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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD/6-311G*
Scale factor How many Source
Molecules Vibrations
0.954 ± 0.109 110 321 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4268 4161 0.975 1 1
LiH Lithium Hydride 1 Σ 1369 1360 0.993 2 2
Li2 Lithium diatomic 1 Σg 348 346 0.996 3 3
NaH sodium hydride 1 Σ 1116 1133 1.015 4 4
Na2 Sodium diatomic 1 Σg 153 158 1.029 5 5
BeH beryllium monohydride 1 Σ 1996 1987 0.996 6 6
MgH magnesium monohydride 1 Σ 1425 1432 1.005 7 7
BH Boron monohydride 1 Σ 2313 2269 0.981 8 8
AlH aluminum monohydride 1 Σ 1666 1625 0.976 9 9
CH Methylidyne 1 Σ 2820 2733 0.969 10 10
C2 Carbon diatomic 1 Σg 1864 1827 0.981 11 11
Si2 Silicon diatomic 1 Σg 508 507 0.998 12 12
NH Imidogen 1 Σ 3250 3126 0.962 13 13
CN Cyano radical 1 Σ 2135 2042 0.957 14 14
N2 Nitrogen diatomic 1 Σg 1658 2330 1.405 15 15
PH phosphorus monohydride 1 Σ 2277 2276 1.000 16 16
CP Carbon monophosphide 1 Σ 1276 1226 0.961 17 17
PN Phosphorus mononitride 1 Σ 1386 1323 0.955 18 18
P2 Phosphorus diatomic 1 Σg 797 775 0.973 19 19
OH Hydroxyl radical 1 Σ 3702 3570 0.964 20 20
LiO lithium oxide 1 Σ 911 799 0.877 21 21
BeO beryllium oxide 1 Σ 1544 1435 0.929 22 22
BO boron monoxide 1 Σ 1935 1862 0.962 23 23
CO Carbon monoxide 1 Σ 2232 2143 0.960 24 24
NaO sodium monoxide 1 Σ 561     25 25
MgO magnesium oxide 1 Σ 721 775 1.075 26 26
SiO Silicon monoxide 1 Σ 1286 1230 0.956 27 27
HS Mercapto radical 1 Σ 2583 2599 1.006 28 28
BeS beryllium sulfide 1 Σ 1017 986 0.969 29 29
BS boron sulfide 1 Σ 1208 1167 0.966 30 30
CS carbon monosulfide 1 Σ 1337 1272 0.952 31 31
SO Sulfur monoxide 1 Σ 1145 1138 0.994 32 32
MgS magnesium sulfide 1 Σ 513 523 1.020 33 33
AlS Aluminum sulfide 1 Σ 612 610 0.998 34 34
SiS silicon monosulfide 1 Σ 769 744 0.968 35 35
S2 Sulfur diatomic 1 Σg 705 720 1.021 36 36
HF Hydrogen fluoride 1 Σ 4085 3961 0.970 37 37
LiF lithium fluoride 1 Σ 964 896 0.929 38 38
BeF Beryllium monofluoride 1 Σ 1242     39 39
CF Fluoromethylidyne 1 Σ 1337 1286 0.962 40 40
NF nitrogen fluoride 1 Σ 1178 1123 0.953 41 41
F2 Fluorine diatomic 1 Σg 886 894 1.009 42 42
NaF sodium fluoride 1 Σ 576 529 0.917 43 43
MgF Magnesium monofluoride 1 Σ 725     44 44
AlF Aluminum monofluoride 1 Σ 821 793 0.966 45 45
SiF silicon monofluoride 1 Σ 861 848 0.985 46 46
PF phosphorus monofluoride 1 Σ 825 838 1.016 47 47
SF Monosulfur monofluoride 1 Σ 791 829 1.047 48 48
HCl Hydrogen chloride 1 Σ 2882 2886 1.001 49 49
LiCl lithium chloride 1 Σ 654 634 0.969 50 50
BeCl beryllium monochloride 1 Σ 859 847 0.985 51 51
BCl boron monochloride 1 Σ 865 829 0.959 52 52
CCl carbon monochloride 1 Σ 878 866 0.986 53 53
ClO Monochlorine monoxide 1 Σ 775 843 1.088 54 54
