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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at HF/cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.908 ± 0.034 116 356 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 3086 2782 0.902 1 1
    2 A1 1996 1746 0.875 1 2
    3 A1 1652 1500 0.908 1 3
    4 B1 1338 1167 0.872 1 4
    5 B2 3155 2843 0.901 1 5
    6 B2 1372 1249 0.910 1 6
CH3OH Methyl alcohol 1 A' 4178 3681 0.881 2 7
    2 A' 3246 3000 0.924 2 8
    3 A' 3140 2844 0.906 2 9
    4 A' 1631 1477 0.906 2 10
    5 A' 1610 1455 0.904 2 11
    6 A' 1481 1345 0.908 2 12
    7 A' 1172 1060 0.904 2 13
    8 A' 1154 1033 0.895 2 14
    9 A" 3183 2960 0.930 2 15
    10 A" 1621 1477 0.911 2 16
    11 A" 1281 1165 0.909 2 17
    12 A" 310 200 0.645 2 18
CH4 Methane 1 A1 3144 2917 0.928 3 19
    2 E 1667 1534 0.920 3 20
    3 T2 3241 3019 0.932 3 21
    4 T2 1455 1306 0.897 3 22
C2H6 Ethane 1 A1g 3159 2896 0.917 4 23
    2 A1g 1548 1388 0.896 4 24
    3 A1g 1049 995 0.949 4 25
    4 A1u 327 289 0.883 4 26
    5 A2u 3152 2915 0.925 4 27
    6 A2u 1522 1370 0.900 4 28
    7 Eg 3195 2969 0.929 4 29
    8 Eg 1614 1468 0.909 4 30
    9 Eg 1324 1190 0.899 4 31
    10 Eu 3222 2974 0.923 4 32
    11 Eu 1619 1460 0.902 4 33
    12 Eu 881 822 0.934 4 34
C2H4 Ethylene 1 Ag 3290 3026 0.920 5 35
    2 Ag 1818 1623 0.893 5 36
    3 Ag 1475 1342 0.910 5 37
    4 Au 1141 1023 0.896 5 38
    5 B1u 3270 2989 0.914 5 39
    6 B1u 1591 1444 0.907 5 40
    7 B2g 1107 940 0.849 5 41
    8 B2u 3371 3105 0.921 5 42
    9 B2u 891 826 0.927 5 43
    10 B3g 3342 3086 0.923 5 44
    11 B3g 1344 1217 0.905 5 45
    12 B3u 1085 949 0.875 5 46
C2H2 Acetylene 1 Σg 3664 3374 0.921 6 47
    2 Σg 2212 1974 0.892 6 48
    3 Σu 3554 3289 0.925 6 49
    4 Πg 811 612 0.755 6 50
    5 Πu 867 730 0.842 6 51
CH3Cl Methyl chloride 1 A1 3217 2966 0.922 7 52
    2 A1 1502 1355 0.902 7 53
    3 A1 770 732 0.951 7 54
    4 E 3315 3042 0.918 7 55
    5 E 1603 1455 0.907 7 56
    6 E 1116 1015 0.910 7 57
CH3NH2 methyl amine 1 A' 3729 3361 0.901 8 58
    2 A' 3193 2961 0.927 8 59
    3 A' 3118 2820 0.904 8 60
    4 A' 1795 1623 0.904 8 61
    5 A' 1618 1473 0.911 8 62
    6 A' 1582 1430 0.904 8 63
    7 A' 1269 1130 0.890 8 64
    8 A' 1134 1044 0.920 8 65
    9 A' 903 780 0.863 8 66
    10 A" 3805 3427 0.901 8 67
    11 A" 3225 2985 0.926 8 68
    12 A" 1635 1485 0.908 8 69
    13 A" 1457 1335 0.917 8 70
    14 A" 1041 1195 1.148 8 71
    15 A" 316 268 0.847 8 72
HCN Hydrogen cyanide 1 Σ 3606 3312 0.918 9 73
    2 Σ 2408 2089 0.867 9 74
    3 Π 878 712 0.811 9 75
CH3SH Methanethiol 1 A' 3271 3000 0.917 10 76
    2 A' 3190 2931 0.919 10 77
    3 A' 2855 2597 0.910 10 78
    4 A' 1608 1475 0.918 10 79
    5 A' 1484 1335 0.900 10 80
    6 A' 1195 1074 0.899 10 81
    7 A' 854 803 0.940 10 82
