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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/aug-cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.909 ± 0.034 116 356 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 3087 2782 0.901 1 1
    2 A1 1993 1746 0.876 1 2
    3 A1 1650 1500 0.909 1 3
    4 B1 1337 1167 0.873 1 4
    5 B2 3156 2843 0.901 1 5
    6 B2 1370 1249 0.911 1 6
CH3OH Methyl alcohol 1 A' 4179 3681 0.881 2 7
    2 A' 3248 3000 0.924 2 8
    3 A' 3142 2844 0.905 2 9
    4 A' 1630 1477 0.906 2 10
    5 A' 1609 1455 0.905 2 11
    6 A' 1479 1345 0.909 2 12
    7 A' 1169 1060 0.907 2 13
    8 A' 1153 1033 0.896 2 14
    9 A" 3185 2960 0.929 2 15
    10 A" 1621 1477 0.911 2 16
    11 A" 1281 1165 0.910 2 17
    12 A" 307 200 0.652 2 18
CH4 Methane 1 A1 3143 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 0.898 3 22
C2H6 Ethane 1 A1g 3158 2896 0.917 4 23
    2 A1g 1548 1388 0.897 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 1323 1190 0.899 4 31
    10 Eu 3222 2974 0.923 4 32
    11 Eu 1619 1460 0.902 4 33
    12 Eu 880 822 0.934 4 34
C2H4 Ethylene 1 Ag 3291 3026 0.920 5 35
    2 Ag 1816 1623 0.894 5 36
    3 Ag 1474 1342 0.910 5 37
    4 Au 1140 1023 0.898 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 892 826 0.926 5 43
    10 B3g 3343 3086 0.923 5 44
    11 B3g 1345 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 2211 1974 0.893 6 48
    3 Σu 3554 3289 0.925 6 49
    4 Πg 812 612 0.754 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 0.908 7 56
    6 E 1116 1015 0.910 7 57
CH3NH2 methyl amine 1 A' 3731 3361 0.901 8 58
    2 A' 3194 2961 0.927 8 59
    3 A' 3119 2820 0.904 8 60
    4 A' 1794 1623 0.905 8 61
    5 A' 1617 1473 0.911 8 62
    6 A' 1582 1430 0.904 8 63
    7 A' 1267 1130 0.892 8 64
    8 A' 1134 1044 0.921 8 65
    9 A' 896 780 0.870 8 66
    10 A" 3807 3427 0.900 8 67
    11 A" 3226 2985 0.925 8 68
    12 A" 1634 1485 0.909 8 69
    13 A" 1455 1335 0.917 8 70
    14 A" 1039 1195 1.150 8 71
    15 A" 314 268 0.854 8 72
HCN Hydrogen cyanide 1 Σ 3607 3312 0.918 9 73
    2 Σ 2407 2089 0.868 9 74
    3 Π 876 712 0.812 9 75
CH3SH Methanethiol 1 A' 3271 3000 0.917 10 76
    2 A' 3190 2931 0.919 10 77
    3 A' 2854 2597 0.910 10 78
    4 A' 1607 1475 0.918 10 79
    5 A' 1484 1335 0.900 10 80
    6 A' 1194 1074 0.899 10 81
    7 A' 854 803 0.940 10 82
    8 A' 763 708 0.928 10 83
    9 A" 3274 3000 0.916 10 84
    10 A" 1592 1430 0.898 10 85
    11 A" 1056 976 0.924 10 86
N2H4 Hydrazine 1 A 3809 3398 0.892 11 87
    2 A 3718 3329 0.895 11 88