ClF Chlorine monofluoride 1 Σ 724 773 1.069 55 55
NaCl Sodium Chloride 1 Σ 364 361 0.992 56 56
MgCl magnesium monochloride 1 Σ 464     57 57
SiCl Clorosilylidyne 1 Σ 524 531 1.015 58 58
PCl phosphorus chloride 1 Σ 521 547 1.051 59 59
SCl sulfur monochloride 1 Σ 536 577 1.077 60 60
Cl2 Chlorine diatomic 1 Σg 523 554 1.060 61 61
BeH2 beryllium dihydride 2 Σu 2222 2159 0.972 62 62
    3 Πu 715 698 0.976 62 63
MgH2 magnesium dihydride 2 Σu 1597 1572 0.984 63 64
    3 Πu 450 440 0.978 63 65
BH2 boron dihydride 2 A1 1004 954 0.949 64 66
AlH2 aluminum dihydride 1 A1 1835 1770 0.964 65 67
    2 A1 760 760 1.000 65 68
    3 B2 1875 1807 0.964 65 69
SiH2 silicon dihydride 1 A1 2018 1996 0.989 66 70
    2 A1 1028 999 0.972 66 71
    3 B2 2015 1993 0.989 66 72
HCN Hydrogen cyanide 1 Σ 3455 3312 0.958 67 73
    2 Σ 2162 2089 0.966 67 74
    3 Π 743 712 0.958 67 75
PH2 Phosphino radical 1 A1 2322 2310 0.995 68 76
    2 A1 1153 1102 0.956 68 77
HCP HCP 1 Σ 3351 3217 0.960 69 78
    2 Σ 1330 1278 0.961 69 79
    3 Π 681 674 0.990 69 80
HPO HPO 1 A' 2110 2095 0.993 70 81
    2 A' 1214 1188 0.978 70 82
    3 A' 1038 986 0.950 70 83
H2O Water 1 A1 3838 3657 0.953 71 84
    2 A1 1753 1595 0.910 71 85
    3 B2 3958 3756 0.949 71 86
BeOH beryllium monohydroxide 2 A' 1296 1246 0.961 72 87
HBO Boron hydride oxide 1 Σ 2878 2850 0.990 73 88
    2 Σ 1876 1826 0.973 73 89
    3 Π 782 756 0.967 73 90
HCO Formyl radical 1 A' 2668 2434 0.913 74 91
    2 A' 1952 1868 0.957 74 92
    3 A' 1144 1081 0.945 74 93
HNO Nitrosyl hydride 1 A' 2965 2684 0.905 75 94
    2 A' 1675 1565 0.935 75 95
    3 A' 1623 1501 0.925 75 96
HO2 Hydroperoxy radical 1 A' 3674 3436 0.935 76 97
    2 A' 1520 1392 0.916 76 98
    3 A' 1180 1098 0.930 76 99
NaOH sodium hydroxide 1 Σ 3939 3637 0.923 77 100
    2 Σ 606 540 0.891 77 101
    3 Π 226 300 1.329 77 102
H2S Hydrogen sulfide 1 A1 2619 2615 0.998 78 103
    2 A1 1256 1183 0.942 78 104
    3 B2 2639 2626 0.995 78 105
HBS hydrogen boron sulfide 1 Σ 2809 2736 0.974 79 106
    2 Σ 1208 1172 0.971 79 107
HCF Fluoromethylene 1 A' 2803 2643 0.943 80 108
    2 A' 1482 1403 0.947 80 109
    3 A' 1248 1189 0.952 80 110
HOF Hypofluorous acid 1 A' 3783 3578 0.946 81 111
    2 A' 1463 1362 0.931 81 112
    3 A' 938 893 0.952 81 113
HOCl hypochlorous acid 1 A' 3804 3609 0.949 82 114
    2 A' 1330 1239 0.931 82 115
    3 A' 704 724 1.029 82 116
BH3 boron trihydride 2 A2" 1147 1148 1.001 83 117
    3 E' 2665 2602 0.976 83 118
    4 E' 1192 1197 1.004 83 119
AlH3 aluminum trihydride 1 A1' 1930 1900 0.984 84 120
    2 A2" 711 698 0.982 84 121
    3 E' 1942 1883 0.970 84 122
    4 E' 785 783 0.998 84 123
C2H2 Acetylene 1 Σg 3514 3374 0.960 85 124
    2 Σg 2026 1974 0.975 85 125
    3 Σu 3414 3289 0.963 85 126
    4 Πg 430 612 1.424 85 127
