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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 3047     10 10
C2 Carbon diatomic 1 Σg 1874 1827 0.975 11 11
SiH Silylidyne 1 Σ 2021 1971 0.975 12 12
NH Imidogen 1 Σ 3262 3126 0.958 13 13
CN Cyano radical 1 Σ 2153 2042 0.949 14 14
N2 Nitrogen diatomic 1 Σg 2448 2330 0.952 15 15
PH phosphorus monohydride 1 Σ 2343 2276 0.972 16 16
    1 Σ 2356 2319 0.984 16 17
PN Phosphorus mononitride 1 Σ 1403 1323 0.943 17 18
P2 Phosphorus diatomic 1 Σg 808 775 0.960 18 19
OH Hydroxyl radical 1 Σ 3703 3570 0.964 19 20
LiO lithium oxide 1 Σ 814 799 0.982 20 21
BeO beryllium oxide 1 Σ 1550 1435 0.925 21 22
BO boron monoxide 1 Σ 1919 1862 0.970 22 23
CO Carbon monoxide 1 Σ 2212 2143 0.969 23 24
NaO sodium monoxide 1 Σ 481     24 25
MgO magnesium oxide 1 Σ 821 775 0.944 25 26
SiO Silicon monoxide 1 Σ 1257 1230 0.978 26 27
HS Mercapto radical 1 Σ 2666 2599 0.975 27 28
BeS beryllium sulfide 1 Σ 1011 986 0.974 28 29
BS boron sulfide 1 Σ 1180 1167 0.989 29 30
CS carbon monosulfide 1 Σ 1306 1272 0.974 30 31
SO Sulfur monoxide 1 Σ 1152 1138 0.988 31 32
    1 Σ 1152 1054 0.915 31 33
MgS magnesium sulfide 1 Σ 526 523 0.995 32 34
AlS Aluminum sulfide 1 Σ 594 610 1.027 33 35
SiS silicon monosulfide 1 Σ 744 744 1.001 34 36
S2 Sulfur diatomic 1 Σg 713 720 1.009 35 37
HF Hydrogen fluoride 1 Σ 4077 3961 0.972 36 38
LiF lithium fluoride 1 Σ 905 896 0.990 37 39
BeF Beryllium monofluoride 1 Σ 1255     38 40
CF Fluoromethylidyne 1 Σ 1293 1286 0.995 39 41
NF nitrogen fluoride 1 Σ 1150 1123 0.977 40 42
F2 Fluorine diatomic 1 Σg 1045 894 0.855 41 43
NaF sodium fluoride 1 Σ 525 529 1.008 42 44
AlF Aluminum monofluoride 1 Σ 770 793 1.029 43 45
SiF silicon monofluoride 1 Σ 824 848 1.029 44 46
SF Monosulfur monofluoride 1 Σ 820 829 1.010 45 47
HCl Hydrogen chloride 1 Σ 2932 2886 0.984 46 48
LiCl lithium chloride 1 Σ 640 634 0.990 47 49
BeCl beryllium monochloride 1 Σ 832 847 1.018 48 50
BCl boron monochloride 1 Σ 819 829 1.013 49 51
CCl carbon monochloride 1 Σ 853 866 1.016 50 52
ClO Monochlorine monoxide 1 Σ 857 843 0.983 51 53
ClF Chlorine monofluoride 1 Σ 786 773 0.983 52 54
NaCl Sodium Chloride 1 Σ 358 361 1.010 53 55
AlCl Aluminum monochloride 1 Σ 454 478 1.052 54 56
SCl sulfur monochloride 1 Σ 559 577 1.031 55 57
Cl2 Chlorine diatomic 1 Σg 539 554 1.028 56 58
BeH2 beryllium dihydride 2 Σu 2260 2159 0.955 57 59
    3 Πu 727 698 0.960 57 60
MgH2 magnesium dihydride 2 Σu 1633 1572 0.962 58 61
    3 Πu 444 440 0.991 58 62
BH2 boron dihydride 2 A1 986 954 0.967 59 63
AlH2 aluminum dihydride 1 A1 1823 1770 0.971 60 64
    2 A1 772 760 0.985 60 65
    3 B2 1864 1807 0.969 60 66
SiH2 silicon dihydride 1 A1 2042 1996 0.977 61 67
    2 A1 1022 999 0.977 61 68
    3 B2 2041 1993 0.976 61 69
NH2 Amino radical 1 A1 3356 3219 0.959 62 70
    2 A1 1530 1497 0.978 62 71
    3 B2 3446 3301 0.958 62 72
