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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at B3LYP/cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.969 ± 0.021 115 344 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2879 2782 0.966 1 1
    2 A1 1821 1746 0.959 1 2
    3 A1 1535 1500 0.977 1 3
    4 B1 1203 1167 0.970 1 4
    5 B2 2933 2843 0.969 1 5
    6 B2 1269 1249 0.984 1 6
CH3OH Methyl alcohol 1 A' 3830 3681 0.961 2 7
    2 A' 3102 3000 0.967 2 8
    3 A' 2987 2844 0.952 2 9
    4 A' 1511 1477 0.977 2 10
    5 A' 1483 1455 0.981 2 11
    6 A' 1372 1345 0.980 2 12
    7 A' 1082 1060 0.979 2 13
    8 A' 1046 1033 0.988 2 14
    9 A" 3031 2960 0.977 2 15
    10 A" 1497 1477 0.987 2 16
    11 A" 1174 1165 0.992 2 17
    12 A" 301 200 0.664 2 18
CH4 Methane 1 A1 3028 2917 0.963 3 19
    2 E 1559 1534 0.984 3 20
    3 T2 3130 3019 0.964 3 21
    4 T2 1341 1306 0.974 3 22
C2H6 Ethane 1 A1g 3026 2896 0.957 4 23
    2 A1g 1422 1388 0.976 4 24
    3 A1g 995 995 1.000 4 25
    4 A1u 303 289 0.953 4 26
    5 A2u 3027 2915 0.963 4 27
    6 A2u 1412 1370 0.970 4 28
    7 Eg 3070 2969 0.967 4 29
    8 Eg 1503 1468 0.977 4 30
    9 Eg 1222 1190 0.974 4 31
    10 Eu 3095 2974 0.961 4 32
    11 Eu 1506 1460 0.969 4 33
    12 Eu 826 822 0.995 4 34
C2H4 Ethylene 1 Ag 3138 3026 0.964 5 35
    2 Ag 1690 1623 0.960 5 36
    3 Ag 1381 1342 0.972 5 37
    4 Au 1065 1023 0.960 5 38
    5 B1u 3125 2989 0.956 5 39
    6 B1u 1480 1444 0.976 5 40
    7 B2g 987 940 0.952 5 41
    8 B2u 3222 3105 0.964 5 42
    9 B2u 836 826 0.988 5 43
    10 B3g 3194 3086 0.966 5 44
    11 B3g 1246 1217 0.977 5 45
    12 B3u 979 949 0.969 5 46
C2H2 Acetylene 1 Σg 3509 3374 0.962 6 47
    2 Σg 2068 1974 0.954 6 48
    3 Σu 3410 3289 0.964 6 49
    4 Πg 657 612 0.931 6 50
    5 Πu 767 730 0.951 6 51
CH3Cl Methyl chloride 1 A1 3069 2966 0.967 7 52
    2 A1 1379 1355 0.982 7 53
    3 A1 715 732 1.024 7 54
    4 E 3163 3042 0.962 7 55
    5 E 1484 1455 0.980 7 56
    6 E 1027 1015 0.988 7 57
CH3NH2 methyl amine 1 A' 3497 3361 0.961 8 58
    2 A' 3053 2961 0.970 8 59
    3 A' 2963 2820 0.952 8 60
    4 A' 1664 1623 0.975 8 61
    5 A' 1499 1473 0.982 8 62
    6 A' 1461 1430 0.979 8 63
    7 A' 1173 1130 0.963 8 64
    8 A' 1056 1044 0.989 8 65
    9 A' 832 780 0.937 8 66
    10 A" 3570 3427 0.960 8 67
    11 A" 3087 2985 0.967 8 68
    12 A" 1518 1485 0.978 8 69
    13 A" 1348 1335 0.991 8 70
    14 A" 975 1195 1.225 8 71
    15 A" 301 268 0.891 8 72
HCN Hydrogen cyanide 1 Σ 3439 3312 0.963 9 73
    2 Σ 2202 2089 0.949 9 74
    3 Π 762 712 0.934 9 75
CH3SH Methanethiol 1 A' 3133 3000 0.958 10 76
    2 A' 3050 2931 0.961 10 77
    3 A' 2672 2597 0.972 10 78
    4 A' 1489 1475 0.990 10 79