    8 A' 763 708 0.928 10 83
    9 A" 3275 3000 0.916 10 84
    10 A" 1593 1430 0.898 10 85
    11 A" 1056 976 0.924 10 86
N2H4 Hydrazine 1 A 3807 3398 0.892 11 87
    2 A 3717 3329 0.896 11 88
    3 A 1830 1642 0.897 11 89
    4 A 1442 1275 0.884 11 90
    5 A 1211 1076 0.889 11 91
    6 A 935 780 0.835 11 92
    7 A 470 377 0.801 11 93
    8 B 3813 3350 0.878 11 94
    9 B 3709 3314 0.893 11 95
    10 B 1815 1628 0.897 11 96
    11 B 1409 1275 0.905 11 97
    12 B 1057 966 0.914 11 98
CH3F Methyl fluoride 1 A1 3183 2930 0.921 12 99
    2 A1 1617 1464 0.905 12 100
    3 A1 1165 1049 0.901 12 101
    4 E 3259 3006 0.922 12 102
    5 E 1619 1467 0.906 12 103
    6 E 1307 1182 0.904 12 104
CH3PH2 Methyl phosphine 1 A' 3253 3000 0.922 13 105
    2 A' 3170 2938 0.927 13 106
    3 A' 2519 2297 0.912 13 107
    4 A' 1586 1450 0.914 13 108
    5 A' 1450 1238 0.854 13 109
    6 A' 1213 1086 0.895 13 110
    7 A' 1080 977 0.905 13 111
    8 A' 787 740 0.940 13 112
    9 A' 729 677 0.929 13 113
    10 A" 3238 2992 0.924 13 114
    11 A" 2516 2312 0.919 13 115
    12 A" 1594 1450 0.910 13 116
    13 A" 1117 1017 0.911 13 117
    15 A" 247 207 0.838 13 118
CO Carbon monoxide 1 Σ 2427 2170 0.894 14 119
    1 Σ 2427 1743 0.718 14 120
H2CS Thioformaldehyde 1 A1 3240 2971 0.917 15 121
    2 A1 1622 1456 0.897 15 122
    3 A1 1173 1059 0.903 15 123
    4 B1 1156 990 0.856 15 124
    5 B2 3326 3025 0.909 15 125
    6 B2 1076 991 0.921 15 126
CH3SiH3 methyl silane 1 A1 3152 2898 0.919 16 127
    2 A1 2314 2166 0.936 16 128
    3 A1 1409 1260 0.894 16 129
    4 A1 1033 940 0.910 16 130
    5 A1 725 700 0.966 16 131
    6 A2 210 187 0.892 16 132
    7 E 3221 2982 0.926 16 133
    8 E 2296 2169 0.945 16 134
    9 E 1575 1403 0.891 16 135
    10 E 1037 980 0.945 16 136
    11 E 952 868 0.912 16 137
    12 E 558 540 0.967 16 138
BeO beryllium oxide 1 Σ 1730 1457 0.842 17 139
MgO magnesium oxide 1 Σ 817 785 0.961 18 140
LiOH lithium hydroxide 1 Σ 4323 3688 0.853 19 141
    2 Σ 980 871 0.888 19 142
    3 Π 359 257 0.715 19 143
NaOH sodium hydroxide 1 Σ 4271 3637 0.851 20 144
    2 Σ 573 540 0.943 20 145
    3 Π 295 300 1.018 20 146
H2 Hydrogen diatomic 1 Σg 4582 4401 0.961 21 147
Si2H6 disilane 1 A1g 2316 2152 0.929 22 148
    2 A1g 1023 909 0.888 22 149
    3 A1g 442 434 0.982 22 150
    4 A1u 137 131 0.957 22 151
    5 A2u 2302 2154 0.936 22 152
    6 A2u 941 844 0.896 22 153
    7 Eg 2297 2155 0.938 22 154
    8 Eg 1020 929 0.911 22 155
    9 Eg 690 625 0.906 22 156
    10 Eu 2307 2179 0.944 22 157
    11 Eu 1035 940 0.908 22 158
    12 Eu 403 379 0.940 22 159
CH2NH Methanimine 1 A' 3702 3263 0.881 23 160
    2 A' 3281 3024 0.922 23 161
    3 A' 3192 2914 0.913 23 162
    4 A' 1865 1638 0.878 23 163
    5 A' 1604 1452 0.905 23 164
    6 A' 1481 1344 0.908 23 165
    7 A' 1153 1058 0.918 23 166
