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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at B3LYP/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 4416 4161 0.942 1 1
LiH Lithium Hydride 1 Σ 1407 1360 0.966 2 2
Li2 Lithium diatomic 1 Σg 346 346 1.002 3 3
NaH sodium hydride 1 Σ 1158 1133 0.979 4 4
Na2 Sodium diatomic 1 Σg 162 158 0.971 5 5
BeH beryllium monohydride 1 Σ 2066 1987 0.962 6 6
MgH magnesium monohydride 1 Σ 1457 1432 0.983 7 7
BH Boron monohydride 1 Σ 2350 2269 0.966 8 8
AlH aluminum monohydride 1 Σ 1645 1625 0.988 9 9
CH Methylidyne 1 Σ 2831 2733 0.965 10 10
    1 Σ 3048     10 11
C2 Carbon diatomic 1 Σg 1875 1827 0.975 11 12
SiH Silylidyne 1 Σ 2013 1971 0.979 12 13
CN Cyano radical 1 Σ 2154 2042 0.948 13 14
N2 Nitrogen diatomic 1 Σg 2447 2330 0.952 14 15
    1 Σg 1818 1733 0.954 14 16
PH phosphorus monohydride 1 Σ 2342 2276 0.972 15 17
    1 Σ 2354 2319 0.985 15 18
PN Phosphorus mononitride 1 Σ 1405 1323 0.941 16 19
P2 Phosphorus diatomic 1 Σg 808 775 0.960 17 20
OH Hydroxyl radical 1 Σ 3703 3570 0.964 18 21
LiO lithium oxide 1 Σ 821 799 0.974 19 22
BeO beryllium oxide 1 Σ 1554 1435 0.923 20 23
BO boron monoxide 1 Σ 1921 1862 0.969 21 24
CO Carbon monoxide 1 Σ 2214 2143 0.968 22 25
    1 Σ 1787     22 26
NaO sodium monoxide 1 Σ 481     23 27
MgO magnesium oxide 1 Σ 826 775 0.939 24 28
SiO Silicon monoxide 1 Σ 1258 1230 0.977 25 29
HS Mercapto radical 1 Σ 2666 2599 0.975 26 30
BeS beryllium sulfide 1 Σ 1012 986 0.974 27 31
CS carbon monosulfide 1 Σ 1305 1272 0.975 28 32
SO Sulfur monoxide 1 Σ 1152 1138 0.988 29 33
    1 Σ 1151 1054 0.916 29 34
MgS magnesium sulfide 1 Σ 527 523 0.993 30 35
SiS silicon monosulfide 1 Σ 744 744 1.000 31 36
S2 Sulfur diatomic 1 Σg 713 720 1.010 32 37
HF Hydrogen fluoride 1 Σ 4086 3961 0.970 33 38
LiF lithium fluoride 1 Σ 911 896 0.984 34 39
CF Fluoromethylidyne 1 Σ 1297 1286 0.992 35 40
F2 Fluorine diatomic 1 Σg 1045 894 0.855 36 41
NaF sodium fluoride 1 Σ 525 529 1.008 37 42
AlF Aluminum monofluoride 1 Σ 778 793 1.019 38 43
SiF silicon monofluoride 1 Σ 829 848 1.022 39 44
SF Monosulfur monofluoride 1 Σ 824 829 1.006 40 45
HCl Hydrogen chloride 1 Σ 2939 2886 0.982 41 46
LiCl lithium chloride 1 Σ 642 634 0.988 42 47
BCl boron monochloride 1 Σ 818 829 1.013 43 48
ClO Monochlorine monoxide 1 Σ 854 843 0.986 44 49
ClF Chlorine monofluoride 1 Σ 787 773 0.983 45 50
NaCl Sodium Chloride 1 Σ 356 361 1.014 46 51
AlCl Aluminum monochloride 1 Σ 455 478 1.050 47 52
SiCl Clorosilylidyne 1 Σ 508 531 1.046 48 53
SCl sulfur monochloride 1 Σ 560 577 1.031 49 54
Cl2 Chlorine diatomic 1 Σg 539 554 1.029 50 55
BeH2 beryllium dihydride 2 Σu 2261 2159 0.955 51 56
    3 Πu 727 698 0.960 51 57
MgH2 magnesium dihydride 2 Σu 1639 1572 0.959 52 58
    3 Πu 437 440 1.007 52 59
SiH2 silicon dihydride 1 A1 2043 1996 0.977 53 60
    2 A1 1023 999 0.977 53 61
    3 B2 2043 1993 0.976 53 62