    5 A' 1359 1335 0.982 10 80
    6 A' 1098 1074 0.978 10 81
    7 A' 799 803 1.005 10 82
    8 A' 699 708 1.013 10 83
    9 A" 3132 3000 0.958 10 84
    10 A" 1476 1430 0.969 10 85
    11 A" 974 976 1.002 10 86
N2H4 Hydrazine 1 A 3551 3398 0.957 11 87
    2 A 3459 3329 0.963 11 88
    3 A 1687 1642 0.973 11 89
    4 A 1330 1275 0.959 11 90
    5 A 1114 1076 0.966 11 91
    6 A 809 780 0.964 11 92
    7 A 441 377 0.854 11 93
    8 B 3557 3350 0.942 11 94
    9 B 3449 3314 0.961 11 95
    10 B 1676 1628 0.971 11 96
    11 B 1299 1275 0.982 11 97
    12 B 989 966 0.976 11 98
CH3F Methyl fluoride 1 A1 3027 2930 0.968 12 99
    2 A1 1488 1464 0.984 12 100
    3 A1 1049 1049 1.000 12 101
    4 E 3106 3006 0.968 12 102
    5 E 1494 1467 0.982 12 103
    6 E 1195 1182 0.989 12 104
CH3PH2 Methyl phosphine 1 A' 3124 3000 0.960 13 105
    2 A' 3040 2938 0.966 13 106
    3 A' 2373 2297 0.968 13 107
    4 A' 1474 1450 0.984 13 108
    5 A' 1328 1238 0.932 13 109
    6 A' 1118 1086 0.972 13 110
    7 A' 995 977 0.982 13 111
    8 A' 739 740 1.001 13 112
    9 A' 669 677 1.011 13 113
    10 A" 3110 2992 0.962 13 114
    11 A" 2377 2312 0.973 13 115
    12 A" 1480 1450 0.980 13 116
    13 A" 1036 1017 0.982 13 117
    15 A" 229 207 0.905 13 118
CO Carbon monoxide 1 Σ 2214 2170 0.980 14 119
    1 Σ 2214 1743 0.787 14 120
H2CS Thioformaldehyde 1 A1 3059 2971 0.971 15 121
    2 A1 1495 1456 0.973 15 122
    3 A1 1088 1059 0.974 15 123
    4 B1 1031 990 0.960 15 124
    5 B2 3139 3025 0.963 15 125
    6 B2 1005 991 0.986 15 126
BeO beryllium oxide 1 Σ 1554 1457 0.938 16 127
MgO magnesium oxide 1 Σ 826 785 0.951 17 128
LiOH lithium hydroxide 1 Σ 3998 3688 0.922 18 129
    2 Σ 963 871 0.904 18 130
    3 Π 355 257 0.723 18 131
NaOH sodium hydroxide 1 Σ 3950 3637 0.921 19 132
    2 Σ 565 540 0.956 19 133
    3 Π 133 300 2.255 19 134
H2 Hydrogen diatomic 1 Σg 4420 4401 0.996 20 135
Si2H6 disilane 1 A1g 2220 2152 0.970 21 136
    2 A1g 928 909 0.980 21 137
    3 A1g 422 434 1.028 21 138
    4 A1u 140 131 0.937 21 139
    5 A2u 2211 2154 0.974 21 140
    6 A2u 855 844 0.986 21 141
    7 Eg 2217 2155 0.972 21 142
    8 Eg 946 929 0.982 21 143
    9 Eg 634 625 0.985 21 144
    10 Eu 2227 2179 0.978 21 145
    11 Eu 961 940 0.978 21 146
    12 Eu 376 379 1.008 21 147
CH2NH Methanimine 1 A' 3429 3263 0.952 22 148
    2 A' 3105 3024 0.974 22 149
    3 A' 3010 2914 0.968 22 150
    4 A' 1712 1638 0.957 22 151
    5 A' 1493 1452 0.973 22 152
    6 A' 1370 1344 0.981 22 153
    7 A' 1074 1058 0.985 22 154
    8 A" 1166 1127 0.966 22 155
    9 A" 1104 1061 0.961 22 156
CN Cyano radical 1 Σ 2154 2069 0.960 23 157
HCO Formyl radical 1 A' 2640 2434 0.922 24 158
    2 A' 1936 1868 0.965 24 159
    3 A' 1107 1081 0.976 24 160