    5 Πu 745 730 0.980 85 128
SiH3 Silyl radical 1 A1 2195 2136 0.973 86 129
    2 A1 768 728 0.947 86 130
    3 E 2227 2185 0.981 86 131
    4 E 936 922 0.985 86 132
NH3 Ammonia 1 A1 3501 3337 0.953 87 133
    2 A1 1180 950 0.805 87 134
    3 E 3632 3444 0.948 87 135
    4 E 1770 1627 0.919 87 136
PH3 Phosphine 1 A1 2357 2323 0.985 88 137
    2 A1 1057 992 0.938 88 138
    3 E 2366 2328 0.984 88 139
    4 E 1161 1118 0.963 88 140
H2CO Formaldehyde 1 A1 2943 2782 0.945 89 141
    2 A1 1828 1746 0.955 89 142
    3 A1 1566 1500 0.958 89 143
    4 B1 1196 1167 0.976 89 144
    5 B2 3011 2843 0.944 89 145
    6 B2 1293 1249 0.966 89 146
H2O2 Hydrogen peroxide 1 A 3819 3599 0.942 90 147
    2 A 1534 1402 0.914 90 148
    3 A 962 877 0.912 90 149
    4 A 336 371 1.106 90 150
    5 B 3821 3608 0.944 90 151
    6 B 1370 1266 0.924 90 152
H2CS Thioformaldehyde 1 A1 3096 2971 0.959 91 153
    2 A1 1539 1456 0.945 91 154
    3 A1 1100 1059 0.963 91 155
    4 B1 1026 990 0.965 91 156
    5 B2 3186 3025 0.949 91 157
    6 B2 1041 991 0.952 91 158
H2S2 Disulfane 1 A 2591 2556 0.986 92 159
    2 A 925 882 0.953 92 160
    3 A 500 515 1.028 92 161
    4 A 434 417 0.961 92 162
    5 B 2591 2559 0.987 92 163
    6 B 923 878 0.951 92 164
CH4 Methane 1 A1 3037 2917 0.961 93 165
    2 E 1587 1534 0.967 93 166
    3 T2 3155 3019 0.957 93 167
    4 T2 1379 1306 0.947 93 168
SiH4 Silane 1 A1 2225 2187 0.983 94 169
    2 E 972 975 1.003 94 170
    3 T2 2230 2191 0.982 94 171
    4 T2 925 914 0.988 94 172
CH2NH Methanimine 1 A' 3459 3263 0.943 95 173
    2 A' 3164 3024 0.956 95 174
    3 A' 3057 2914 0.953 95 175
    4 A' 1714 1638 0.956 95 176
    5 A' 1509 1452 0.962 95 177
    6 A' 1425 1344 0.943 95 178
    7 A' 1102 1058 0.960 95 179
    8 A" 1186 1127 0.950 95 180
    9 A" 1087 1061 0.975 95 181
CH3F Methyl fluoride 1 A1 3054 2930 0.960 96 182
    2 A1 1535 1464 0.954 96 183
    3 A1 1104 1049 0.950 96 184
    4 E 3142 3006 0.957 96 185
    5 E 1530 1467 0.959 96 186
    6 E 1223 1182 0.966 96 187
SiH3F monofluorosilane 1 A1 2258 2206 0.977 97 188
    2 A1 1032 990 0.959 97 189
    3 A1 880 872 0.991 97 190
    4 E 2262 2196 0.971 97 191
    5 E 967 956 0.988 97 192
    6 E 751 728 0.969 97 193
CH3Cl Methyl chloride 1 A1 3088 2966 0.960 98 194
    2 A1 1444 1355 0.938 98 195
    3 A1 761 732 0.962 98 196
    4 E 3188 3042 0.954 98 197
    5 E 1510 1455 0.963 98 198
    6 E 1068 1015 0.950 98 199
SiH3Cl chlorosilane 1 A1 2255 2201 0.976 99 200
    2 A1 972 949 0.976 99 201
    3 A1 550 551 1.001 99 202
    4 E 2266 2195 0.969 99 203
    5 E 961 954 0.993 99 204
    6 E 684 664 0.971 99 205
C2H4 Ethylene 1 Ag 3159 3026 0.958 100 206
    2 Ag 1697 1623 0.956 100 207
    3 Ag 1383 1342 0.971 100 208
