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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at HSEh1PBE/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.961 ± 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 4413 4161 0.943 1 1
LiH Lithium Hydride 1 Σ 1405 1360 0.968 2 2
Li2 Lithium diatomic 1 Σg 339 346 1.022 3 3
NaH sodium hydride 1 Σ 1159 1133 0.978 4 4
Na2 Sodium diatomic 1 Σg 157 158 1.002 5 5
BeH beryllium monohydride 1 Σ 2039 1987 0.974 6 6
C2 Carbon diatomic 1 Σg 1902 1827 0.961 7 7
CN Cyano radical 1 Σ 2183 2042 0.936 8 8
N2 Nitrogen diatomic 1 Σg 2483 2330 0.938 9 9
    1 Σg 1870 1733 0.927 9 10
P2 Phosphorus diatomic 1 Σg 824 775 0.940 10 11
OH Hydroxyl radical 1 Σ 3757 3570 0.950 11 12
BeO beryllium oxide 1 Σ 1565 1435 0.917 12 13
CO Carbon monoxide 1 Σ 2236 2143 0.958 13 14
    1 Σ 1840     13 15
HS Mercapto radical 1 Σ 2711 2599 0.959 14 16
SO Sulfur monoxide 1 Σ 1188 1138 0.958 15 17
    1 Σ 1184 1054 0.890 15 18
HF Hydrogen fluoride 1 Σ 4152 3961 0.954 16 19
F2 Fluorine diatomic 1 Σg 1092 894 0.819 17 20
SF Monosulfur monofluoride 1 Σ 857 829 0.967 18 21
HCl Hydrogen chloride 1 Σ 2991 2886 0.965 19 22
NaCl Sodium Chloride 1 Σ 357 361 1.012 20 23
AlCl Aluminum monochloride 1 Σ 467 478 1.022 21 24
SCl sulfur monochloride 1 Σ 589 577 0.979 22 25
Cl2 Chlorine diatomic 1 Σg 572 554 0.969 23 26
BeH2 beryllium dihydride 2 Σu 2242 2159 0.963 24 27
    3 Πu 714 698 0.977 24 28
SiH2 silicon dihydride 1 A1 2041 1996 0.978 25 29
    2 A1 1010 999 0.989 25 30
    3 B2 2044 1993 0.975 25 31
HCN Hydrogen cyanide 1 Σ 3462 3312 0.957 26 32
    2 Σ 2220 2089 0.941 26 33
    3 Π 772 712 0.923 26 34
H2O Water 1 A1 3858 3657 0.948 27 35
    2 A1 1645 1595 0.970 27 36
    3 B2 3961 3756 0.948 27 37
CO2 Carbon dioxide 1 Σg 1393 1333 0.957 28 38
    2 Σu 2459 2349 0.955 28 39
    3 Πu 683 667 0.976 28 40
N2O Nitrous oxide 1 Σ 2411 2224 0.923 29 41
    2 Σ 1375 1285 0.935 29 42
    3 Π 642 589 0.918 29 43
SO2 Sulfur dioxide 1 A1 1199 1151 0.960 30 44
    2 A1 526 518 0.984 30 45
    3 B2 1391 1362 0.979 30 46
BH3 boron trihydride 2 A2" 1147 1148 1.000 31 47
    3 E' 2690 2602 0.967 31 48
    4 E' 1191 1197 1.005 31 49
C2H2 Acetylene 1 Σg 3531 3374 0.956 32 50
    2 Σg 2083 1974 0.948 32 51
    3 Σu 3425 3289 0.960 32 52
    4 Πg 667 612 0.918 32 53
    5 Πu 775 730 0.942 32 54
NH3 Ammonia 1 A1 3499 3337 0.954 33 55
    2 A1 1065 950 0.892 33 56
    3 E 3624 3444 0.950 33 57
    4 E 1675 1627 0.971 33 58
H2CO Formaldehyde 1 A1 2897 2782 0.960 34 59
    2 A1 1853 1746 0.942 34 60
    3 A1 1534 1500 0.978 34 61
