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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/6-311G*
Scale factor How many Source
Molecules Vibrations
0.963 ± 0.111 111 322 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2908 2782 0.957 1 1
    2 A1 1780 1746 0.981 1 2
    3 A1 1550 1500 0.968 1 3
    4 B1 1175 1167 0.993 1 4
    5 B2 2972 2843 0.957 1 5
    6 B2 1278 1249 0.977 1 6
CH3OH Methyl alcohol 1 A' 3819 3681 0.964 2 7
    2 A' 3124 3000 0.960 2 8
    3 A' 2985 2844 0.953 2 9
    4 A' 1535 1477 0.962 2 10
    5 A' 1510 1455 0.964 2 11
    6 A' 1419 1345 0.948 2 12
    7 A' 1095 1060 0.968 2 13
    8 A' 1080 1033 0.957 2 14
    9 A" 3038 2960 0.974 2 15
    10 A" 1520 1477 0.972 2 16
    11 A" 1184 1165 0.984 2 17
    12 A" 364 200 0.550 2 18
CH4 Methane 1 A1 3019 2917 0.966 3 19
    2 E 1580 1534 0.971 3 20
    3 T2 3139 3019 0.962 3 21
    4 T2 1372 1306 0.952 3 22
C2H6 Ethane 1 A1g 3024 2896 0.958 4 23
    2 A1g 1452 1388 0.956 4 24
    3 A1g 1019 995 0.976 4 25
    4 A1u 316 289 0.915 4 26
    5 A2u 3021 2915 0.965 4 27
    6 A2u 1430 1370 0.958 4 28
    7 Eg 3082 2969 0.963 4 29
    8 Eg 1525 1468 0.963 4 30
    9 Eg 1237 1190 0.962 4 31
    10 Eu 3104 2974 0.958 4 32
    11 Eu 1529 1460 0.955 4 33
    12 Eu 825 822 0.996 4 34
C2H4 Ethylene 1 Ag 3136 3026 0.965 5 35
    2 Ag 1668 1623 0.973 5 36
    3 Ag 1366 1342 0.983 5 37
    4 Au 1035 1023 0.988 5 38
    5 B1u 3119 2989 0.958 5 39
    6 B1u 1478 1444 0.976 5 40
    7 B2g 887 940 1.060 5 41
    8 B2u 3225 3105 0.963 5 42
    9 B2u 832 826 0.993 5 43
    10 B3g 3199 3086 0.965 5 44
    11 B3g 1241 1217 0.981 5 45
    12 B3u 944 949 1.006 5 46
C2H2 Acetylene 1 Σg 3488 3374 0.967 6 47
    2 Σg 1978 1974 0.998 6 48
    3 Σu 3394 3289 0.969 6 49
    4 Πg 338 612 1.808 6 50
    5 Πu 722 730 1.010 6 51
CH3Cl Methyl chloride 1 A1 3067 2966 0.967 7 52
    2 A1 1432 1355 0.946 7 53
    3 A1 746 732 0.981 7 54
    4 E 3168 3042 0.960 7 55
    5 E 1501 1455 0.969 7 56
    6 E 1059 1015 0.958 7 57
CH3NH2 methyl amine 1 A' 3491 3361 0.963 8 58
    2 A' 3066 2961 0.966 8 59
    3 A' 2971 2820 0.949 8 60
    4 A' 1741 1623 0.932 8 61
    5 A' 1520 1473 0.969 8 62
    6 A' 1482 1430 0.965 8 63
    7 A' 1207 1130 0.937 8 64
    8 A' 1072 1044 0.974 8 65
    9 A' 919 780 0.849 8 66
    10 A" 3574 3427 0.959 8 67
    11 A" 3105 2985 0.961 8 68
    12 A" 1539 1485 0.965 8 69
    13 A" 1385 1335 0.964 8 70
    14 A" 986 1195 1.211 8 71
    15 A" 333 268 0.805 8 72