    8 A" 1256 1127 0.898 23 167
    9 A" 1229 1061 0.863 23 168
CN Cyano radical 1 Σ 2026 2069 1.021 24 169
HCO Formyl radical 1 A' 2853 2434 0.853 25 170
    2 A' 2121 1868 0.881 25 171
    3 A' 1225 1081 0.882 25 172
CS carbon monosulfide 1 Σ 1422 1285 0.904 26 173
HO2 Hydroperoxy radical 1 A' 4060 3436 0.846 27 174
    2 A' 1608 1392 0.866 27 175
    3 A' 1264 1098 0.868 27 176
CH Methylidyne 1 Σ 3034 2861 0.943 28 177
    1 Σ 3349 2861 0.854 28 178
    1 Σ 3034 3145 1.037 28 179
    1 Σ 3349 3145 0.939 28 180
    1 Σ 3034 2931 0.966 28 181
    1 Σ 3349 2931 0.875 28 182
OH Hydroxyl radical 1 Σ 4042 3738 0.925 29 183
CF Fluoromethylidyne 1 Σ 1411 1308 0.927 30 184
CCl carbon monochloride 1 Σ 871 877 1.006 31 185
HCP HCP 1 Σ 3514 3217 0.916 32 186
    2 Σ 1467 1278 0.871 32 187
    3 Π 827 674 0.815 32 188
HNC hydrogen isocyanide 1 Σ 4047 3653 0.903 33 189
    2 Σ 2286 2029 0.888 33 190
    3 Π 543 477 0.879 33 191
LiCl lithium chloride 1 Σ 642 643 1.001 34 192
LiH Lithium Hydride 1 Σ 1429 1405 0.983 35 193
NaH sodium hydride 1 Σ 1164 1172 1.007 36 194
HCl Hydrogen chloride 1 Σ 3140 2991 0.952 37 195
NaCl Sodium Chloride 1 Σ 356 365 1.025 38 196
HF Hydrogen fluoride 1 Σ 4477 4138 0.924 39 197
NH3 Ammonia 1 A1 3689 3337 0.905 40 198
    2 A1 1112 950 0.854 40 199
    3 E 3811 3444 0.904 40 200
    4 E 1790 1627 0.909 40 201
NaF sodium fluoride 1 Σ 539 536 0.994 41 202
MgH2 magnesium dihydride 2 Σu 1669 1572 0.942 42 203
    3 Πu 459 440 0.959 42 204
H2O2 Hydrogen peroxide 1 A 4138 3599 0.870 43 205
    2 A 1610 1402 0.871 43 206
    3 A 1164 877 0.754 43 207
    4 A 415 371 0.894 43 208
    5 B 4137 3608 0.872 43 209
    6 B 1493 1266 0.848 43 210
N2 Nitrogen diatomic 1 Σg 2730 2359 0.864 44 211
H2O Water 1 A1 4129 3657 0.886 45 212
    2 A1 1751 1595 0.911 45 213
    3 B2 4229 3756 0.888 45 214
F2 Fluorine diatomic 1 Σg 1264 917 0.726 46 215
Cl2 Chlorine diatomic 1 Σg 614 560 0.911 47 216
H2S Hydrogen sulfide 1 A1 2859 2615 0.915 48 217
    2 A1 1318 1183 0.898 48 218
    3 B2 2868 2626 0.916 48 219
AlH3 aluminum trihydride 1 A1' 2012 1900 0.944 49 220
    2 A2" 757 698 0.922 49 221
    3 E' 2000 1883 0.941 49 222
    4 E' 847 783 0.925 49 223
BeH2 beryllium dihydride 2 Σu 2288 2159 0.944 50 224
    3 Πu 744 698 0.938 50 225
LiF lithium fluoride 1 Σ 945 911 0.963 51 226
ClF Chlorine monofluoride 1 Σ 918 783 0.853 52 227
HOCl hypochlorous acid 1 A' 4131 3609 0.874 53 228
    2 A' 1389 1239 0.892 53 229
    3 A' 870 724 0.833 53 230
NH2OH hydroxylamine 1 A' 4177 3650 0.874 54 231
    2 A' 3708 3294 0.888 54 232
    3 A' 1820 1605 0.882 54 233
    4 A' 1524 1353 0.888 54 234
    5 A' 1238 1115 0.901 54 235
    6 A' 1114 895 0.804 54 236
    7 A" 3788 3359 0.887 54 237
    8 A" 1463 1295 0.885 54 238
    9 A" 446 386 0.865 54 239
PH3 Phosphine 1 A1 2536 2323 0.916 55 240
