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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at B3LYP/aug-cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.969 ± 0.021 115 344 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4420 4161 0.941 1 1
LiH Lithium Hydride 1 Σ 1420 1360 0.958 2 2
Li2 Lithium diatomic 1 Σg 342 346 1.012 3 3
NaH sodium hydride 1 Σ 1181 1133 0.960 4 4
Na2 Sodium diatomic 1 Σg 162 158 0.970 5 5
BeH beryllium monohydride 1 Σ 2063 1987 0.963 6 6
MgH magnesium monohydride 1 Σ 1463 1432 0.979 7 7
BH Boron monohydride 1 Σ 2354 2269 0.964 8 8
AlH aluminum monohydride 1 Σ 1644 1625 0.988 9 9
CH Methylidyne 1 Σ 2831 2733 0.965 10 10
    1 Σ 3047     10 11
C2 Carbon diatomic 1 Σg 1874 1827 0.975 11 12
SiH Silylidyne 1 Σ 2013 1971 0.979 12 13
NH Imidogen 1 Σ 3262 3126 0.958 13 14
CN Cyano radical 1 Σ 2153 2042 0.949 14 15
N2 Nitrogen diatomic 1 Σg 2448 2330 0.952 15 16
    1 Σg 1815 1733 0.955 15 17
PH phosphorus monohydride 1 Σ 2343 2276 0.972 16 18
    1 Σ 2356 2319 0.984 16 19
PN Phosphorus mononitride 1 Σ 1405 1323 0.942 17 20
P2 Phosphorus diatomic 1 Σg 808 775 0.960 18 21
OH Hydroxyl radical 1 Σ 3703 3570 0.964 19 22
LiO lithium oxide 1 Σ 814 799 0.982 20 23
BeO beryllium oxide 1 Σ 1550 1435 0.925 21 24
BO boron monoxide 1 Σ 1919 1862 0.970 22 25
CO Carbon monoxide 1 Σ 2212 2143 0.969 23 26
    1 Σ 1785     23 27
NaO sodium monoxide 1 Σ 481     24 28
MgO magnesium oxide 1 Σ 821 775 0.944 25 29
SiO Silicon monoxide 1 Σ 1256 1230 0.979 26 30
HS Mercapto radical 1 Σ 2666 2599 0.975 27 31
BeS beryllium sulfide 1 Σ 1011 986 0.974 28 32
BS boron sulfide 1 Σ 1180 1167 0.989 29 33
CS carbon monosulfide 1 Σ 1306 1272 0.974 30 34
SO Sulfur monoxide 1 Σ 1151 1138 0.988 31 35
    1 Σ 1151 1054 0.916 31 36
MgS magnesium sulfide 1 Σ 526 523 0.995 32 37
AlS Aluminum sulfide 1 Σ 594 610 1.027 33 38
SiS silicon monosulfide 1 Σ 744 744 1.001 34 39
S2 Sulfur diatomic 1 Σg 713 720 1.009 35 40
HF Hydrogen fluoride 1 Σ 4077 3961 0.972 36 41
LiF lithium fluoride 1 Σ 905 896 0.990 37 42
BeF Beryllium monofluoride 1 Σ 1255     38 43
CF Fluoromethylidyne 1 Σ 1293 1286 0.995 39 44
NF nitrogen fluoride 1 Σ 1150 1123 0.977 40 45
F2 Fluorine diatomic 1 Σg 1045 894 0.855 41 46
NaF sodium fluoride 1 Σ 525 529 1.008 42 47
AlF Aluminum monofluoride 1 Σ 771 793 1.028 43 48
SiF silicon monofluoride 1 Σ 824 848 1.029 44 49
SF Monosulfur monofluoride 1 Σ 820 829 1.010 45 50
HCl Hydrogen chloride 1 Σ 2938 2886 0.982 46 51
LiCl lithium chloride 1 Σ 640 634 0.990 47 52
BeCl beryllium monochloride 1 Σ 832 847 1.018 48 53
BCl boron monochloride 1 Σ 819 829 1.013 49 54
CCl carbon monochloride 1 Σ 853 866 1.016 50 55
ClO Monochlorine monoxide 1 Σ 857 843 0.983 51 56
ClF Chlorine monofluoride 1 Σ 786 773 0.983 52 57
NaCl Sodium Chloride 1 Σ 358 361 1.010 53 58
AlCl Aluminum monochloride 1 Σ 454 478 1.052 54 59
SiCl Clorosilylidyne 1 Σ 507 531 1.047 55 60
SCl sulfur monochloride 1 Σ 559 577 1.031 56 61
Cl2 Chlorine diatomic 1 Σg 539 554 1.028 57 62
BeH2 beryllium dihydride 2 Σu 2260 2159 0.955 58 63
    3 Πu 727 698 0.960 58 64