    4 B1 1206 1167 0.967 34 62
    5 B2 2955 2843 0.962 34 63
    6 B2 1269 1249 0.985 34 64
BF3 Borane, trifluoro- 1 A1' 897 888 0.989 35 65
    2 A2" 686 691 1.007 35 66
    3 E' 1477 1449 0.981 35 67
    4 E' 477 480 1.006 35 68
AlF3 Aluminum trifluoride 1 A1' 689 690 1.001 36 69
    2 A2" 292 297 1.017 36 70
    3 E' 957 935 0.977 36 71
    4 E' 238 263 1.106 36 72
CH4 Methane 1 A1 3044 2917 0.958 37 73
    2 E 1554 1534 0.987 37 74
    3 T2 3164 3019 0.954 37 75
    4 T2 1329 1306 0.983 37 76
C2H4 Ethylene 1 Ag 3158 3026 0.958 38 77
    2 Ag 1704 1623 0.952 38 78
    3 Ag 1381 1342 0.972 38 79
    4 Au 1071 1023 0.955 38 80
    5 B1u 3143 2989 0.951 38 81
    6 B1u 1468 1444 0.983 38 82
    7 B2g 986 940 0.953 38 83
    8 B2u 3247 3105 0.956 38 84
    9 B2u 828 826 0.998 38 85
    10 B3g 3219 3086 0.959 38 86
    11 B3g 1240 1217 0.982 38 87
    12 B3u 980 949 0.968 38 88
CH3OH Methyl alcohol 1 A' 3886 3681 0.947 39 89
    2 A' 3124 3000 0.960 39 90
    3 A' 3001 2844 0.948 39 91
    4 A' 1508 1477 0.979 39 92
    5 A' 1478 1455 0.984 39 93
    6 A' 1380 1345 0.975 39 94
    7 A' 1106 1060 0.958 39 95
    8 A' 1066 1033 0.969 39 96
    9 A" 3051 2960 0.970 39 97
    10 A" 1492 1477 0.990 39 98
    11 A" 1174 1165 0.992 39 99
    12 A" 304 200 0.658 39 100
CHONH2 formamide 1 A' 3760 3564 0.948 40 101
    2 A' 3617 3439 0.951 40 102
    3 A' 2949 2854 0.968 40 103
    4 A' 1836 1754 0.955 40 104
    5 A' 1618 1577 0.975 40 105
    6 A' 1422 1390 0.977 40 106
    7 A' 1285 1258 0.979 40 107
    8 A' 1062 1046 0.985 40 108
    9 A' 568 581 1.023 40 109
    10 A" 1052 1021 0.971 40 110
    11 A" 652 603 0.925 40 111
    12 A" 219 289 1.315 40 112
B2Cl4 Diboron tetrachloride 1 A1 1849 1122 0.607 41 113
    2 A1 485 401 0.827 41 114
    3 A1 176 176 0.998 41 115
    5 B2 816 728 0.892 41 116
    6 B2 286 289 1.010 41 117
    7 E 969 917 0.946 41 118
    8 E 262 512 1.958 41 119
    9 E 113i 104 -0.920 41 120
CH2N4 1H-Tetrazole 1 A' 3683 3447 0.936 42 121
    2 A' 3294 3102 0.942 42 122
    3 A' 1531 1441 0.941 42 123
    4 A' 1480 1384 0.935 42 124
    5 A' 1332 1259 0.945 42 125
    6 A' 1286 1159 0.902 42 126
    7 A' 1160 1084 0.934 42 127
    8 A' 1094 1015 0.928 42 128
    9 A' 1084 1002 0.925 42 129
    10 A' 1028 969 0.942 42 130
    11 A' 993 925 0.932 42 131
    12 A" 877 906 1.033 42 132
    13 A" 758 663 0.874 42 133
    14 A" 704 658 0.935 42 134
    15 A" 609 578 0.949 42 135
C2H6 Ethane 1 A1g 3046 2954 0.970 43 136
    2 A1g 1419 1388 0.978 43 137
    3 A1g 1023 995 0.973 43 138
    4 A1u 308 289 0.940 43 139