    3 A 1830 1642 0.897 11 89
    4 A 1439 1275 0.886 11 90
    5 A 1210 1076 0.890 11 91
    6 A 930 780 0.839 11 92
    7 A 468 377 0.804 11 93
    8 B 3814 3350 0.878 11 94
    9 B 3710 3314 0.893 11 95
    10 B 1814 1628 0.898 11 96
    11 B 1407 1275 0.906 11 97
    12 B 1050 966 0.920 11 98
CH3F Methyl fluoride 1 A1 3183 2930 0.921 12 99
    2 A1 1615 1464 0.906 12 100
    3 A1 1162 1049 0.903 12 101
    4 E 3260 3006 0.922 12 102
    5 E 1618 1467 0.906 12 103
    6 E 1306 1182 0.905 12 104
CH3PH2 Methyl phosphine 1 A' 3252 3000 0.922 13 105
    2 A' 3169 2938 0.927 13 106
    3 A' 2519 2297 0.912 13 107
    4 A' 1586 1450 0.914 13 108
    5 A' 1449 1238 0.854 13 109
    6 A' 1212 1086 0.896 13 110
    7 A' 1079 977 0.906 13 111
    8 A' 787 740 0.941 13 112
    9 A' 729 677 0.928 13 113
    10 A" 3237 2992 0.924 13 114
    11 A" 2515 2312 0.919 13 115
    12 A" 1594 1450 0.910 13 116
    13 A" 1116 1017 0.911 13 117
    15 A" 247 207 0.839 13 118
CO Carbon monoxide 1 Σ 2426 2170 0.894 14 119
    1 Σ 2426 1743 0.719 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 209 187 0.893 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 951 868 0.912 16 137
    12 E 558 540 0.968 16 138
BeO beryllium oxide 1 Σ 1724 1457 0.845 17 139
MgO magnesium oxide 1 Σ 818 785 0.960 18 140
LiOH lithium hydroxide 1 Σ 4321 3688 0.853 19 141
    2 Σ 971 871 0.896 19 142
    3 Π 357 257 0.718 19 143
NaOH sodium hydroxide 1 Σ 4270 3637 0.852 20 144
    2 Σ 566 540 0.955 20 145
    3 Π 308 300 0.973 20 146
H2 Hydrogen diatomic 1 Σg 4582 4401 0.961 21 147
Si2H6 disilane 1 A1g 2318 2152 0.928 22 148
    2 A1g 1022 909 0.889 22 149
    3 A1g 442 434 0.982 22 150
    4 A1u 131 131 0.997 22 151
    5 A2u 2304 2154 0.935 22 152
    6 A2u 940 844 0.897 22 153
    7 Eg 2299 2155 0.937 22 154
    8 Eg 1019 929 0.912 22 155
    9 Eg 689 625 0.907 22 156
    10 Eu 2309 2179 0.944 22 157
    11 Eu 1034 940 0.909 22 158
    12 Eu 402 379 0.944 22 159
CH2NH Methanimine 1 A' 3705 3263 0.881 23 160
    2 A' 3282 3024 0.921 23 161
    3 A' 3192 2914 0.913 23 162
    4 A' 1863 1638 0.879 23 163
    5 A' 1604 1452 0.905 23 164
    6 A' 1480 1344 0.908 23 165
    7 A' 1153 1058 0.918 23 166
    8 A" 1253 1127 0.900 23 167
    9 A" 1228 1061 0.864 23 168
CN Cyano radical 1 Σ 2025 2069 1.022 24 169
HCO Formyl radical 1 A' 2858 2434 0.852 25 170
    2 A' 2119 1868 0.882 25 171
    3 A' 1223 1081 0.884 25 172
CS carbon monosulfide 1 Σ 1422 1285 0.904 26 173
HO2 Hydroperoxy radical 1 A' 4058 3436 0.847 27 174
    2 A' 1606 1392 0.867 27 175