HCN Hydrogen cyanide 1 Σ 3439 3312 0.963 63 73
    2 Σ 2201 2089 0.949 63 74
    3 Π 758 712 0.939 63 75
HNC hydrogen isocyanide 1 Σ 3800 3653 0.961 64 76
    2 Σ 2104 2029 0.964 64 77
    3 Π 468 477 1.019 64 78
HCP HCP 1 Σ 3348 3217 0.961 65 79
    2 Σ 1342 1278 0.952 65 80
    3 Π 721 674 0.936 65 81
HPO HPO 1 A' 2090 2095 1.003 66 82
    2 A' 1220 1188 0.974 66 83
    3 A' 1002 986 0.984 66 84
H2O Water 1 A1 3804 3657 0.961 67 85
    2 A1 1630 1595 0.979 67 86
    3 B2 3905 3756 0.962 67 87
LiOH lithium hydroxide 1 Σ 4000 3688 0.922 68 88
    2 Σ 952 871 0.914 68 89
    3 Π 341 257 0.752 68 90
BeOH beryllium monohydroxide 2 A' 1281 1246 0.972 69 91
HBO Boron hydride oxide 1 Σ 2892 2850 0.986 70 92
    2 Σ 1867 1826 0.978 70 93
    3 Π 775 756 0.975 70 94
HCO Formyl radical 1 A' 2649 2434 0.919 71 95
    2 A' 1934 1868 0.966 71 96
    3 A' 1105 1081 0.978 71 97
HNO Nitrosyl hydride 1 A' 2856 2684 0.940 72 98
    2 A' 1668 1565 0.939 72 99
    3 A' 1562 1501 0.961 72 100
HO2 Hydroperoxy radical 1 A' 3595 3436 0.956 73 101
    2 A' 1435 1392 0.970 73 102
    3 A' 1166 1098 0.942 73 103
NaOH sodium hydroxide 1 Σ 3951 3637 0.921 74 104
    2 Σ 558 540 0.968 74 105
    3 Π 172 300 1.747 74 106
H2S Hydrogen sulfide 1 A1 2680 2615 0.976 75 107
    2 A1 1209 1183 0.979 75 108
    3 B2 2693 2626 0.975 75 109
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 76 110
    2 Σ 1187 1172 0.988 76 111
HCF Fluoromethylene 1 A' 2762 2643 0.957 77 112
    2 A' 1438 1403 0.976 77 113
    3 A' 1198 1189 0.993 77 114
HOF Hypofluorous acid 1 A' 3727 3578 0.960 78 115
    2 A' 1409 1362 0.967 78 116
    3 A' 981 893 0.911 78 117
HOCl hypochlorous acid 1 A' 3769 3609 0.958 79 118
    2 A' 1262 1239 0.982 79 119
    3 A' 741 724 0.978 79 120
BH3 boron trihydride 2 A2" 1161 1148 0.989 80 121
    3 E' 2690 2602 0.967 80 122
    4 E' 1206 1197 0.992 80 123
AlH3 aluminum trihydride 1 A1' 1943 1900 0.978 81 124
    2 A2" 712 698 0.980 81 125
    3 E' 1949 1883 0.966 81 126
    4 E' 799 783 0.981 81 127
C2H2 Acetylene 1 Σg 3511 3374 0.961 82 128
    2 Σg 2067 1974 0.955 82 129
    3 Σu 3412 3289 0.964 82 130
    4 Πg 670 612 0.913 82 131
    5 Πu 765 730 0.954 82 132
SiH3 Silyl radical 1 A1 2195 2136 0.973 83 133
    2 A1 766 728 0.951 83 134
    3 E 2232 2185 0.979 83 135
    4 E 937 922 0.984 83 136
NH3 Ammonia 1 A1 3470 3337 0.962 84 137
    2 A1 1023 950 0.928 84 138
    3 E 3590 3444 0.959 84 139
    4 E 1664 1627 0.978 84 140
PH3 Phosphine 1 A1 2387 2323 0.973 85 141
    2 A1 1017 992 0.975 85 142
    3 E 2393 2328 0.973 85 143
    4 E 1139 1118 0.982 85 144
H2CO Formaldehyde 1 A1 2881 2782 0.966 86 145
    2 A1 1817 1746 0.961 86 146
    3 A1 1533 1500 0.979 86 147
    4 B1 1201 1167 0.972 86 148
    5 B2 2936 2843 0.968 86 149
    6 B2 1267 1249 0.986 86 150
H2O2 Hydrogen peroxide 1 A 3763 3599 0.956 87 151
    2 A 1438 1402 0.975 87 152