MgH2 magnesium dihydride 2 Σu 1633 1572 0.962 59 65
    3 Πu 444 440 0.991 59 66
BH2 boron dihydride 2 A1 986 954 0.967 60 67
AlH2 aluminum dihydride 1 A1 1823 1770 0.971 61 68
    2 A1 772 760 0.985 61 69
    3 B2 1864 1807 0.969 61 70
SiH2 silicon dihydride 1 A1 2042 1996 0.977 62 71
    2 A1 1022 999 0.977 62 72
    3 B2 2041 1993 0.976 62 73
NH2 Amino radical 1 A1 3356 3219 0.959 63 74
    2 A1 1530 1497 0.978 63 75
    3 B2 3446 3301 0.958 63 76
HCN Hydrogen cyanide 1 Σ 3439 3312 0.963 64 77
    2 Σ 2201 2089 0.949 64 78
    3 Π 758 712 0.939 64 79
HNC hydrogen isocyanide 1 Σ 3800 3653 0.961 65 80
    2 Σ 2104 2029 0.964 65 81
    3 Π 468 477 1.019 65 82
HCP Phosphaethyne 1 Σ 3348 3217 0.961 66 83
    2 Σ 1342 1278 0.952 66 84
    3 Π 721 674 0.936 66 85
HPO Hydrogen phosphorus oxide 1 A' 2090 2095 1.003 67 86
    2 A' 1220 1188 0.974 67 87
    3 A' 1002 986 0.984 67 88
H2O Water 1 A1 3804 3657 0.961 68 89
    2 A1 1630 1595 0.979 68 90
    3 B2 3905 3756 0.962 68 91
LiOH lithium hydroxide 1 Σ 4000 3688 0.922 69 92
    2 Σ 952 871 0.914 69 93
    3 Π 341 257 0.752 69 94
BeOH beryllium monohydroxide 2 A' 1281 1246 0.972 70 95
HBO Boron hydride oxide 1 Σ 2892 2850 0.986 71 96
    2 Σ 1867 1826 0.978 71 97
    3 Π 775 756 0.975 71 98
HCO Formyl radical 1 A' 2652 2434 0.918 72 99
    2 A' 1934 1868 0.966 72 100
    3 A' 1104 1081 0.979 72 101
HNO Nitrosyl hydride 1 A' 2861 2684 0.938 73 102
    2 A' 1667 1565 0.939 73 103
    3 A' 1561 1501 0.961 73 104
HO2 Hydroperoxy radical 1 A' 3595 3436 0.956 74 105
    2 A' 1435 1392 0.970 74 106
    3 A' 1166 1098 0.942 74 107
NaOH sodium hydroxide 1 Σ 3951 3637 0.921 75 108
    2 Σ 558 540 0.968 75 109
    3 Π 172 300 1.747 75 110
H2S Hydrogen sulfide 1 A1 2680 2615 0.976 76 111
    2 A1 1209 1183 0.979 76 112
    3 B2 2693 2626 0.975 76 113
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 77 114
    2 Σ 1187 1172 0.987 77 115
HCF Fluoromethylene 1 A' 2762 2643 0.957 78 116
    2 A' 1438 1403 0.976 78 117
    3 A' 1198 1189 0.993 78 118
HOF Hypofluorous acid 1 A' 3727 3578 0.960 79 119
    2 A' 1409 1362 0.967 79 120
    3 A' 982 893 0.909 79 121
HOCl hypochlorous acid 1 A' 3769 3609 0.958 80 122
    2 A' 1262 1239 0.982 80 123
    3 A' 741 724 0.978 80 124
BH3 boron trihydride 2 A2" 1161 1148 0.989 81 125
    3 E' 2690 2602 0.967 81 126
    4 E' 1206 1197 0.992 81 127
AlH3 aluminum trihydride 1 A1' 1943 1900 0.978 82 128
    2 A2" 712 698 0.980 82 129
    3 E' 1949 1883 0.966 82 130
    4 E' 799 783 0.981 82 131
C2H2 Acetylene 1 Σg 3511 3374 0.961 83 132
    2 Σg 2067 1974 0.955 83 133
    3 Σu 3412 3289 0.964 83 134
    4 Πg 670 612 0.913 83 135
    5 Πu 765 730 0.954 83 136
SiH3 Silyl radical 1 A1 2198 2136 0.972 84 137
    2 A1 765 728 0.951 84 138
    3 E 2235 2185 0.978 84 139
    4 E 937 922 0.984 84 140
NH3 Ammonia 1 A1 3470 3337 0.962 85 141
    2 A1 1023 950 0.928 85 142
    3 E 3590 3444 0.959 85 143
    4 E 1664 1627 0.978 85 144
PH3 Phosphine 1 A1 2387 2323 0.973 86 145
    2 A1 1017 992 0.975 86 146
    3 E 2393 2328 0.973 86 147