    5 A2u 3047 2896 0.951 43 140
    6 A2u 1402 1379 0.983 43 141
    7 Eg 3101 2969 0.957 43 142
    8 Eg 1498 1468 0.980 43 143
    9 Eg 1218 1190 0.977 43 144
    10 Eu 3126 2985 0.955 43 145
    11 Eu 1499 1469 0.980 43 146
    12 Eu 822 822 1.000 43 147
C3H5 Allyl radical 1 A1 3260 3114 0.955 44 148
    2 A1 3161 3048 0.964 44 149
    4 A1 1516 1488 0.982 44 150
    5 A1 1276 1245 0.975 44 151
    6 A1 1042 1066 1.023 44 152
    7 A1 424 427 1.008 44 153
    9 A2 557 549 0.985 44 154
    10 B1 1014 968 0.955 44 155
    11 B1 821 802 0.977 44 156
    12 B1 532 518 0.974 44 157
    13 B2 3257 3105 0.953 44 158
    14 B2 3155 3016 0.956 44 159
    15 B2 1513 1463 0.967 44 160
    16 B2 1420 1389 0.978 44 161
    17 B2 1210 1182 0.977 44 162
C3H3NO Oxazole 1 A' 3312 3170 0.957 45 163
    2 A' 3283 3144 0.958 45 164
    3 A' 3275 3141 0.959 45 165
    4 A' 1601 1537 0.960 45 166
    5 A' 1553 1504 0.968 45 167
    6 A' 1378 1324 0.961 45 168
    7 A' 1278 1252 0.980 45 169
    8 A' 1186 1139 0.960 45 170
    9 A' 1150 1086 0.945 45 171
    10 A' 1117 1078 0.965 45 172
    11 A' 1092 1046 0.958 45 173
    12 A' 936 899 0.961 45 174
    13 A' 921 854 0.927 45 175
    14 A" 897 907 1.011 45 176
    15 A" 859 830 0.966 45 177
    16 A" 778 750 0.964 45 178
    17 A" 673 647 0.961 45 179
    18 A" 637 607 0.953 45 180
C3H6 Cyclopropane 1 A1' 3155 3038 0.963 46 181
    2 A1' 1520 1479 0.973 46 182
    3 A1' 1237 1188 0.960 46 183
    4 A1" 1156 1126 0.974 46 184
    5 A2' 1091 1070 0.981 46 185
    6 A2" 3246 3103 0.956 46 186
    7 A2" 858 854 0.995 46 187
    8 E' 3147 3025 0.961 46 188
    9 E' 1468 1438 0.980 46 189
    10 E' 1055 1029 0.975 46 190
    11 E' 915 866 0.947 46 191
    12 E" 3225 3082 0.956 46 192
    13 E" 1212 1188 0.980 46 193
    14 E" 741 739 0.997 46 194
CH2CHCH3 Propene 1 A' 3233 3090 0.956 47 195
    2 A' 3150 3013 0.957 47 196
    3 A' 3142 2991 0.952 47 197
    4 A' 3120 2954 0.947 47 198
    5 A' 3034 2871 0.946 47 199
    6 A' 1729 1650 0.954 47 200
    7 A' 1486 1470 0.989 47 201
    8 A' 1445 1420 0.982 47 202
    9 A' 1400 1378 0.984 47 203
    10 A' 1327 1297 0.978 47 204
    11 A' 1193 1171 0.981 47 205
    12 A' 943 963 1.022 47 206
    13 A' 940 920 0.979 47 207
    14 A' 424 428 1.010 47 208
    15 A" 3088 2954 0.957 47 209
    16 A" 1472 1443 0.981 47 210
    17 A" 1070 1045 0.976 47 211
    18 A" 1032 991 0.960 47 212
    19 A" 949 912 0.961 47 213
    20 A" 594 578 0.973 47 214
    21 A" 210 174 0.828 47 215
CHCCH2CH3 1-Butyne 1 A' 3485 3332 0.956 48 216
    2 A' 3134 2988 0.953 48 217
    3 A' 3057     48 218
