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III.B.3.b. (XIII.C.2.)

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
H2CO Formaldehyde 1 A1 2943 2782 0.945 1 1
    2 A1 1828 1746 0.955 1 2
    3 A1 1566 1500 0.958 1 3
    4 B1 1196 1167 0.976 1 4
    5 B2 3011 2843 0.944 1 5
    6 B2 1293 1249 0.966 1 6
CH3OH Methyl alcohol 1 A' 3860 3681 0.954 2 7
    2 A' 3143 3000 0.955 2 8
    3 A' 3009 2844 0.945 2 9
    4 A' 1544 1477 0.956 2 10
    5 A' 1521 1455 0.957 2 11
    6 A' 1427 1345 0.942 2 12
    7 A' 1108 1060 0.956 2 13
    8 A' 1095 1033 0.944 2 14
    9 A" 3062 2960 0.967 2 15
    10 A" 1529 1477 0.966 2 16
    11 A" 1194 1165 0.975 2 17
    12 A" 361 200 0.553 2 18
CH4 Methane 1 A1 3037 2917 0.960 3 19
    2 E 1587 1534 0.967 3 20
    3 T2 3155 3019 0.957 3 21
    4 T2 1379 1306 0.947 3 22
C2H6 Ethane 1 A1g 3044 2896 0.951 4 23
    2 A1g 1463 1388 0.949 4 24
    3 A1g 1029 995 0.967 4 25
    4 A1u 315 289 0.916 4 26
    5 A2u 3041 2915 0.959 4 27
    6 A2u 1440 1370 0.951 4 28
    7 Eg 3100 2969 0.958 4 29
    8 Eg 1533 1468 0.957 4 30
    9 Eg 1245 1190 0.956 4 31
    10 Eu 3123 2974 0.952 4 32
    11 Eu 1537 1460 0.950 4 33
    12 Eu 832 822 0.988 4 34
C2H4 Ethylene 1 Ag 3159 3026 0.958 5 35
    2 Ag 1697 1623 0.956 5 36
    3 Ag 1383 1342 0.971 5 37
    4 Au 1051 1023 0.974 5 38
    5 B1u 3141 2989 0.952 5 39
    6 B1u 1489 1444 0.969 5 40
    7 B2g 918 940 1.023 5 41
    8 B2u 3246 3105 0.957 5 42
    9 B2u 839 826 0.984 5 43
    10 B3g 3220 3086 0.958 5 44
    11 B3g 1251 1217 0.973 5 45
    12 B3u 963 949 0.985 5 46
C2H2 Acetylene 1 Σg 3514 3374 0.960 6 47
    2 Σg 2026 1974 0.975 6 48
    3 Σu 3414 3289 0.963 6 49
    4 Πg 430 612 1.424 6 50
    5 Πu 745 730 0.980 6 51
CH3Cl Methyl chloride 1 A1 3088 2966 0.960 7 52
    2 A1 1444 1355 0.938 7 53
    3 A1 761 732 0.962 7 54
    4 E 3188 3042 0.954 7 55
    5 E 1510 1455 0.963 7 56
    6 E 1068 1015 0.950 7 57
HCN Hydrogen cyanide 1 Σ 3455 3312 0.958 8 58
    2 Σ 2162 2089 0.966 8 59
    3 Π 743 712 0.958 8 60
CH3SH Methanethiol 1 A' 3156 3000 0.951 9 61
    2 A' 3067 2931 0.956 9 62
    3 A' 2616 2597 0.993 9 63
    4 A' 1517 1475 0.972 9 64
    5 A' 1425 1335 0.937 9 65
    6 A' 1132 1074 0.949 9 66
    7 A' 819 803 0.981 9 67
    8 A' 738 708 0.959 9 68
    9 A" 3154 3000 0.951 9 69
    10 A" 1506 1430 0.949 9 70
    11 A" 1015 976 0.962 9 71
N2H4 Hydrazine 1 A 3606 3398 0.942 10 72
    2 A 3503 3329 0.950 10 73
    3 A 1777 1642 0.924 10 74
    4 A 1398 1275 0.912 10 75
    5 A 1169 1076 0.920 10 76
    6 A 921 780 0.847 10 77
    7 A 447 377 0.842 10 78
    8 B 3612 3350 0.928 10 79
    9 B 3490 3314 0.950 10 80
    10 B 1761 1628 0.924 10 81
    11 B 1353 1275 0.942 10 82
    12 B 1089 966 0.887 10 83
CH3F Methyl fluoride 1 A1 3054 2930 0.960 11 84
    2 A1 1535 1464 0.954 11 85
    3 A1 1104 1049 0.950 11 86