    4 Au 1051 1023 0.974 100 209
    5 B1u 3141 2989 0.952 100 210
    6 B1u 1489 1444 0.969 100 211
    7 B2g 918 940 1.023 100 212
    8 B2u 3246 3105 0.957 100 213
    9 B2u 839 826 0.984 100 214
    10 B3g 3220 3086 0.958 100 215
    11 B3g 1251 1217 0.973 100 216
    12 B3u 963 949 0.985 100 217
N2H4 Hydrazine 1 A 3606 3398 0.942 101 218
    2 A 3503 3329 0.950 101 219
    3 A 1777 1642 0.924 101 220
    4 A 1398 1275 0.912 101 221
    5 A 1169 1076 0.920 101 222
    6 A 921 780 0.847 101 223
    7 A 447 377 0.842 101 224
    8 B 3612 3350 0.928 101 225
    9 B 3490 3314 0.950 101 226
    10 B 1761 1628 0.924 101 227
    11 B 1353 1275 0.942 101 228
    12 B 1089 966 0.887 101 229
CH3OH Methyl alcohol 1 A' 3860 3681 0.954 102 230
    2 A' 3143 3000 0.954 102 231
    3 A' 3010 2844 0.945 102 232
    4 A' 1545 1477 0.956 102 233
    5 A' 1521 1455 0.957 102 234
    6 A' 1427 1345 0.942 102 235
    7 A' 1109 1060 0.956 102 236
    8 A' 1095 1033 0.943 102 237
    9 A" 3063 2960 0.966 102 238
    10 A" 1530 1477 0.966 102 239
    11 A" 1195 1165 0.975 102 240
    12 A" 360 200 0.555 102 241
CH3SH Methanethiol 1 A' 3156 3000 0.951 103 242
    2 A' 3067 2931 0.956 103 243
    3 A' 2616 2597 0.993 103 244
    4 A' 1518 1475 0.972 103 245
    5 A' 1425 1335 0.937 103 246
    6 A' 1133 1074 0.948 103 247
    7 A' 819 803 0.980 103 248
    8 A' 739 708 0.958 103 249
    9 A" 3155 3000 0.951 103 250
    10 A" 1506 1430 0.949 103 251
    11 A" 1015 976 0.961 103 252
C2H6 Ethane 1 A1g 3044 2954 0.970 104 253
    2 A1g 1463 1388 0.949 104 254
    3 A1g 1028 995 0.968 104 255
    4 A1u 316 289 0.914 104 256
    5 A2u 3041 2896 0.952 104 257
    6 A2u 1440 1379 0.958 104 258
    7 Eg 3101 2969 0.958 104 259
    8 Eg 1533 1468 0.957 104 260
    9 Eg 1245 1190 0.956 104 261
    10 Eu 3123 2985 0.956 104 262
    11 Eu 1537 1469 0.956 104 263
    12 Eu 832 822 0.988 104 264
CH3SiH3 methyl silane 1 A1 3041 2898 0.953 105 265
    2 A1 2213 2166 0.979 105 266
    3 A1 1355 1260 0.930 105 267
    4 A1 953 940 0.986 105 268
    5 A1 713 700 0.982 105 269
    6 A2 181 187 1.031 105 270
    7 E 3120 2982 0.956 105 271
    8 E 2211 2169 0.981 105 272
    9 E 1500 1403 0.935 105 273
    10 E 963 980 1.018 105 274
    11 E 915 868 0.949 105 275
    12 E 529 540 1.020 105 276
Si2H6 disilane 1 A1g 2207 2152 0.975 106 277
    2 A1g 941 909 0.966 106 278
    3 A1g 444 434 0.979 106 279
    4 A1u 143 131 0.917 106 280
    5 A2u 2197 2154 0.981 106 281
    6 A2u 866 844 0.975 106 282
    7 Eg 2205 2155 0.977 106 283
    8 Eg 940 929 0.988 106 284
    9 Eg 652 625 0.959 106 285
    10 Eu 2213 2179 0.984 106 286
    11 Eu 956 940 0.983 106 287
    12 Eu 393 379 0.966 106 288

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