    4 E 1139 1118 0.982 86 148
H2CO Formaldehyde 1 A1 2881 2782 0.966 87 149
    2 A1 1817 1746 0.961 87 150
    3 A1 1533 1500 0.979 87 151
    4 B1 1201 1167 0.972 87 152
    5 B2 2936 2843 0.968 87 153
    6 B2 1267 1249 0.986 87 154
H2O2 Hydrogen peroxide 1 A 3763 3599 0.956 88 155
    2 A 1438 1402 0.975 88 156
    3 A 949 877 0.924 88 157
    4 A 375 371 0.988 88 158
    5 B 3762 3608 0.959 88 159
    6 B 1326 1266 0.955 88 160
H2CS Thioformaldehyde 1 A1 3060 2971 0.971 89 161
    2 A1 1495 1456 0.973 89 162
    3 A1 1087 1059 0.974 89 163
    4 B1 1031 990 0.960 89 164
    5 B2 3140 3025 0.963 89 165
    6 B2 1005 991 0.986 89 166
H2S2 Disulfane 1 A 2620 2556 0.976 90 167
    2 A 889 882 0.993 90 168
    3 A 500 515 1.029 90 169
    4 A 428 417 0.976 90 170
    5 B 2622 2559 0.976 90 171
    6 B 889 878 0.987 90 172
CH4 Methane 1 A1 3027 2917 0.964 91 173
    2 E 1559 1534 0.984 91 174
    3 T2 3129 3019 0.965 91 175
    4 T2 1341 1306 0.974 91 176
SiH4 Silane 1 A1 2241 2187 0.976 92 177
    2 E 979 975 0.996 92 178
    3 T2 2243 2191 0.977 92 179
    4 T2 922 914 0.991 92 180
CH2NH Methanimine 1 A' 3432 3263 0.951 93 181
    2 A' 3108 3024 0.973 93 182
    3 A' 3013 2914 0.967 93 183
    4 A' 1710 1638 0.958 93 184
    5 A' 1492 1452 0.973 93 185
    6 A' 1368 1344 0.983 93 186
    7 A' 1074 1058 0.986 93 187
    8 A" 1163 1127 0.969 93 188
    9 A" 1103 1061 0.962 93 189
NH2OH hydroxylamine 1 A' 3814 3650 0.957 94 190
    2 A' 3442 3294 0.957 94 191
    3 A' 1665 1605 0.964 94 192
    4 A' 1394 1353 0.971 94 193
    5 A' 1141 1115 0.977 94 194
    6 A' 929 895 0.964 94 195
    7 A" 3519 3359 0.954 94 196
    8 A" 1328 1295 0.975 94 197
    9 A" 415 386 0.931 94 198
CH3F Methyl fluoride 1 A1 3030 2930 0.967 95 199
    2 A1 1484 1464 0.986 95 200
    3 A1 1042 1049 1.006 95 201
    4 E 3110 3006 0.966 95 202
    5 E 1495 1467 0.981 95 203
    6 E 1194 1182 0.990 95 204
SiH3F monofluorosilane 1 A1 2256 2206 0.978 96 205
    2 A1 992 990 0.998 96 206
    3 A1 858 872 1.017 96 207
    4 E 2259 2196 0.972 96 208
    5 E 967 956 0.989 96 209
    6 E 724 728 1.005 96 210
CH3Cl Methyl chloride 1 A1 3070 2966 0.966 97 211
    2 A1 1379 1355 0.982 97 212
    3 A1 712 732 1.028 97 213
    4 E 3165 3042 0.961 97 214
    5 E 1484 1455 0.980 97 215
    6 E 1027 1015 0.988 97 216
SiH3Cl chlorosilane 1 A1 2256 2201 0.976 98 217
    2 A1 953 949 0.996 98 218
    3 A1 530 551 1.039 98 219
    4 E 2265 2195 0.969 98 220
    5 E 959 954 0.995 98 221
    6 E 660 664 1.007 98 222
C2H4 Ethylene 1 Ag 3138 3026 0.964 99 223
    2 Ag 1688 1623 0.961 99 224
    3 Ag 1381 1342 0.972 99 225
    4 Au 1064 1023 0.961 99 226
    5 B1u 3125 2989 0.956 99 227
    6 B1u 1480 1444 0.975 99 228
    7 B2g 987 940 0.952 99 229
    8 B2u 3222 3105 0.964 99 230
    9 B2u 836 826 0.988 99 231
    10 B3g 3194 3086 0.966 99 232
    11 B3g 1248 1217 0.975 99 233
    12 B3u 980 949 0.969 99 234
N2H4 Hydrazine 1 A 3555 3398 0.956 100 235
    2 A 3462 3329 0.962 100 236
    3 A 1686 1642 0.974 100 237
    4 A 1325 1275 0.963 100 238
    5 A 1112 1076 0.968 100 239