    4 E 3142 3006 0.957 11 87
    5 E 1530 1467 0.959 11 88
    6 E 1223 1182 0.966 11 89
CH3PH2 Methyl phosphine 1 A 3142 3000 0.955 12 90
    2 A 3054 2938 0.962 12 91
    3 A 2343 2297 0.980 12 92
    4 A 1507 1450 0.962 12 93
    5 A 1392 1238 0.889 12 94
    6 A 1138 1086 0.954 12 95
    7 A 1029 977 0.949 12 96
    8 A 759 740 0.975 12 97
    9 A 703 677 0.964 12 98
    10 A 3132 2992 0.955 12 99
    11 A 2348 2312 0.985 12 100
    12 A 1511 1450 0.960 12 101
    13 A 1062 1017 0.957 12 102
    15 A 229 207 0.904 12 103
CO Carbon monoxide 1 Σ 2232 2170 0.972 13 104
H2CS Thioformaldehyde 1 A1 3096 2971 0.959 14 105
    2 A1 1539 1456 0.945 14 106
    3 A1 1100 1059 0.963 14 107
    4 B1 1026 990 0.965 14 108
    5 B2 3186 3025 0.949 14 109
    6 B2 1041 991 0.952 14 110
CH3SiH3 methyl silane 1 A1 3041 2898 0.953 15 111
    2 A1 2213 2166 0.979 15 112
    3 A1 1355 1260 0.930 15 113
    4 A1 953 940 0.986 15 114
    5 A1 713 700 0.982 15 115
    6 A2 181 187 1.031 15 116
    7 E 3120 2982 0.956 15 117
    8 E 2211 2169 0.981 15 118
    9 E 1500 1403 0.935 15 119
    10 E 963 980 1.018 15 120
    11 E 915 868 0.949 15 121
    12 E 529 540 1.020 15 122
BeO beryllium oxide 1 Σ 1544 1457 0.943 16 123
MgO magnesium oxide 1 Σ 721 785 1.089 17 124
NaOH sodium hydroxide 1 Σ 3939 3637 0.923 18 125
    2 Σ 606 540 0.891 18 126
    3 Π 226 300 1.329 18 127
H2 Hydrogen diatomic 1 Σg 4268 4401 1.031 19 128
Si2H6 disilane 1 A1g 2207 2152 0.975 20 129
    2 A1g 941 909 0.966 20 130
    3 A1g 444 434 0.979 20 131
    4 A1u 143 131 0.917 20 132
    5 A2u 2197 2154 0.981 20 133
    6 A2u 866 844 0.975 20 134
    7 Eg 2205 2155 0.977 20 135
    8 Eg 940 929 0.988 20 136
    9 Eg 652 625 0.959 20 137
    10 Eu 2213 2179 0.984 20 138
    11 Eu 956 940 0.983 20 139
    12 Eu 393 379 0.966 20 140
CH2NH Methanimine 1 A' 3459 3263 0.943 21 141
    2 A' 3164 3024 0.956 21 142
    3 A' 3057 2914 0.953 21 143
    4 A' 1714 1638 0.956 21 144
    5 A' 1509 1452 0.962 21 145
    6 A' 1425 1344 0.943 21 146
    7 A' 1102 1058 0.960 21 147
    8 A" 1186 1127 0.950 21 148
    9 A" 1087 1061 0.975 21 149
CN Cyano radical 1 Σ 2135 2069 0.969 22 150
HCO Formyl radical 1 A' 2668 2434 0.913 23 151
    2 A' 1952 1868 0.957 23 152
    3 A' 1144 1081 0.945 23 153
CS carbon monosulfide 1 Σ 1337 1285 0.961 24 154
HO2 Hydroperoxy radical 1 A' 3673 3436 0.936 25 155
    2 A' 1519 1392 0.916 25 156
    3 A' 1180 1098 0.930 25 157
CH Methylidyne 1 Σ 2820 2861 1.014 26 158
OH Hydroxyl radical 1 Σ 3702 3738 1.010 27 159
CF Fluoromethylidyne 1 Σ 1337 1308 0.978 28 160
CCl carbon monochloride 1 Σ 878 877 0.999 29 161
HCP HCP 1 Σ 3351 3217 0.960 30 162
    2 Σ 1330 1278 0.961 30 163
    3 Π 681 674 0.990 30 164
LiCl lithium chloride 1 Σ 654 643 0.983 31 165
LiH Lithium Hydride 1 Σ 1369 1405 1.027 32 166
NaH sodium hydride 1 Σ 1116 1172 1.050 33 167