    3 A' 1266 1098 0.867 27 176
CH Methylidyne 1 Σ 3036 2861 0.942 28 177
    1 Σ 3349 2861 0.854 28 178
    1 Σ 3036 3145 1.036 28 179
    1 Σ 3349 3145 0.939 28 180
    1 Σ 3036 2931 0.965 28 181
    1 Σ 3349 2931 0.875 28 182
OH Hydroxyl radical 1 Σ 4041 3738 0.925 29 183
CF Fluoromethylidyne 1 Σ 1409 1308 0.928 30 184
CCl carbon monochloride 1 Σ 872 877 1.006 31 185
HCP HCP 1 Σ 3513 3217 0.916 32 186
    2 Σ 1466 1278 0.872 32 187
    3 Π 827 674 0.815 32 188
HNC hydrogen isocyanide 1 Σ 4046 3653 0.903 33 189
    2 Σ 2284 2029 0.888 33 190
    3 Π 540 477 0.883 33 191
LiCl lithium chloride 1 Σ 641 643 1.002 34 192
LiH Lithium Hydride 1 Σ 1427 1405 0.985 35 193
NaH sodium hydride 1 Σ 1175 1172 0.997 36 194
HCl Hydrogen chloride 1 Σ 3139 2991 0.953 37 195
NaCl Sodium Chloride 1 Σ 356 365 1.024 38 196
HF Hydrogen fluoride 1 Σ 4472 4138 0.925 39 197
NH3 Ammonia 1 A1 3690 3337 0.904 40 198
    2 A1 1095 950 0.867 40 199
    3 E 3815 3444 0.903 40 200
    4 E 1787 1627 0.911 40 201
NaF sodium fluoride 1 Σ 542 536 0.989 41 202
MgH2 magnesium dihydride 2 Σu 1668 1572 0.942 42 203
    3 Πu 459 440 0.958 42 204
H2O2 Hydrogen peroxide 1 A 4137 3599 0.870 43 205
    2 A 1609 1402 0.871 43 206
    3 A 1163 877 0.754 43 207
    4 A 408 371 0.909 43 208
    5 B 4136 3608 0.872 43 209
    6 B 1491 1266 0.849 43 210
N2 Nitrogen diatomic 1 Σg 2729 2359 0.864 44 211
H2O Water 1 A1 4130 3657 0.886 45 212
    2 A1 1748 1595 0.912 45 213
    3 B2 4230 3756 0.888 45 214
F2 Fluorine diatomic 1 Σg 1266 917 0.725 46 215
Cl2 Chlorine diatomic 1 Σg 615 560 0.910 47 216
H2S Hydrogen sulfide 1 A1 2859 2615 0.915 48 217
    2 A1 1317 1183 0.898 48 218
    3 B2 2868 2626 0.916 48 219
AlH3 aluminum trihydride 1 A1' 2015 1900 0.943 49 220
    2 A2" 756 698 0.923 49 221
    3 E' 2003 1883 0.940 49 222
    4 E' 846 783 0.926 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 942 911 0.966 51 226
ClF Chlorine monofluoride 1 Σ 918 783 0.854 52 227
HOCl hypochlorous acid 1 A' 4131 3609 0.874 53 228
    2 A' 1385 1239 0.894 53 229
    3 A' 871 724 0.832 53 230
NH2OH hydroxylamine 1 A' 4174 3650 0.874 54 231
    2 A' 3708 3294 0.888 54 232
    3 A' 1819 1605 0.882 54 233
    4 A' 1522 1353 0.889 54 234
    5 A' 1236 1115 0.902 54 235
    6 A' 1112 895 0.805 54 236
    7 A" 3788 3359 0.887 54 237
    8 A" 1463 1295 0.885 54 238
    9 A" 448 386 0.862 54 239
PH3 Phosphine 1 A1 2536 2323 0.916 55 240
    2 A1 1100 992 0.902 55 241
    3 E 2533 2328 0.919 55 242
    4 E 1234 1118 0.906 55 243
SiH4 Silane 1 A1 2337 2187 0.936 56 244