NH2 Amino radical 1 A1 3352 3219 0.960 54 63
    2 A1 1536 1497 0.975 54 64
    3 B2 3440 3301 0.960 54 65
HCN Hydrogen cyanide 1 Σ 3439 3312 0.963 55 66
    2 Σ 2202 2089 0.949 55 67
    3 Π 762 712 0.935 55 68
HNC hydrogen isocyanide 1 Σ 3802 3653 0.961 56 69
    2 Σ 2107 2029 0.963 56 70
    3 Π 473 477 1.009 56 71
HCP Phosphaethyne 1 Σ 3348 3217 0.961 57 72
    2 Σ 1343 1278 0.952 57 73
    3 Π 721 674 0.935 57 74
HPO Hydrogen phosphorus oxide 1 A' 2085 2095 1.005 58 75
    2 A' 1223 1188 0.971 58 76
    3 A' 1004 986 0.982 58 77
H2O Water 1 A1 3805 3657 0.961 59 78
    2 A1 1635 1595 0.975 59 79
    3 B2 3906 3756 0.962 59 80
LiOH lithium hydroxide 1 Σ 3994 3688 0.923 60 81
    2 Σ 965 871 0.902 60 82
    3 Π 361 257 0.710 60 83
BeOH beryllium monohydroxide 2 A' 1292 1246 0.964 61 84
HBO Boron hydride oxide 1 Σ 2893 2850 0.985 62 85
    2 Σ 1869 1826 0.977 62 86
    3 Π 776 756 0.975 62 87
HCO Formyl radical 1 A' 2644 2434 0.921 63 88
    2 A' 1936 1868 0.965 63 89
    3 A' 1106 1081 0.977 63 90
HNO Nitrosyl hydride 1 A' 2852 2684 0.941 64 91
    2 A' 1667 1565 0.939 64 92
    3 A' 1566 1501 0.958 64 93
HO2 Hydroperoxy radical 1 A' 3600 3436 0.954 65 94
    2 A' 1436 1392 0.969 65 95
    3 A' 1165 1098 0.942 65 96
NaOH sodium hydroxide 1 Σ 3950 3637 0.921 66 97
    2 Σ 565 540 0.956 66 98
    3 Π 133 300 2.255 66 99
H2S Hydrogen sulfide 1 A1 2681 2615 0.976 67 100
    2 A1 1209 1183 0.978 67 101
    3 B2 2694 2626 0.975 67 102
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 68 103
    2 Σ 1188 1172 0.987 68 104
HCF Fluoromethylene 1 A' 2760 2643 0.958 69 105
    2 A' 1440 1403 0.975 69 106
    3 A' 1201 1189 0.990 69 107
HOF Hypofluorous acid 1 A' 3731 3578 0.959 70 108
    2 A' 1409 1362 0.967 70 109
    3 A' 984 893 0.908 70 110
HOCl hypochlorous acid 1 A' 3770 3609 0.957 71 111
    2 A' 1266 1239 0.978 71 112
    3 A' 740 724 0.978 71 113
BH3 boron trihydride 2 A2" 1161 1148 0.988 72 114
    3 E' 2690 2602 0.967 72 115
    4 E' 1206 1197 0.992 72 116
AlH3 aluminum trihydride 1 A1' 1943 1900 0.978 73 117
    2 A2" 712 698 0.980 73 118
    3 E' 1949 1883 0.966 73 119
    4 E' 800 783 0.979 73 120
C2H2 Acetylene 1 Σg 3511 3374 0.961 74 121
    2 Σg 2068 1974 0.954 74 122
    3 Σu 3413 3289 0.964 74 123
    4 Πg 656 612 0.933 74 124
    5 Πu 766 730 0.953 74 125
SiH3 Silyl radical 1 A1 2199 2136 0.972 75 126
    2 A1 766 728 0.951 75 127
    3 E 2236 2185 0.977 75 128
    4 E 938 922 0.983 75 129
NH3 Ammonia 1 A1 3467 3337 0.963 76 130
    2 A1 1051 950 0.904 76 131
    3 E 3583 3444 0.961 76 132
    4 E 1670 1627 0.974 76 133
PH3 Phosphine 1 A1 2387 2323 0.973 77 134
    2 A1 1018 992 0.974 77 135
    3 E 2393 2328 0.973 77 136
    4 E 1139 1118 0.981 77 137
H2CO Formaldehyde 1 A1 2879 2782 0.966 78 138
    2 A1 1820 1746 0.959 78 139
    3 A1 1535 1500 0.977 78 140
    4 B1 1203 1167 0.970 78 141
    5 B2 2933 2843 0.969 78 142