HCN Hydrogen cyanide 1 Σ 3426 3312 0.967 9 73
    2 Σ 2097 2089 0.996 9 74
    3 Π 720 712 0.989 9 75
CH3SH Methanethiol 1 A' 3136 3000 0.957 10 76
    2 A' 3045 2931 0.962 10 77
    3 A' 2590 2597 1.003 10 78
    4 A' 1508 1475 0.978 10 79
    5 A' 1413 1335 0.945 10 80
    6 A' 1122 1074 0.957 10 81
    7 A' 810 803 0.991 10 82
    8 A' 726 708 0.975 10 83
    9 A" 3133 3000 0.957 10 84
    10 A" 1497 1430 0.955 10 85
    11 A" 1007 976 0.969 10 86
N2H4 Hydrazine 1 A 3575 3398 0.951 11 87
    2 A 3468 3329 0.960 11 88
    3 A 1764 1642 0.931 11 89
    4 A 1388 1275 0.918 11 90
    5 A 1158 1076 0.929 11 91
    6 A 905 780 0.862 11 92
    7 A 438 377 0.859 11 93
    8 B 3581 3350 0.936 11 94
    9 B 3454 3314 0.959 11 95
    10 B 1747 1628 0.932 11 96
    11 B 1342 1275 0.950 11 97
    12 B 1090 966 0.886 11 98
CH3F Methyl fluoride 1 A1 3031 2930 0.967 12 99
    2 A1 1524 1464 0.961 12 100
    3 A1 1084 1049 0.968 12 101
    4 E 3120 3006 0.963 12 102
    5 E 1521 1467 0.965 12 103
    6 E 1213 1182 0.975 12 104
CH3PH2 Methyl phosphine 1 A' 3123 3000 0.961 13 105
    2 A' 3034 2938 0.968 13 106
    3 A' 2321 2297 0.990 13 107
    4 A' 1498 1450 0.968 13 108
    5 A' 1381 1238 0.896 13 109
    6 A' 1129 1086 0.962 13 110
    7 A' 1021 977 0.957 13 111
    8 A' 752 740 0.984 13 112
    9 A' 693 677 0.977 13 113
    10 A" 3113 2992 0.961 13 114
    11 A" 2327 2312 0.993 13 115
    12 A" 1502 1450 0.965 13 116
    13 A" 1054 1017 0.965 13 117
    15 A" 228 207 0.906 13 118
CO Carbon monoxide 1 Σ 2151 2170 1.009 14 119
    1 Σ 2151 1743 0.810 14 120
H2CS Thioformaldehyde 1 A1 3068 2971 0.968 15 121
    2 A1 1525 1456 0.955 15 122
    3 A1 1065 1059 0.994 15 123
    4 B1 1005 990 0.986 15 124
    5 B2 3159 3025 0.958 15 125
    6 B2 1032 991 0.960 15 126
CH3SiH3 methyl silane 1 A1 3021 2898 0.959 16 127
    2 A1 2201 2166 0.984 16 128
    3 A1 1345 1260 0.937 16 129
    4 A1 946 940 0.993 16 130
    5 A1 708 700 0.989 16 131
    6 A2 182 187 1.030 16 132
    7 E 3101 2982 0.962 16 133
    8 E 2201 2169 0.986 16 134
    9 E 1492 1403 0.940 16 135
    10 E 957 980 1.024 16 136
    11 E 909 868 0.955 16 137
    12 E 524 540 1.030 16 138
BeO beryllium oxide 1 Σ 1491 1457 0.977 17 139
MgO magnesium oxide 1 Σ 714 785 1.100 18 140
NaOH sodium hydroxide 1 Σ 3901 3637 0.932 19 141
    2 Σ 604 540 0.894 19 142
    3 Π 235 300 1.275 19 143
H2 Hydrogen diatomic 1 Σg 4268 4401 1.031 20 144
Si2H6 disilane 1 A1g 2194 2152 0.981 21 145
    2 A1g 934 909 0.973 21 146