HCl Hydrogen chloride 1 Σ 2882 2991 1.038 34 168
NaCl Sodium Chloride 1 Σ 364 365 1.002 35 169
HF Hydrogen fluoride 1 Σ 4091 4138 1.012 36 170
NH3 Ammonia 1 A1 3501 3337 0.953 37 171
    2 A1 1180 950 0.805 37 172
    3 E 3632 3444 0.948 37 173
    4 E 1770 1627 0.919 37 174
NaF sodium fluoride 1 Σ 576 536 0.929 38 175
MgH2 magnesium dihydride 2 Σu 1597 1572 0.984 39 176
    3 Πu 450 440 0.978 39 177
H2O2 Hydrogen peroxide 1 A 3819 3599 0.942 40 178
    2 A 1534 1402 0.914 40 179
    3 A 962 877 0.912 40 180
    4 A 336 371 1.106 40 181
    5 B 3821 3608 0.944 40 182
    6 B 1370 1266 0.924 40 183
N2 Nitrogen diatomic 1 Σg 2412 2359 0.978 41 184
H2O Water 1 A1 3839 3657 0.953 42 185
    2 A1 1752 1595 0.911 42 186
    3 B2 3959 3756 0.949 42 187
F2 Fluorine diatomic 1 Σg 886 917 1.035 43 188
Cl2 Chlorine diatomic 1 Σg 523 560 1.070 44 189
H2S Hydrogen sulfide 1 A1 2619 2615 0.998 45 190
    2 A1 1256 1183 0.942 45 191
    3 B2 2639 2626 0.995 45 192
AlH3 aluminum trihydride 1 A1' 1929 1900 0.985 46 193
    2 A2" 711 698 0.981 46 194
    3 E' 1940 1883 0.970 46 195
    4 E' 785 783 0.997 46 196
BeH2 beryllium dihydride 2 Σu 2222 2159 0.972 47 197
    3 Πu 715 698 0.976 47 198
LiF lithium fluoride 1 Σ 964 911 0.944 48 199
ClF Chlorine monofluoride 1 Σ 724 783 1.082 49 200
HOCl hypochlorous acid 1 A' 3809 3609 0.948 50 201
    2 A' 1329 1239 0.932 50 202
    3 A' 703 724 1.030 50 203
PH3 Phosphine 1 A1 2357 2323 0.985 51 204
    2 A1 1057 992 0.938 51 205
    3 E 2366 2328 0.984 51 206
    4 E 1161 1118 0.963 51 207
SiH4 Silane 1 A1 2225 2187 0.983 52 208
    2 E 972 975 1.003 52 209
    3 T2 2230 2191 0.983 52 210
    4 T2 925 914 0.988 52 211
SiO Silicon monoxide 1 Σ 1286 1242 0.965 53 212
SiF silicon monofluoride 1 Σ 861 857 0.996 54 213
MgS magnesium sulfide 1 Σ 513 529 1.030 55 214
C2 Carbon diatomic 1 Σg 1864 1855 0.995 56 215
LiO lithium oxide 1 Σ 911 815 0.894 57 216
P2 Phosphorus diatomic 1 Σg 797 781 0.980 58 217
BS boron sulfide 1 Σ 1208 1180 0.977 59 218
AlS Aluminum sulfide 1 Σ 612 617 1.009 60 219
CP Carbon monophosphide 1 Σ 1276 1240 0.972 61 220
NaO sodium monoxide 1 Σ 561 492 0.878 62 221
SiS silicon monosulfide 1 Σ 769 750 0.975 63 222
BO boron monoxide 1 Σ 1935 1885 0.974 64 223
Si2 Silicon diatomic 1 Σg 508 511 1.006 65 224
BH3 boron trihydride 2 A2" 1147 1148 1.001 66 225
    3 E' 2665 2602 0.976 66 226
    4 E' 1192 1197 1.004 66 227
HCF Fluoromethylene 1 A' 2803 2643 0.943 67 228
    2 A' 1482 1403 0.947 67 229
    3 A' 1248 1189 0.952 67 230
H2S2 HSSH 1 A 2590 2556 0.987 68 231
    2 A 925 882 0.953 68 232
    3 A 501 515 1.027 68 233
    4 A 433 417 0.964 68 234
    5 B 2590 2559 0.988 68 235
    6 B 924 878 0.950 68 236
SiH3Cl chlorosilane 1 A1 2255 2201 0.976 69 237
    2 A1 972 949 0.976 69 238
    3 A1 550 551 1.002 69 239
    4 E 2267 2195 0.968 69 240
    5 E 961 954 0.993 69 241