CS carbon monosulfide 1 Σ 1305 1285 0.984 25 161
HO2 Hydroperoxy radical 1 A' 3599 3436 0.955 26 162
    2 A' 1436 1392 0.969 26 163
    3 A' 1166 1098 0.941 26 164
CH Methylidyne 1 Σ 2826 2861 1.012 27 165
    1 Σ 3048 2861 0.939 27 166
    1 Σ 2826 3145 1.113 27 167
    1 Σ 3048 3145 1.032 27 168
    1 Σ 2826 2931 1.037 27 169
    1 Σ 3048 2931 0.961 27 170
OH Hydroxyl radical 1 Σ 3703 3738 1.009 28 171
CF Fluoromethylidyne 1 Σ 1297 1308 1.009 29 172
CCl carbon monochloride 1 Σ 852 877 1.030 30 173
HCP HCP 1 Σ 3348 3217 0.961 31 174
    2 Σ 1343 1278 0.952 31 175
    3 Π 721 674 0.935 31 176
HNC hydrogen isocyanide 1 Σ 3802 3653 0.961 32 177
    2 Σ 2107 2029 0.963 32 178
    3 Π 473 477 1.009 32 179
LiCl lithium chloride 1 Σ 642 643 1.002 33 180
LiH Lithium Hydride 1 Σ 1407 1405 0.999 34 181
NaH sodium hydride 1 Σ 1158 1172 1.012 35 182
HCl Hydrogen chloride 1 Σ 2934 2991 1.020 36 183
NaCl Sodium Chloride 1 Σ 356 365 1.024 37 184
HF Hydrogen fluoride 1 Σ 4086 4138 1.013 38 185
NH3 Ammonia 1 A1 3471 3337 0.961 39 186
    2 A1 1048 950 0.907 39 187
    3 E 3588 3444 0.960 39 188
    4 E 1670 1627 0.974 39 189
NaF sodium fluoride 1 Σ 524 536 1.021 40 190
MgH2 magnesium dihydride 2 Σu 1638 1572 0.959 41 191
    3 Πu 437 440 1.006 41 192
H2O2 Hydrogen peroxide 1 A 3767 3599 0.955 42 193
    2 A 1439 1402 0.974 42 194
    3 A 951 877 0.922 42 195
    4 A 379 371 0.978 42 196
    5 B 3765 3608 0.958 42 197
    6 B 1327 1266 0.954 42 198
N2 Nitrogen diatomic 1 Σg 2448 2359 0.964 43 199
H2O Water 1 A1 3806 3657 0.961 44 200
    2 A1 1635 1595 0.976 44 201
    3 B2 3906 3756 0.962 44 202
F2 Fluorine diatomic 1 Σg 1045 917 0.877 45 203
Cl2 Chlorine diatomic 1 Σg 539 560 1.039 46 204
H2S Hydrogen sulfide 1 A1 2687 2615 0.973 47 205
    2 A1 1210 1183 0.977 47 206
    3 B2 2700 2626 0.973 47 207
AlH3 aluminum trihydride 1 A1' 1944 1900 0.977 48 208
    2 A2" 712 698 0.981 48 209
    3 E' 1950 1883 0.965 48 210
    4 E' 800 783 0.979 48 211
BeH2 beryllium dihydride 2 Σu 2259 2159 0.956 49 212
    3 Πu 728 698 0.959 49 213
LiF lithium fluoride 1 Σ 911 911 1.000 50 214
ClF Chlorine monofluoride 1 Σ 787 783 0.996 51 215
HOCl hypochlorous acid 1 A' 3771 3609 0.957 52 216
    2 A' 1264 1239 0.980 52 217
    3 A' 738 724 0.982 52 218
NH2OH hydroxylamine 1 A' 3814 3650 0.957 53 219
    2 A' 3439 3294 0.958 53 220
    3 A' 1667 1605 0.963 53 221
    4 A' 1398 1353 0.968 53 222
    5 A' 1148 1115 0.972 53 223
    6 A' 930 895 0.963 53 224
    7 A" 3515 3359 0.956 53 225
    8 A" 1329 1295 0.974 53 226
    9 A" 414 386 0.933 53 227
PH3 Phosphine 1 A1 2387 2323 0.973 54 228
    2 A1 1018 992 0.974 54 229
    3 E 2393 2328 0.973 54 230
    4 E 1139 1118 0.981 54 231
SiH4 Silane 1 A1 2238 2187 0.977 55 232