    3 A1g 441 434 0.984 21 147
    4 A1u 145 131 0.901 21 148
    5 A2u 2185 2154 0.986 21 149
    6 A2u 859 844 0.982 21 150
    7 Eg 2194 2155 0.982 21 151
    8 Eg 935 929 0.994 21 152
    9 Eg 647 625 0.966 21 153
    10 Eu 2202 2179 0.989 21 154
    11 Eu 950 940 0.989 21 155
    12 Eu 389 379 0.974 21 156
CH2NH Methanimine 1 A' 3419 3263 0.954 22 157
    2 A' 3141 3024 0.963 22 158
    3 A' 3029 2914 0.962 22 159
    4 A' 1675 1638 0.978 22 160
    5 A' 1489 1452 0.975 22 161
    6 A' 1414 1344 0.951 22 162
    7 A' 1092 1058 0.969 22 163
    8 A" 1170 1127 0.963 22 164
    9 A" 1065 1061 0.996 22 165
CN Cyano radical 1 Σ 2100 2069 0.985 23 166
HCO Formyl radical 1 A' 2624 2434 0.928 24 167
    2 A' 1880 1868 0.994 24 168
    3 A' 1133 1081 0.954 24 169
CS carbon monosulfide 1 Σ 1263 1285 1.018 25 170
HO2 Hydroperoxy radical 1 A' 3628 3436 0.947 26 171
    2 A' 1491 1392 0.933 26 172
    3 A' 1130 1098 0.971 26 173
CH Methylidyne 1 Σ 2802 2861 1.021 27 174
    1 Σ 2802 3145 1.122 27 175
    1 Σ 2802 2931 1.046 27 176
OH Hydroxyl radical 1 Σ 3678 3738 1.016 28 177
CF Fluoromethylidyne 1 Σ 1302 1308 1.004 29 178
CCl carbon monochloride 1 Σ 857 877 1.024 30 179
HCP HCP 1 Σ 3325 3217 0.968 31 180
    2 Σ 1286 1278 0.994 31 181
    3 Π 650 674 1.037 31 182
LiCl lithium chloride 1 Σ 653 643 0.985 32 183
LiH Lithium Hydride 1 Σ 1369 1405 1.027 33 184
NaH sodium hydride 1 Σ 1116 1172 1.050 34 185
HCl Hydrogen chloride 1 Σ 2858 2991 1.046 35 186
NaCl Sodium Chloride 1 Σ 363 365 1.003 36 187
HF Hydrogen fluoride 1 Σ 4060 4138 1.019 37 188
NH3 Ammonia 1 A1 3472 3337 0.961 38 189
    2 A1 1184 950 0.802 38 190
    3 E 3607 3444 0.955 38 191
    4 E 1762 1627 0.923 38 192
NaF sodium fluoride 1 Σ 574 536 0.933 39 193
MgH2 magnesium dihydride 2 Σu 1595 1572 0.986 40 194
    3 Πu 448 440 0.981 40 195
H2O2 Hydrogen peroxide 1 A 3779 3599 0.952 41 196
    2 A 1507 1402 0.930 41 197
    3 A 898 877 0.977 41 198
    4 A 317 371 1.169 41 199
    5 B 3782 3608 0.954 41 200
    6 B 1336 1266 0.948 41 201
N2 Nitrogen diatomic 1 Σg 2334 2359 1.011 42 202
H2O Water 1 A1 3807 3657 0.961 43 203
    2 A1 1746 1595 0.914 43 204
    3 B2 3930 3756 0.956 43 205
F2 Fluorine diatomic 1 Σg 777 917 1.180 44 206
Cl2 Chlorine diatomic 1 Σg 502 560 1.115 45 207
H2S Hydrogen sulfide 1 A1 2596 2615 1.007 46 208
    2 A1 1247 1183 0.949 46 209
    3 B2 2617 2626 1.003 46 210
AlH3 aluminum trihydride 1 A1' 1922 1900 0.989 47 211
    2 A2" 708 698 0.985 47 212