    6 E 684 664 0.971 69 242
SiH3F monofluorosilane 1 A1 2258 2206 0.977 70 243
    2 A1 1032 990 0.959 70 244
    3 A1 880 872 0.991 70 245
    4 E 2262 2196 0.971 70 246
    5 E 967 956 0.988 70 247
    6 E 751 728 0.969 70 248
AlF Aluminum monofluoride 1 Σ 821 802 0.978 71 249
BeF Beryllium monofluoride 1 Σ 1242 1247 1.004 72 250
BeH beryllium monohydride 1 Σ 1996 2061 1.033 73 251
BeS beryllium sulfide 1 Σ 1017 998 0.982 74 252
PH2 Phosphino radical 1 A1 2322 2310 0.995 75 253
    2 A1 1153 1102 0.956 75 254
SiH3 Silyl radical 1 A1 2195 2136 0.973 76 255
    2 A1 768 728 0.947 76 256
    3 E 2227 2185 0.981 76 257
    4 E 936 922 0.985 76 258
BH Boron monohydride 1 Σ 2313 2367 1.023 77 259
NH2 Amino radical 1 A1 3363 3219 0.957 78 260
    2 A1 1620 1497 0.924 78 261
    3 B2 3462 3301 0.954 78 262
NH Imidogen 1 Σ 3250 3283 1.010 79 263
BeCl beryllium chloride 1 Σ 859 847 0.985 80 264
HPO HPO 1 A' 2110 2095 0.993 81 265
    2 A' 1214 1188 0.978 81 266
    3 A' 1038 986 0.950 81 267
SiH2 silicon dihydride 1 A1 2018 1996 0.989 82 268
    2 A1 1028 999 0.972 82 269
    3 B2 2015 1993 0.989 82 270
SO Sulfur monoxide 1 Σ 1145 1151 1.005 83 271
SH Mercapto radical 1 Σ 2583 2696 1.044 84 272
SiCl Clorosilylidyne 1 Σ 524 536 1.023 85 273
NF nitrogen fluoride 1 Σ 1178 1141 0.969 86 274
PH phosphorus monohydride 1 Σ 2279 2364 1.037 87 275
AlH aluminum monohydride 1 Σ 1666 1682 1.010 88 276
HOF Hypofluorous acid 1 A' 3783 3537 0.935 89 277
    2 A' 1463 1393 0.952 89 278
    3 A' 938 886 0.945 89 279
HNO Nitrosyl hydride 1 A' 2965 2684 0.905 90 280
    2 A' 1675 1565 0.935 90 281
    3 A' 1623 1501 0.925 90 282
MgH magnesium monohydride 1 Σ 1425 1493 1.047 91 283
Li2 Lithium diatomic 1 Σg 348 351 1.011 92 284
BH2 boron dihydride 2 A1 1004 954 0.949 93 285
AlH2 aluminum dihydride 1 A1 1835 1770 0.964 94 286
    2 A1 760 760 1.000 94 287
    3 B2 1875 1807 0.964 94 288
HBS hydrogen boron sulfide 1 Σ 2809 2736 0.974 95 289
    2 Σ 1208 1172 0.971 95 290
MgF Magnesium monofluoride 1 Σ 725 712 0.981 96 291
MgCl magnesium monochloride 1 Σ 464 462 0.997 97 292
ClO Monochlorine monoxide 1 Σ 775 854 1.101 98 293
SCl sulfur monochloride 1 Σ 536 575 1.073 99 294
PF phosphorus monofluoride 1 Σ 825 847 1.027 100 295
SF Monosulfur monofluoride 1 Σ 791 838 1.058 101 296
PCl phosphorus chloride 1 Σ 521 577 1.108 102 297
PN Phosphorus mononitride 1 Σ 1386 1337 0.965 103 298
BCl boron monochloride 1 Σ 865 840 0.971 104 299
HBO Boron hydride oxide 1 Σ 2878 2850 0.990 105 300
    2 Σ 1876 1826 0.973 105 301
    3 Π 782 756 0.967 105 302
BeOH beryllium hydroxide 2 A' 1296 1246 0.961 106 303
S2 Sulfur diatomic 1 Σg 705 726 1.029 107 304
Na2 Sodium diatomic 1 Σg 153 159 1.038 108 305

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.

180
160
140
120
100
80
60
40
20
0
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