 3093 2969 0.960 49 259
    21 B2 1504 1485 0.987 49 260
    22 B2 1349 1261 0.935 49 261
    23 B2 1121 1081 0.964 49 262
    24 B2 959 935 0.975 49 263
CH3CHClCH3 Propane, 2-chloro- 1 A' 3175 3005 0.946 50 264
    2 A' 3154 2955 0.937 50 265
    3 A' 3118 2927 0.939 50 266
    4 A' 3069 2878 0.938 50 267
    5 A' 1517 1472 0.971 50 268
    6 A' 1502 1454 0.968 50 269
    7 A' 1429 1390 0.973 50 270
    8 A' 1300 1270 0.977 50 271
    9 A' 1194 1163 0.974 50 272
    10 A' 1089 1065 0.978 50 273
    11 A' 914 888 0.972 50 274
    12 A' 638 633 0.992 50 275
    13 A' 424 418 0.985 50 276
    14 A' 341 336 0.986 50 277
    15 A' 277 253 0.914 50 278
    16 A" 3172 2997 0.945 50 279
    17 A" 3148 2985 0.948 50 280
    18 A" 3065 2947 0.961 50 281
    19 A" 1494 1472 0.985 50 282
    20 A" 1489 1454 0.977 50 283
    21 A" 1418 1377 0.971 50 284
    22 A" 1364 1334 0.978 50 285
    23 A" 1167 1123 0.962 50 286
    24 A" 959 972 1.014 50 287
    25 A" 944 936 0.992 50 288
    26 A" 326 317 0.974 50 289
    27 A" 248 276 1.112 50 290

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