    3 E' 1935 1883 0.973 47 213
    4 E' 783 783 1.001 47 214
BeH2 beryllium dihydride 2 Σu 2219 2159 0.973 48 215
    3 Πu 714 698 0.978 48 216
LiF lithium fluoride 1 Σ 959 911 0.949 49 217
ClF Chlorine monofluoride 1 Σ 687 783 1.141 50 218
HOCl hypochlorous acid 1 A' 3762 3609 0.959 51 219
    2 A' 1308 1239 0.947 51 220
    3 A' 664 724 1.090 51 221
PH3 Phosphine 1 A1 2338 2323 0.993 52 222
    2 A1 1051 992 0.944 52 223
    3 E 2348 2328 0.991 52 224
    4 E 1153 1118 0.970 52 225
SiH4 Silane 1 A1 2215 2187 0.987 53 226
    2 E 968 975 1.007 53 227
    3 T2 2221 2191 0.986 53 228
    4 T2 919 914 0.994 53 229
SiO Silicon monoxide 1 Σ 1211 1242 1.025 54 230
SiF silicon monofluoride 1 Σ 849 857 1.009 55 231
MgS magnesium sulfide 1 Σ 515 529 1.026 56 232
SiN Silicon nitride 1 Σ 1188 1151 0.969 57 233
C2 Carbon diatomic 1 Σg 1814 1855 1.023 58 234
LiO lithium oxide 1 Σ 905 815 0.900 59 235
P2 Phosphorus diatomic 1 Σg 764 781 1.023 60 236
BS boron sulfide 1 Σ 1161 1180 1.016 61 237
AlS Aluminum sulfide 1 Σ 615 617 1.003 62 238
CP Carbon monophosphide 1 Σ 1272 1240 0.975 63 239
NaO sodium monoxide 1 Σ 558 492 0.883 64 240
SiS silicon monosulfide 1 Σ 726 750 1.032 65 241
BO boron monoxide 1 Σ 1857 1885 1.015 66 242
Si2 Silicon diatomic 1 Σg 490 511 1.042 67 243
BH3 boron trihydride 2 A2" 1143 1148 1.004 68 244
    3 E' 2657 2602 0.979 68 245
    4 E' 1188 1197 1.007 68 246
HCF Fluoromethylene 1 A' 2769 2643 0.955 69 247
    1 A' 3128 2643 0.845 69 248
    2 A' 1466 1403 0.957 69 249
    2 A' 1270 1403 1.105 69 250
    3 A' 1217 1189 0.977 69 251
    3 A' 1130 1189 1.052 69 252
H2S2 HSSH 1 A 2561 2556 0.998 70 253
    2 A 912 882 0.968 70 254
    3 A 487 515 1.057 70 255
    4 A 429 417 0.973 70 256
    5 B 2562 2559 0.999 70 257
    6 B 909 878 0.966 70 258
SiH3Cl chlorosilane 1 A1 2242 2201 0.982 71 259
    2 A1 967 949 0.982 71 260
    3 A1 546 551 1.009 71 261
    4 E 2254 2195 0.974 71 262
    5 E 955 954 0.999 71 263
    6 E 679 664 0.978 71 264
SiH3F monofluorosilane 1 A1 2245 2206 0.983 72 265
    2 A1 1028 990 0.963 72 266
    3 A1 872 872 1.000 72 267
    4 E 2250 2196 0.976 72 268
    5 E 961 956 0.994 72 269
    6 E 747 728 0.975 72 270
AlF Aluminum monofluoride 1 Σ 814 802 0.985 73 271
BeF Beryllium monofluoride 1 Σ 1232 1247 1.013 74 272
BeH beryllium monohydride 1 Σ 1990 2061 1.036 75 273
BeS beryllium sulfide 1 Σ 970 998 1.029 76 274
PH2 Phosphino radical 1 A1 2303 2310 1.003 77 275
    2 A1 1145 1102 0.962 77 276