    6 B2 1269 1249 0.984 78 143
H2O2 Hydrogen peroxide 1 A 3766 3599 0.956 79 144
    2 A 1439 1402 0.974 79 145
    3 A 950 877 0.923 79 146
    4 A 381 371 0.974 79 147
    5 B 3764 3608 0.958 79 148
    6 B 1327 1266 0.954 79 149
H2CS Thioformaldehyde 1 A1 3061 2971 0.971 80 150
    2 A1 1494 1456 0.974 80 151
    3 A1 1087 1059 0.974 80 152
    4 B1 1030 990 0.961 80 153
    5 B2 3142 3025 0.963 80 154
    6 B2 1005 991 0.986 80 155
H2S2 Disulfane 1 A 2619 2556 0.976 81 156
    2 A 889 882 0.992 81 157
    3 A 501 515 1.027 81 158
    4 A 431 417 0.969 81 159
    5 B 2621 2559 0.976 81 160
    6 B 890 878 0.986 81 161
CH4 Methane 1 A1 3027 2917 0.964 82 162
    2 E 1559 1534 0.984 82 163
    3 T2 3129 3019 0.965 82 164
    4 T2 1341 1306 0.974 82 165
SiH4 Silane 1 A1 2241 2187 0.976 83 166
    2 E 979 975 0.996 83 167
    3 T2 2245 2191 0.976 83 168
    4 T2 923 914 0.991 83 169
CH2NH Methanimine 1 A' 3431 3263 0.951 84 170
    2 A' 3105 3024 0.974 84 171
    3 A' 3011 2914 0.968 84 172
    4 A' 1711 1638 0.957 84 173
    5 A' 1492 1452 0.973 84 174
    6 A' 1371 1344 0.981 84 175
    7 A' 1075 1058 0.985 84 176
    8 A" 1167 1127 0.966 84 177
    9 A" 1103 1061 0.961 84 178
NH2OH hydroxylamine 1 A' 3816 3650 0.956 85 179
    2 A' 3440 3294 0.958 85 180
    3 A' 1666 1605 0.963 85 181
    4 A' 1398 1353 0.968 85 182
    5 A' 1147 1115 0.972 85 183
    6 A' 929 895 0.963 85 184
    7 A" 3516 3359 0.955 85 185
    8 A" 1329 1295 0.974 85 186
    9 A" 411 386 0.940 85 187
CH3F Methyl fluoride 1 A1 3028 2930 0.968 86 188
    2 A1 1488 1464 0.984 86 189
    3 A1 1049 1049 1.000 86 190
    4 E 3106 3006 0.968 86 191
    5 E 1494 1467 0.982 86 192
    6 E 1195 1182 0.989 86 193
SiH3F monofluorosilane 1 A1 2256 2206 0.978 87 194
    2 A1 995 990 0.995 87 195
    3 A1 862 872 1.012 87 196
    4 E 2260 2196 0.971 87 197
    5 E 967 956 0.988 87 198
    6 E 727 728 1.002 87 199
CH3Cl Methyl chloride 1 A1 3070 2966 0.966 88 200
    2 A1 1378 1355 0.983 88 201
    3 A1 713 732 1.027 88 202
    4 E 3165 3042 0.961 88 203
    5 E 1483 1455 0.981 88 204
    6 E 1027 1015 0.989 88 205
SiH3Cl chlorosilane 1 A1 2256 2201 0.975 89 206
    2 A1 954 949 0.995 89 207
    3 A1 531 551 1.037 89 208
    4 E 2266 2195 0.969 89 209
    5 E 960 954 0.994 89 210
    6 E 660 664 1.006 89 211
C2H4 Ethylene 1 Ag 3138 3026 0.965 90 212
    2 Ag 1690 1623 0.960 90 213
    3 Ag 1381 1342 0.972 90 214
    4 Au 1065 1023 0.960 90 215
    5 B1u 3125 2989 0.956 90 216
    6 B1u 1479 1444 0.976 90 217
    7 B2g 987 940 0.952 90 218
    8 B2u 3222 3105 0.964 90 219
    9 B2u 836 826 0.988 90 220
    10 B3g 3194 3086 0.966 90 221
    11 B3g 1246 1217 0.977 90 222
    12 B3u 980 949 0.969 90 223
N2H4 Hydrazine 1 A 3552 3398 0.957 91 224
    2 A 3460 3329 0.962 91 225
    3 A 1687 1642 0.973 91 226
    4 A 1329 1275 0.959 91 227
    5 A 1113 1076 0.967 91 228
    6 A 808 780 0.966 91 229