    2 E 1043 975 0.935 56 245
    3 T2 2323 2191 0.943 56 246
    4 T2 1009 914 0.906 56 247
SiO Silicon monoxide 1 Σ 1405 1242 0.884 57 248
SiF silicon monofluoride 1 Σ 904 857 0.948 58 249
MgS magnesium sulfide 1 Σ 549 529 0.963 59 250
SiN Silicon nitride 1 Σ 969 1151 1.188 60 251
C2 Carbon diatomic 1 Σg 1904 1855 0.974 61 252
    1 Σg 1792 1855 1.035 61 253
LiO lithium oxide 1 Σ 849 815 0.959 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 615 617 1.003 65 257
CP Carbon monophosphide 1 Σ 1021 1240 1.214 66 258
NaO sodium monoxide 1 Σ 503 492 0.979 67 259
SiS silicon monosulfide 1 Σ 815 750 0.920 68 260
BO boron monoxide 1 Σ 2081 1885 0.906 69 261
Si2 Silicon diatomic 1 Σg 592 511 0.863 70 262
    1 Σg 619 511 0.825 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' 3011 2643 0.878 72 267
    2 A' 1539 1403 0.912 72 268
    3 A' 1322 1189 0.899 72 269
H2S2 HSSH 1 A 2836 2556 0.901 73 270
    2 A 984 882 0.897 73 271
    3 A 562 515 0.915 73 272
    4 A 453 417 0.922 73 273
    5 B 2836 2559 0.902 73 274
    6 B 988 878 0.889 73 275
SiH3Cl chlorosilane 1 A1 2362 2201 0.932 74 276
    2 A1 1032 949 0.919 74 277
    3 A1 557 551 0.989 74 278
    4 E 2359 2195 0.931 74 279
    5 E 1036 954 0.921 74 280
    6 E 712 664 0.932 74 281
SiH3F monofluorosilane 1 A1 2360 2206 0.935 75 282
    2 A1 1071 990 0.925 75 283
    3 A1 934 872 0.934 75 284
    4 E 2348 2196 0.935 75 285
    5 E 1043 956 0.916 75 286
    6 E 783 728 0.929 75 287
AlCl Aluminum monochloride 1 Σ 474 482 1.015 76 288
AlF Aluminum monofluoride 1 Σ 838 802 0.957 77 289
BeF Beryllium monofluoride 1 Σ 1312 1247 0.951 78 290
BeH beryllium monohydride 1 Σ 2124 2061 0.970 79 291
BeS beryllium sulfide 1 Σ 1065 998 0.937 80 292
PH2 Phosphino radical 1 A1 2512 2310 0.920 81 293
    2 A1 1220 1102 0.903 81 294
SiH3 silyl 1 A1 2307 2136 0.926 82 295
    2 A1 882 728 0.825 82 296
    3 E 2322 2185 0.941 82 297
    4 E 1010 922 0.913 82 298
BH Boron monohydride 1 Σ 2488 2367 0.951 83 299
NH2 Amino radical 1 A1 3605 3219 0.893 84 300
    2 A1 1637 1497 0.915 84 301
    3 B2 3692 3301 0.894 84 302
NH Imidogen 1 Σ 3513 3283 0.934 85 303
    1 Σ 3596 3283 0.913 85 304
    1 Σ 3513 3314 0.943 85 305
    1 Σ 3596 3314 0.922 85 306
SiH Silylidyne 1 Σ 2128 2043 0.960 86 307
BeCl beryllium chloride 1 Σ 846 847 1.001 87 308
HPO HPO 1 A' 2305 2095 0.909 88 309
    2 A' 1389 1188 0.855 88 310
    3 A' 1100 986 0.896 88 311
SiH2 silicon dihydride 1 A1 2157 1996 0.925 89 312
    2 A1 1104 999 0.905 89 313
    3 B2 2145 1993 0.929 89 314
SO Sulfur monoxide 1 Σ 1340 1151 0.859 90 315