SiH3 silyl 1 A1 2183 2136 0.979 78 277
    2 A1 764 728 0.953 78 278
    3 E 2216 2185 0.986 78 279
    4 E 932 922 0.990 78 280
BH Boron monohydride 1 Σ 2303 2367 1.028 79 281
NH2 Amino radical 1 A1 3336 3219 0.965 80 282
    2 A1 1614 1497 0.928 80 283
    3 B2 3437 3301 0.961 80 284
NH Imidogen 1 Σ 3221 3283 1.019 81 285
    1 Σ 3221 3314 1.029 81 286
BeCl beryllium chloride 1 Σ 856 847 0.990 82 287
HPO HPO 1 A' 2058 2095 1.018 83 288
    2 A' 1161 1188 1.023 83 289
    3 A' 1019 986 0.967 83 290
SiH2 silicon dihydride 1 A1 2006 1996 0.995 84 291
    1 A1 2153 1996 0.927 84 292
    2 A1 1020 999 0.979 84 293
    2 A1 881 999 1.133 84 294
    3 B2 2004 1993 0.994 84 295
    3 B2 2213 1993 0.901 84 296
SO Sulfur monoxide 1 Σ 1095 1151 1.051 85 297
SH Mercapto radical 1 Σ 2559 2696 1.054 86 298
SiCl Clorosilylidyne 1 Σ 517 536 1.035 87 299
NF nitrogen fluoride 1 Σ 1137 1141 1.004 88 300
PH phosphorus monohydride 1 Σ 2259 2364 1.047 89 301
    1 Σ 2259 2415 1.069 89 302
    1 Σ 2259 2403 1.064 89 303
AlH aluminum monohydride 1 Σ 1659 1682 1.014 90 304
HOF Hypofluorous acid 1 A' 3739 3537 0.946 91 305
    2 A' 1423 1393 0.979 91 306
    3 A' 860 886 1.030 91 307
HNO Nitrosyl hydride 1 A' 2896 2684 0.927 92 308
    2 A' 1611 1565 0.972 92 309
    3 A' 1574 1501 0.954 92 310
MgH magnesium monohydride 1 Σ 1420 1493 1.051 93 311
Li2 Lithium diatomic 1 Σg 348 351 1.011 94 312
BH2 boron dihydride 2 A1 1002 954 0.952 95 313
AlH2 aluminum dihydride 1 A1 1826 1770 0.969 96 314
    2 A1 757 760 1.004 96 315
    3 B2 1866 1807 0.968 96 316
HBS hydrogen boron sulfide 1 Σ 2791 2736 0.980 97 317
    2 Σ 1172 1172 1.000 97 318
MgF Magnesium monofluoride 1 Σ 720 712 0.989 98 319
MgCl magnesium monochloride 1 Σ 462 462 1.001 99 320
ClO Monochlorine monoxide 1 Σ 745 854 1.146 100 321
SCl sulfur monochloride 1 Σ 521 575 1.103 101 322
PF phosphorus monofluoride 1 Σ 809 847 1.047 102 323
SF Monosulfur monofluoride 1 Σ 766 838 1.094 103 324
PCl phosphorus chloride 1 Σ 511 577 1.129 104 325
PN Phosphorus mononitride 1 Σ 1324 1337 1.010 105 326
BCl boron monochloride 1 Σ 856 840 0.982 106 327
HBO Boron hydride oxide 1 Σ 2860 2850 0.996 107 328
    2 Σ 1820 1826 1.003 107 329
    3 Π 765 756 0.989 107 330
BeOH beryllium hydroxide 2 A' 1285 1246 0.969 108 331
S2 Sulfur diatomic 1 Σg 677 726 1.071 109 332
Na2 Sodium diatomic 1 Σg 153 159 1.039 110 333

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.

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