    7 A 440 377 0.856 91 230
    8 B 3558 3350 0.941 91 231
    9 B 3451 3314 0.960 91 232
    10 B 1676 1628 0.972 91 233
    11 B 1299 1275 0.982 91 234
    12 B 988 966 0.978 91 235
CH3OH Methyl alcohol 1 A' 3836 3681 0.960 92 236
    2 A' 3106 3000 0.966 92 237
    3 A' 2990 2844 0.951 92 238
    4 A' 1510 1477 0.978 92 239
    5 A' 1482 1455 0.982 92 240
    6 A' 1372 1345 0.981 92 241
    7 A' 1080 1060 0.981 92 242
    8 A' 1043 1033 0.990 92 243
    9 A" 3034 2960 0.976 92 244
    10 A" 1497 1477 0.987 92 245
    11 A" 1173 1165 0.993 92 246
    12 A" 294 200 0.681 92 247
CH3SH Methanethiol 1 A' 3133 3000 0.958 93 248
    2 A' 3050 2931 0.961 93 249
    3 A' 2671 2597 0.972 93 250
    4 A' 1489 1475 0.991 93 251
    5 A' 1359 1335 0.982 93 252
    6 A' 1097 1074 0.979 93 253
    7 A' 798 803 1.006 93 254
    8 A' 698 708 1.014 93 255
    9 A" 3133 3000 0.958 93 256
    10 A" 1476 1430 0.969 93 257
    11 A" 974 976 1.002 93 258
CH3NH2 methyl amine 1 A' 3498 3361 0.961 94 259
    2 A' 3054 2961 0.970 94 260
    3 A' 2963 2820 0.952 94 261
    4 A' 1664 1623 0.976 94 262
    5 A' 1499 1473 0.982 94 263
    6 A' 1461 1430 0.979 94 264
    7 A' 1172 1130 0.964 94 265
    8 A' 1055 1044 0.989 94 266
    9 A' 830 780 0.939 94 267
    10 A" 3572 3427 0.959 94 268
    11 A" 3087 2985 0.967 94 269
    12 A" 1518 1485 0.978 94 270
    13 A" 1347 1335 0.991 94 271
    14 A" 975     94 272
    15 A" 297 268 0.901 94 273
B2H6 Diborane 1 Ag 2619 2530 0.966 95 274
    2 Ag 2178 2088 0.959 95 275
    3 Ag 1205 1183 0.982 95 276
    4 Ag 800 790 0.987 95 277
    5 Au 850 833 0.980 95 278
    6 B1g 2692 2596 0.964 95 279
    7 B1g 940 915 0.973 95 280
    8 B1u 1994 1930 0.968 95 281
    9 B1u 991 973 0.981 95 282
    10 B2g 1859 1760 0.947 95 283
    11 B2g 894 860 0.962 95 284
    12 B2u 2707 2609 0.964 95 285
    13 B2u 954 949 0.995 95 286
    14 B2u 362 369 1.018 95 287
    15 B3g 1021 1020 0.999 95 288
    16 B3u 2606 2520 0.967 95 289
    17 B3u 1716 1603 0.934 95 290
    18 B3u 1198 1172 0.978 95 291
C2H6 Ethane 1 A1g 3025 2954 0.977 96 292
    2 A1g 1423 1388 0.975 96 293
    3 A1g 995 995 1.000 96 294
    4 A1u 304 289 0.952 96 295
    5 A2u 3026 2896 0.957 96 296
    6 A2u 1413 1379 0.976 96 297
    7 Eg 3069 2969 0.967 96 298
    8 Eg 1503 1468 0.977 96 299
    9 Eg 1223 1190 0.973 96 300
    10 Eu 3094 2985 0.965 96 301
    11 Eu 1506 1469 0.975 96 302
    12 Eu 827 822 0.994 96 303
Si2H6 disilane 1 A1g 2221 2152 0.969 97 304
    2 A1g 928 909 0.980 97 305
    3 A1g 423 434 1.027 97 306
    4 A1u 138 131 0.951 97 307
    5 A2u 2212 2154 0.974 97 308
    6 A2u 855 844 0.987 97 309
    7 Eg 2218 2155 0.972 97 310
    8 Eg 946 929 0.982 97 311
    9 Eg 634 625 0.986 97 312
    10 Eu 2228 2179 0.978 97 313
    11 Eu 960 940 0.978 97 314
    12 Eu 376 379 1.010 97 315

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