    2 A1 1101 992 0.901 55 241
    3 E 2533 2328 0.919 55 242
    4 E 1235 1118 0.906 55 243
SiH4 Silane 1 A1 2337 2187 0.936 56 244
    2 E 1043 975 0.934 56 245
    3 T2 2323 2191 0.943 56 246
    4 T2 1009 914 0.905 56 247
SiO Silicon monoxide 1 Σ 1408 1242 0.882 57 248
SiF silicon monofluoride 1 Σ 907 857 0.945 58 249
MgS magnesium sulfide 1 Σ 550 529 0.962 59 250
SiN Silicon nitride 1 Σ 970 1151 1.187 60 251
C2 Carbon diatomic 1 Σg 1904 1855 0.974 61 252
    1 Σg 1793 1855 1.035 61 253
LiO lithium oxide 1 Σ 855 815 0.953 62 254
P2 Phosphorus diatomic 1 Σg 912 781 0.856 63 255
BS boron sulfide 1 Σ 1254 1180 0.941 64 256
AlS Aluminum sulfide 1 Σ 616 617 1.002 65 257
CP Carbon monophosphide 1 Σ 1021 1240 1.214 66 258
NaO sodium monoxide 1 Σ 526 492 0.936 67 259
SiS silicon monosulfide 1 Σ 816 750 0.919 68 260
BO boron monoxide 1 Σ 2082 1885 0.905 69 261
Si2 Silicon diatomic 1 Σg 574 511 0.890 70 262
    1 Σg 620 511 0.824 70 263
BH3 boron trihydride 2 A2" 1222 1148 0.939 71 264
    3 E' 2750 2602 0.946 71 265
    4 E' 1293 1197 0.925 71 266
HCF Fluoromethylene 1 A' 3010 2643 0.878 72 267
    1 A' 3327 2643 0.794 72 268
    2 A' 1542 1403 0.910 72 269
    2 A' 1351 1403 1.039 72 270
    3 A' 1324 1189 0.898 72 271
    3 A' 1228 1189 0.968 72 272
H2S2 HSSH 1 A 2836 2556 0.901 73 273
    2 A 984 882 0.897 73 274
    3 A 562 515 0.915 73 275
    4 A 454 417 0.919 73 276
    5 B 2837 2559 0.902 73 277
    6 B 988 878 0.889 73 278
SiH3Cl chlorosilane 1 A1 2362 2201 0.932 74 279
    2 A1 1033 949 0.919 74 280
    3 A1 559 551 0.985 74 281
    4 E 2359 2195 0.930 74 282
    5 E 1036 954 0.921 74 283
    6 E 713 664 0.932 74 284
SiH3F monofluorosilane 1 A1 2360 2206 0.935 75 285
    2 A1 1072 990 0.923 75 286
    3 A1 936 872 0.931 75 287
    4 E 2348 2196 0.935 75 288
    5 E 1044 956 0.916 75 289
    6 E 784 728 0.928 75 290
AlCl Aluminum monochloride 1 Σ 475 482 1.014 76 291
AlF Aluminum monofluoride 1 Σ 842 802 0.953 77 292
BeF Beryllium monofluoride 1 Σ 1315 1247 0.949 78 293
BeH beryllium monohydride 1 Σ 2122 2061 0.971 79 294
BeS beryllium sulfide 1 Σ 1067 998 0.935 80 295
PH2 Phosphino radical 1 A1 2512 2310 0.920 81 296
    2 A1 1220 1102 0.903 81 297
SiH3 silyl 1 A1 2306 2136 0.926 82 298
    2 A1 884 728 0.824 82 299
    3 E 2320 2185 0.942 82 300
    4 E 1010 922 0.913 82 301
BH Boron monohydride 1 Σ 2486 2367 0.952 83 302
NH2 Amino radical 1 A1 3602 3219 0.894 84 303
    2 A1 1641 1497 0.913 84 304
    3 B2 3688 3301 0.895 84 305
NH Imidogen 1 Σ 3512 3283 0.935 85 306
    1 Σ 3593 3283 0.914 85 307
    1 Σ 3512 3314 0.944 85 308
    1 Σ 3593 3314 0.922 85 309
SiH Silylidyne 1 Σ 2127 2043 0.960 86 310
BeCl beryllium chloride 1 Σ 846 847 1.000 87 311
HPO HPO 1 A' 2303 2095 0.910 88 312
    2 A' 1391 1188 0.854 88 313
    3 A' 1100 986 0.896 88 314
SiH2 silicon dihydride 1 A1 2157 1996 0.925 89 315