    1 Σ 1354 1151 0.850 90 316
SH Mercapto radical 1 Σ 2841 2696 0.949 91 317
SiCl Clorosilylidyne 1 Σ 527 536 1.016 92 318
NF nitrogen fluoride 1 Σ 1265 1141 0.902 93 319
    1 Σ 1336 1141 0.854 93 320
PH phosphorus monohydride 1 Σ 2497 2364 0.947 94 321
    1 Σ 2511 2364 0.941 94 322
    1 Σ 2497 2415 0.967 94 323
    1 Σ 2511 2415 0.962 94 324
    1 Σ 2497 2403 0.962 94 325
    1 Σ 2511 2403 0.957 94 326
AlH aluminum monohydride 1 Σ 1733 1682 0.971 95 327
HOF Hypofluorous acid 1 A' 4106 3537 0.862 96 328
    2 A' 1596 1393 0.873 96 329
    3 A' 1181 886 0.750 96 330
HNO Nitrosyl hydride 1 A' 3307 2684 0.812 97 331
    2 A' 1937 1565 0.808 97 332
    3 A' 1709 1501 0.878 97 333
MgH magnesium monohydride 1 Σ 1544 1493 0.967 98 334
Li2 Lithium diatomic 1 Σg 337 351 1.041 99 335
BH2 boron dihydride 2 A1 1103 954 0.865 100 336
AlH2 aluminum dihydride 1 A1 1933 1770 0.916 101 337
    2 A1 822 760 0.924 101 338
    3 B2 1950 1807 0.927 101 339
HBS hydrogen boron sulfide 1 Σ 2933 2736 0.933 102 340
    2 Σ 1238 1172 0.947 102 341
MgF Magnesium monofluoride 1 Σ 746 712 0.954 103 342
MgCl magnesium monochloride 1 Σ 466 462 0.992 104 343
ClO Monochlorine monoxide 1 Σ 846 854 1.009 105 344
SCl sulfur monochloride 1 Σ 594 575 0.968 106 345
PF phosphorus monofluoride 1 Σ 907 847 0.934 107 346
    1 Σ 924 847 0.917 107 347
SF Monosulfur monofluoride 1 Σ 920 838 0.910 108 348
PCl phosphorus chloride 1 Σ 554 577 1.042 109 349
    1 Σ 577 577 1.000 109 350
PN Phosphorus mononitride 1 Σ 1591 1337 0.840 110 351
B2H6 Diborane 1 Ag 2697 2524 0.936 111 352
    2 Ag 2238 2104 0.940 111 353
    3 Ag 1297 1180 0.910 111 354
    4 Ag 819 794 0.969 111 355
    5 Au 890 833 0.936 111 356
    6 B1g 2764 2591 0.938 111 357
    7 B1g 993 915 0.922 111 358
    8 B1u 2013 1915 0.951 111 359
    9 B1u 1062 973 0.916 111 360
    10 B2g 1897 1768 0.932 111 361
    11 B2g 900 850 0.944 111 362
    12 B2u 2780 2612 0.940 111 363
    13 B2u 1094 950 0.868 111 364
    14 B2u 412 368 0.893 111 365
    15 B3g 1160 1012 0.872 111 366
    16 B3u 2678 2525 0.943 111 367
    17 B3u 1783 1602 0.898 111 368
    18 B3u 1278 1177 0.921 111 369
BCl boron monochloride 1 Σ 852 840 0.987 112 370
HBO Boron hydride oxide 1 Σ 2988 2850 0.954 113 371
    2 Σ 1999 1826 0.913 113 372
    3 Π 860 756 0.879 113 373
BeOH beryllium hydroxide 2 A' 1318 1246 0.945 114 374
S2 Sulfur diatomic 1 Σg 817 726 0.888 115 375
    1 Σg 816 726 0.889 115 376
Na2 Sodium diatomic 1 Σg 155 159 1.024 116 377

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