    4 A' 3044     48 219
    5 A' 2237 2116 0.946 48 220
    6 A' 1499 1470 0.980 48 221
    7 A' 1469 1446 0.984 48 222
    8 A' 1407 1385 0.984 48 223
    9 A' 1349 1322 0.980 48 224
    10 A' 1092 1070 0.980 48 225
    11 A' 1041 1008 0.968 48 226
    12 A' 860 840 0.976 48 227
    13 A' 681 634 0.931 48 228
    14 A' 526 509 0.968 48 229
    15 A' 203 197 0.967 48 230
    16 A" 3139 2988 0.952 48 231
    17 A" 3075 2939 0.956 48 232
    18 A" 1489 1462 0.982 48 233
    19 A" 1287 1261 0.980 48 234
    20 A" 1104 1090 0.987 48 235
    21 A" 787 782 0.994 48 236
    22 A" 672 630 0.937 48 237
    23 A" 367 344 0.937 48 238
    24 A" 218 213 0.974 48 239
C4H6 Bicyclo[1.1.0]butane 1 A1 3268 3131 0.958 49 240
    2 A1 3182 3044 0.956 49 241
    3 A1 3072 2935 0.955 49 242
    4 A1 1530 1501 0.981 49 243
    5 A1 1318 1266 0.960 49 244
    6 A1 1116 1081 0.968 49 245
    7 A1 908 839 0.924 49 246
    8 A1 707 657 0.929 49 247
    9 A1 431 423 0.981 49 248
    10 A2 1181 1172 0.992 49 249
    11 A2 1081 1063 0.983 49 250
    12 A2 936 909 0.971 49 251
    13 A2 869 838 0.965 49 252
    14 B1 3254 3120 0.959 49 253
    15 B1 1180 1110 0.941 49 254
    16 B1 1134 1092 0.963 49 255
    17 B1 1012 980 0.968 49 256
    18 B1 772 737 0.955 49 257
    19 B2 3185 3044 0.956 49 258
    20 B2 3077 2969 0.965 49 259
    21 B2 1486 1485 0.999 49 260
    22 B2 1332 1261 0.947 49 261
    23 B2 1109 1081 0.975 49 262
    24 B2 951 935 0.983 49 263
CH3CHClCH3 Propane, 2-chloro- 1 A' 3146 3005 0.955 50 264
    2 A' 3125 2955 0.946 50 265
    3 A' 3094 2927 0.946 50 266
    4 A' 3049 2878 0.944 50 267
    5 A' 1500 1472 0.981 50 268
    6 A' 1485 1454 0.979 50 269
    7 A' 1414 1390 0.983 50 270
    8 A' 1284 1270 0.989 50 271
    9 A' 1187 1163 0.980 50 272
    10 A' 1080 1065 0.987 50 273
    11 A' 908 888 0.978 50 274
    12 A' 635 633 0.997 50 275
    13 A' 420 418 0.994 50 276
    14 A' 335 336 1.002 50 277
    15 A' 268 253 0.945 50 278
    16 A" 3142 2997 0.954 50 279
    17 A" 3117 2985 0.958 50 280
    18 A" 3045 2947 0.968 50 281
    19 A" 1479 1472 0.995 50 282
    20 A" 1473 1454 0.987 50 283
    21 A" 1401 1377 0.983 50 284
    22 A" 1359 1334 0.982 50 285
    23 A" 1160 1123 0.968 50 286
    24 A" 954 972 1.019 50 287
    25 A" 938 936 0.998 50 288
    26 A" 322 317 0.985 50 289
    27 A" 241 276 1.147 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.

40 180 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 160 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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