    1 A1 2311 1996 0.864 89 316
    2 A1 1104 999 0.905 89 317
    2 A1 960 999 1.041 89 318
    3 B2 2145 1993 0.929 89 319
    3 B2 2352 1993 0.847 89 320
SO Sulfur monoxide 1 Σ 1341 1151 0.858 90 321
    1 Σ 1355 1151 0.850 90 322
SH Mercapto radical 1 Σ 2840 2696 0.949 91 323
SiCl Clorosilylidyne 1 Σ 528 536 1.015 92 324
NF nitrogen fluoride 1 Σ 1265 1141 0.902 93 325
    1 Σ 1337 1141 0.854 93 326
PH phosphorus monohydride 1 Σ 2496 2364 0.947 94 327
    1 Σ 2511 2364 0.941 94 328
    1 Σ 2496 2415 0.968 94 329
    1 Σ 2511 2415 0.962 94 330
    1 Σ 2496 2403 0.963 94 331
    1 Σ 2511 2403 0.957 94 332
AlH aluminum monohydride 1 Σ 1733 1682 0.971 95 333
HOF Hypofluorous acid 1 A' 4106 3537 0.861 96 334
    2 A' 1597 1393 0.872 96 335
    3 A' 1180 886 0.751 96 336
HNO Nitrosyl hydride 1 A' 3303 2684 0.813 97 337
    2 A' 1940 1565 0.807 97 338
    3 A' 1712 1501 0.877 97 339
MgH magnesium monohydride 1 Σ 1545 1493 0.966 98 340
Li2 Lithium diatomic 1 Σg 338 351 1.041 99 341
BH2 boron dihydride 2 A1 1103 954 0.865 100 342
AlH2 aluminum dihydride 1 A1 1933 1770 0.916 101 343
    2 A1 823 760 0.923 101 344
    3 B2 1949 1807 0.927 101 345
HBS hydrogen boron sulfide 1 Σ 2933 2736 0.933 102 346
    2 Σ 1238 1172 0.947 102 347
MgF Magnesium monofluoride 1 Σ 751 712 0.947 103 348
MgCl magnesium monochloride 1 Σ 467 462 0.990 104 349
ClO Monochlorine monoxide 1 Σ 846 854 1.009 105 350
SCl sulfur monochloride 1 Σ 594 575 0.968 106 351
PF phosphorus monofluoride 1 Σ 909 847 0.932 107 352
    1 Σ 925 847 0.915 107 353
SF Monosulfur monofluoride 1 Σ 922 838 0.909 108 354
PCl phosphorus chloride 1 Σ 554 577 1.041 109 355
    1 Σ 577 577 1.000 109 356
PN Phosphorus mononitride 1 Σ 1592 1337 0.840 110 357
B2H6 Diborane 1 Ag 2697 2524 0.936 111 358
    2 Ag 2237 2104 0.941 111 359
    3 Ag 1297 1180 0.910 111 360
    4 Ag 819 794 0.970 111 361
    5 Au 890 833 0.936 111 362
    6 B1g 2763 2591 0.938 111 363
    7 B1g 993 915 0.921 111 364
    8 B1u 2012 1915 0.952 111 365
    9 B1u 1062 973 0.916 111 366
    10 B2g 1897 1768 0.932 111 367
    11 B2g 900 850 0.944 111 368
    12 B2u 2779 2612 0.940 111 369
    13 B2u 1094 950 0.868 111 370
    14 B2u 412 368 0.893 111 371
    15 B3g 1160 1012 0.872 111 372
    16 B3u 2678 2525 0.943 111 373
    17 B3u 1783 1602 0.898 111 374
    18 B3u 1278 1177 0.921 111 375
BCl boron monochloride 1 Σ 852 840 0.986 112 376
HBO Boron hydride oxide 1 Σ 2989 2850 0.954 113 377
    2 Σ 2001 1826 0.912 113 378
    3 Π 861 756 0.878 113 379
BeOH beryllium hydroxide 2 A' 1326 1246 0.939 114 380
S2 Sulfur diatomic 1 Σg 818 726 0.887 115 381
    1 Σg 816 726 0.889 115 382
Na2 Sodium diatomic 1 Σg 156 159 1.021 116 383

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.

200
150
100
50
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