    2 E 979 975 0.996 55 233
    3 T2 2242 2191 0.977 55 234
    4 T2 923 914 0.991 55 235
SiO Silicon monoxide 1 Σ 1260 1242 0.986 56 236
SiF silicon monofluoride 1 Σ 829 857 1.034 57 237
MgS magnesium sulfide 1 Σ 527 529 1.003 58 238
SiN Silicon nitride 1 Σ 1185 1151 0.971 59 239
C2 Carbon diatomic 1 Σg 1875 1855 0.989 60 240
    1 Σg 1693 1855 1.096 60 241
LiO lithium oxide 1 Σ 821 815 0.993 61 242
P2 Phosphorus diatomic 1 Σg 808 781 0.967 62 243
BS boron sulfide 1 Σ 1181 1180 0.999 63 244
AlS Aluminum sulfide 1 Σ 595 617 1.037 64 245
CP Carbon monophosphide 1 Σ 1281 1240 0.968 65 246
NaO sodium monoxide 1 Σ 481 492 1.023 66 247
SiS silicon monosulfide 1 Σ 744 750 1.007 67 248
BO boron monoxide 1 Σ 1921 1885 0.981 68 249
Si2 Silicon diatomic 1 Σg 498 511 1.026 69 250
    1 Σg 600 511 0.852 69 251
BH3 boron trihydride 2 A2" 1161 1148 0.988 70 252
    3 E' 2690 2602 0.967 70 253
    4 E' 1206 1197 0.992 70 254
HCF Fluoromethylene 1 A' 2761 2643 0.957 71 255
    1 A' 3103 2643 0.852 71 256
    2 A' 1440 1403 0.974 71 257
    2 A' 1256 1403 1.117 71 258
    3 A' 1200 1189 0.990 71 259
    3 A' 1111 1189 1.070 71 260
H2S2 HSSH 1 A 2620 2556 0.976 72 261
    2 A 888 882 0.993 72 262
    3 A 500 515 1.028 72 263
    4 A 430 417 0.972 72 264
    5 B 2622 2559 0.976 72 265
    6 B 889 878 0.987 72 266
SiH3Cl chlorosilane 1 A1 2253 2201 0.977 73 267
    2 A1 954 949 0.995 73 268
    3 A1 532 551 1.036 73 269
    4 E 2263 2195 0.970 73 270
    5 E 960 954 0.994 73 271
    6 E 660 664 1.006 73 272
SiH3F monofluorosilane 1 A1 2253 2206 0.979 74 273
    2 A1 996 990 0.994 74 274
    3 A1 861 872 1.012 74 275
    4 E 2257 2196 0.973 74 276
    5 E 967 956 0.988 74 277
    6 E 727 728 1.001 74 278
AlCl Aluminum monochloride 1 Σ 455 482 1.060 75 279
AlF Aluminum monofluoride 1 Σ 777 802 1.032 76 280
BeF Beryllium monofluoride 1 Σ 1261 1247 0.989 77 281
BeH beryllium monohydride 1 Σ 2066 2061 0.998 78 282
BeS beryllium sulfide 1 Σ 1012 998 0.986 79 283
PH2 Phosphino radical 1 A1 2364 2310 0.977 80 284
    2 A1 1127 1102 0.978 80 285
SiH3 silyl 1 A1 2191 2136 0.975 81 286
    2 A1 771 728 0.945 81 287
    3 E 2229 2185 0.981 81 288
    4 E 938 922 0.982 81 289
BH Boron monohydride 1 Σ 2353 2367 1.006 82 290
NH2 Amino radical 1 A1 3350 3219 0.961 83 291
    2 A1 1536 1497 0.975 83 292
    3 B2 3438 3301 0.960 83 293
NH Imidogen 1 Σ 3257 3283 1.008 84 294
    1 Σ 3298 3283 0.995 84 295
    1 Σ 3257 3314 1.018 84 296
    1 Σ 3298 3314 1.005 84 297
SiH Silylidyne 1 Σ 2021 2043 1.011 85 298
BeCl beryllium chloride 1 Σ 833 847 1.017 86 299
HPO HPO 1 A' 2085 2095 1.005 87 300
    2 A' 1223 1188 0.971 87 301
    3 A' 1004 986 0.982 87 302
SiH2 silicon dihydride 1 A1 2043 1996 0.977 88 303