    6 A 800 780 0.975 100 240
    7 A 442 377 0.852 100 241
    8 B 3561 3350 0.941 100 242
    9 B 3454 3314 0.959 100 243
    10 B 1674 1628 0.973 100 244
    11 B 1296 1275 0.984 100 245
    12 B 971 966 0.995 100 246
CH3OH Methyl alcohol 1 A' 3837 3681 0.959 101 247
    2 A' 3109 3000 0.965 101 248
    3 A' 2993 2844 0.950 101 249
    4 A' 1510 1477 0.978 101 250
    5 A' 1480 1455 0.983 101 251
    6 A' 1367 1345 0.984 101 252
    7 A' 1078 1060 0.984 101 253
    8 A' 1041 1033 0.993 101 254
    9 A" 3039 2960 0.974 101 255
    10 A" 1499 1477 0.985 101 256
    11 A" 1173 1165 0.993 101 257
    12 A" 289 200 0.692 101 258
CH3SH Methanethiol 1 A' 3133 3000 0.958 102 259
    2 A' 3051 2931 0.961 102 260
    3 A' 2670 2597 0.973 102 261
    4 A' 1490 1475 0.990 102 262
    5 A' 1359 1335 0.982 102 263
    6 A' 1097 1074 0.979 102 264
    7 A' 798 803 1.006 102 265
    8 A' 698 708 1.015 102 266
    9 A" 3133 3000 0.958 102 267
    10 A" 1477 1430 0.968 102 268
    11 A" 974 976 1.002 102 269
CH3NH2 methyl amine 1 A' 3502 3361 0.960 103 270
    2 A' 3055 2961 0.969 103 271
    3 A' 2966 2820 0.951 103 272
    4 A' 1661 1623 0.977 103 273
    5 A' 1500 1473 0.982 103 274
    6 A' 1461 1430 0.979 103 275
    7 A' 1168 1130 0.967 103 276
    8 A' 1055 1044 0.990 103 277
    9 A' 817 780 0.954 103 278
    10 A" 3577 3427 0.958 103 279
    11 A" 3090 2985 0.966 103 280
    12 A" 1519 1485 0.978 103 281
    13 A" 1345 1335 0.993 103 282
    14 A" 973     103 283
    15 A" 291 268 0.921 103 284
B2H6 Diborane 1 Ag 2620 2530 0.966 104 285
    2 Ag 2178 2088 0.959 104 286
    3 Ag 1207 1183 0.980 104 287
    4 Ag 800 790 0.987 104 288
    5 Au 851 833 0.979 104 289
    6 B1g 2693 2596 0.964 104 290
    7 B1g 940 915 0.973 104 291
    8 B1u 1995 1930 0.967 104 292
    9 B1u 992 973 0.980 104 293
    10 B2g 1858 1760 0.947 104 294
    11 B2g 895 860 0.961 104 295
    12 B2u 2707 2609 0.964 104 296
    13 B2u 954 949 0.995 104 297
    14 B2u 362 369 1.017 104 298
    15 B3g 1022 1020 0.998 104 299
    16 B3u 2607 2520 0.967 104 300
    17 B3u 1716 1603 0.934 104 301
    18 B3u 1199 1172 0.978 104 302
C2H6 Ethane 1 A1g 3025 2954 0.977 105 303
    2 A1g 1423 1388 0.976 105 304
    3 A1g 995 995 1.000 105 305
    4 A1u 303 289 0.953 105 306
    5 A2u 3026 2896 0.957 105 307
    6 A2u 1414 1379 0.976 105 308
    7 Eg 3069 2969 0.967 105 309
    8 Eg 1503 1468 0.976 105 310
    9 Eg 1223 1190 0.973 105 311
    10 Eu 3094 2985 0.965 105 312
    11 Eu 1507 1469 0.975 105 313
    12 Eu 827 822 0.994 105 314
Si2H6 disilane 1 A1g 2220 2152 0.969 106 315
    2 A1g 928 909 0.980 106 316
    3 A1g 423 434 1.027 106 317
    4 A1u 137 131 0.954 106 318
    5 A2u 2212 2154 0.974 106 319
    6 A2u 855 844 0.987 106 320
    7 Eg 2217 2155 0.972 106 321
    8 Eg 946 929 0.982 106 322
    9 Eg 634 625 0.986 106 323
    10 Eu 2226 2179 0.979 106 324
    11 Eu 960 940 0.979 106 325
    12 Eu 375 379 1.011 106 326

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.

40 160 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