    3 A 949 877 0.924 87 153
    4 A 375 371 0.988 87 154
    5 B 3762 3608 0.959 87 155
    6 B 1326 1266 0.955 87 156
H2CS Thioformaldehyde 1 A1 3060 2971 0.971 88 157
    2 A1 1495 1456 0.973 88 158
    3 A1 1087 1059 0.974 88 159
    4 B1 1031 990 0.960 88 160
    5 B2 3140 3025 0.963 88 161
    6 B2 1005 991 0.986 88 162
H2S2 Disulfane 1 A 2620 2556 0.976 89 163
    2 A 889 882 0.993 89 164
    3 A 500 515 1.029 89 165
    4 A 428 417 0.976 89 166
    5 B 2622 2559 0.976 89 167
    6 B 889 878 0.987 89 168
CH4 Methane 1 A1 3027 2917 0.964 90 169
    2 E 1559 1534 0.984 90 170
    3 T2 3129 3019 0.965 90 171
    4 T2 1341 1306 0.974 90 172
SiH4 Silane 1 A1 2241 2187 0.976 91 173
    2 E 979 975 0.996 91 174
    3 T2 2243 2191 0.977 91 175
    4 T2 922 914 0.991 91 176
CH2NH Methanimine 1 A' 3432 3263 0.951 92 177
    2 A' 3108 3024 0.973 92 178
    3 A' 3013 2914 0.967 92 179
    4 A' 1710 1638 0.958 92 180
    5 A' 1492 1452 0.973 92 181
    6 A' 1368 1344 0.983 92 182
    7 A' 1074 1058 0.986 92 183
    8 A" 1163 1127 0.969 92 184
    9 A" 1103 1061 0.962 92 185
NH2OH hydroxylamine 1 A' 3811 3650 0.958 93 186
    2 A' 3441 3294 0.957 93 187
    3 A' 1666 1605 0.963 93 188
    4 A' 1394 1353 0.971 93 189
    5 A' 1142 1115 0.977 93 190
    6 A' 929 895 0.963 93 191
    7 A" 3518 3359 0.955 93 192
    8 A" 1328 1295 0.975 93 193
    9 A" 417 386 0.925 93 194
CH3F Methyl fluoride 1 A1 3030 2930 0.967 94 195
    2 A1 1484 1464 0.986 94 196
    3 A1 1042 1049 1.006 94 197
    4 E 3110 3006 0.966 94 198
    5 E 1495 1467 0.981 94 199
    6 E 1194 1182 0.990 94 200
SiH3F monofluorosilane 1 A1 2253 2206 0.979 95 201
    2 A1 992 990 0.998 95 202
    3 A1 857 872 1.017 95 203
    4 E 2256 2196 0.973 95 204
    5 E 967 956 0.989 95 205
    6 E 724 728 1.005 95 206
CH3Cl Methyl chloride 1 A1 3070 2966 0.966 96 207
    2 A1 1379 1355 0.982 96 208
    3 A1 712 732 1.028 96 209
    4 E 3165 3042 0.961 96 210
    5 E 1484 1455 0.980 96 211
    6 E 1027 1015 0.988 96 212
SiH3Cl chlorosilane 1 A1 2256 2201 0.976 97 213
    2 A1 953 949 0.996 97 214
    3 A1 530 551 1.039 97 215
    4 E 2265 2195 0.969 97 216
    5 E 959 954 0.995 97 217
    6 E 660 664 1.007 97 218
C2H4 Ethylene 1 Ag 3138 3026 0.964 98 219
    2 Ag 1688 1623 0.961 98 220
    3 Ag 1381 1342 0.972 98 221
    4 Au 1064 1023 0.961 98 222
    5 B1u 3125 2989 0.956 98 223
    6 B1u 1480 1444 0.975 98 224
    7 B2g 987 940 0.952 98 225
    8 B2u 3222 3105 0.964 98 226
    9 B2u 836 826 0.988 98 227
    10 B3g 3194 3086 0.966 98 228
    11 B3g 1248 1217 0.975 98 229
    12 B3u 980 949 0.969 98 230
N2H4 Hydrazine 1 A 3555 3398 0.956 99 231
    2 A 3462 3329 0.962 99 232
    3 A 1686 1642 0.974 99 233
    4 A 1325 1275 0.963 99 234
    5 A 1112 1076 0.968 99 235
    6 A 800 780 0.975 99 236
    7 A 442 377 0.852 99 237
    8 B 3561 3350 0.941 99 238
    9 B 3454 3314 0.959 99 239