    1 A1 2154 1996 0.926 88 304
    2 A1 1023 999 0.977 88 305
    2 A1 891 999 1.122 88 306
    3 B2 2042 1993 0.976 88 307
    3 B2 2224 1993 0.896 88 308
SO Sulfur monoxide 1 Σ 1153 1151 0.998 89 309
    1 Σ 1152 1151 0.999 89 310
SH Mercapto radical 1 Σ 2665 2696 1.012 90 311
SiCl Clorosilylidyne 1 Σ 508 536 1.055 91 312
NF nitrogen fluoride 1 Σ 1153 1141 0.990 92 313
    1 Σ 1199 1141 0.952 92 314
PH phosphorus monohydride 1 Σ 2336 2364 1.012 93 315
    1 Σ 2354 2364 1.004 93 316
    1 Σ 2336 2415 1.034 93 317
    1 Σ 2354 2415 1.026 93 318
    1 Σ 2336 2403 1.029 93 319
    1 Σ 2354 2403 1.021 93 320
AlH aluminum monohydride 1 Σ 1645 1682 1.023 94 321
HOF Hypofluorous acid 1 A' 3731 3537 0.948 95 322
    2 A' 1409 1393 0.988 95 323
    3 A' 983 886 0.902 95 324
HNO Nitrosyl hydride 1 A' 2846 2684 0.943 96 325
    2 A' 1667 1565 0.939 96 326
    3 A' 1566 1501 0.958 96 327
MgH magnesium monohydride 1 Σ 1463 1493 1.020 97 328
Li2 Lithium diatomic 1 Σg 346 351 1.017 98 329
BH2 boron dihydride 2 A1 986 954 0.967 99 330
AlH2 aluminum dihydride 1 A1 1823 1770 0.971 100 331
    2 A1 773 760 0.983 100 332
    3 B2 1865 1807 0.969 100 333
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 101 334
    2 Σ 1188 1172 0.987 101 335
MgF Magnesium monofluoride 1 Σ 705 712 1.009 102 336
MgCl magnesium monochloride 1 Σ 446 462 1.036 103 337
ClO Monochlorine monoxide 1 Σ 852 854 1.002 104 338
SCl sulfur monochloride 1 Σ 559 575 1.027 105 339
PF phosphorus monofluoride 1 Σ 825 847 1.026 106 340
    1 Σ 836 847 1.013 106 341
SF Monosulfur monofluoride 1 Σ 823 838 1.017 107 342
PCl phosphorus chloride 1 Σ 529 577 1.090 108 343
    1 Σ 549 577 1.052 108 344
PN Phosphorus mononitride 1 Σ 1404 1337 0.952 109 345
B2H6 Diborane 1 Ag 2619 2524 0.964 110 346
    2 Ag 2176 2104 0.967 110 347
    3 Ag 1206 1180 0.978 110 348
    4 Ag 801 794 0.992 110 349
    5 Au 851 833 0.979 110 350
    6 B1g 2692 2591 0.962 110 351
    7 B1g 942 915 0.972 110 352
    8 B1u 1992 1915 0.961 110 353
    9 B1u 992 973 0.981 110 354
    10 B2g 1859 1768 0.951 110 355
    11 B2g 894 850 0.951 110 356
    12 B2u 2707 2612 0.965 110 357
    13 B2u 956 950 0.994 110 358
    14 B2u 364 368 1.010 110 359
    15 B3g 1022 1012 0.991 110 360
    16 B3u 2606 2525 0.969 110 361
    17 B3u 1716 1602 0.933 110 362
    18 B3u 1199 1177 0.982 110 363
BCl boron monochloride 1 Σ 818 840 1.027 111 364
HBO Boron hydride oxide 1 Σ 2893 2850 0.985 112 365
    2 Σ 1869 1826 0.977 112 366
    3 Π 776 756 0.975 112 367
BeOH beryllium hydroxide 2 A' 1294 1246 0.962 113 368
S2 Sulfur diatomic 1 Σg 713 726 1.018 114 369
    1 Σg 709 726 1.023 114 370
Na2 Sodium diatomic 1 Σg 161 159 0.991 115 371

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