    10 B 1674 1628 0.973 99 240
    11 B 1296 1275 0.984 99 241
    12 B 971 966 0.995 99 242
CH3OH Methyl alcohol 1 A' 3837 3681 0.959 100 243
    2 A' 3109 3000 0.965 100 244
    3 A' 2993 2844 0.950 100 245
    4 A' 1510 1477 0.978 100 246
    5 A' 1480 1455 0.983 100 247
    6 A' 1367 1345 0.984 100 248
    7 A' 1078 1060 0.984 100 249
    8 A' 1041 1033 0.993 100 250
    9 A" 3039 2960 0.974 100 251
    10 A" 1499 1477 0.985 100 252
    11 A" 1173 1165 0.993 100 253
    12 A" 289 200 0.692 100 254
CH3SH Methanethiol 1 A' 3133 3000 0.958 101 255
    2 A' 3051 2931 0.961 101 256
    3 A' 2670 2597 0.973 101 257
    4 A' 1490 1475 0.990 101 258
    5 A' 1359 1335 0.982 101 259
    6 A' 1097 1074 0.979 101 260
    7 A' 798 803 1.006 101 261
    8 A' 698 708 1.015 101 262
    9 A" 3133 3000 0.958 101 263
    10 A" 1477 1430 0.968 101 264
    11 A" 974 976 1.002 101 265
CH3NH2 methyl amine 1 A' 3500 3361 0.960 102 266
    2 A' 3055 2961 0.969 102 267
    3 A' 2966 2820 0.951 102 268
    4 A' 1661 1623 0.977 102 269
    5 A' 1500 1473 0.982 102 270
    6 A' 1462 1430 0.978 102 271
    7 A' 1169 1130 0.967 102 272
    8 A' 1055 1044 0.989 102 273
    9 A' 819 780 0.952 102 274
    10 A" 3575 3427 0.959 102 275
    11 A" 3090 2985 0.966 102 276
    12 A" 1519 1485 0.978 102 277
    13 A" 1345 1335 0.992 102 278
    14 A" 974     102 279
    15 A" 294 268 0.910 102 280
B2H6 Diborane 1 Ag 2620 2530 0.966 103 281
    2 Ag 2178 2088 0.959 103 282
    3 Ag 1207 1183 0.980 103 283
    4 Ag 800 790 0.987 103 284
    5 Au 851 833 0.979 103 285
    6 B1g 2693 2596 0.964 103 286
    7 B1g 940 915 0.973 103 287
    8 B1u 1995 1930 0.967 103 288
    9 B1u 992 973 0.980 103 289
    10 B2g 1858 1760 0.947 103 290
    11 B2g 895 860 0.961 103 291
    12 B2u 2707 2609 0.964 103 292
    13 B2u 954 949 0.995 103 293
    14 B2u 362 369 1.017 103 294
    15 B3g 1022 1020 0.998 103 295
    16 B3u 2607 2520 0.967 103 296
    17 B3u 1716 1603 0.934 103 297
    18 B3u 1199 1172 0.978 103 298
C2H6 Ethane 1 A1g 3025 2954 0.977 104 299
    2 A1g 1423 1388 0.976 104 300
    3 A1g 995 995 1.000 104 301
    4 A1u 303 289 0.953 104 302
    5 A2u 3026 2896 0.957 104 303
    6 A2u 1414 1379 0.976 104 304
    7 Eg 3069 2969 0.967 104 305
    8 Eg 1503 1468 0.976 104 306
    9 Eg 1223 1190 0.973 104 307
    10 Eu 3094 2985 0.965 104 308
    11 Eu 1507 1469 0.975 104 309
    12 Eu 827 822 0.994 104 310
Si2H6 disilane 1 A1g 2220 2152 0.969 105 311
    2 A1g 928 909 0.980 105 312
    3 A1g 423 434 1.027 105 313
    4 A1u 137 131 0.954 105 314
    5 A2u 2212 2154 0.974 105 315
    6 A2u 855 844 0.987 105 316
    7 Eg 2217 2155 0.972 105 317
    8 Eg 946 929 0.982 105 318
    9 Eg 634 625 0.986 105 319
    10 Eu 2226 2179 0.979 105 320
    11 Eu 960 940 0.979 105 321
    12 Eu 375 379 1.011 105 322

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