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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 2934 2843 0.969 1 5
    6 B2 1269 1249 0.984 1 6
CH3OH Methyl alcohol 1 A' 3834 3681 0.960 2 7
    2 A' 3102 3000 0.967 2 8
    3 A' 2988 2844 0.952 2 9
    4 A' 1511 1477 0.978 2 10
    5 A' 1483 1455 0.981 2 11
    6 A' 1372 1345 0.980 2 12
    7 A' 1082 1060 0.980 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" 296 200 0.675 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     8 71
    15 A" 301 268 0.891 8 72
HCN Hydrogen cyanide 1 Σ 3440 3312 0.963 9 73
    2 Σ 2202 2089 0.949 9 74
    3 Π 762 712 0.935 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
H2CS Thioformaldehyde 1 A1 3059 2971 0.971 15 120
    2 A1 1495 1456 0.973 15 121
    3 A1 1088 1059 0.974 15 122
    4 B1 1031 990 0.960 15 123
    5 B2 3139 3025 0.963 15 124
    6 B2 1005 991 0.986 15 125
BeO beryllium oxide 1 Σ 1554 1457 0.938 16 126
MgO magnesium oxide 1 Σ 826 785 0.951 17 127
LiOH lithium hydroxide 1 Σ 3998 3688 0.922 18 128
    2 Σ 963 871 0.904 18 129
    3 Π 355 257 0.723 18 130
NaOH sodium hydroxide 1 Σ 3950 3637 0.921 19 131
    2 Σ 565 540 0.956 19 132
    3 Π 133 300 2.255 19 133
H2 Hydrogen diatomic 1 Σg 4420 4401 0.996 20 134
Si2H6 disilane 1 A1g 2220 2152 0.970 21 135
    2 A1g 928 909 0.980 21 136
    3 A1g 422 434 1.028 21 137
    4 A1u 140 131 0.937 21 138
    5 A2u 2211 2154 0.974 21 139
    6 A2u 855 844 0.986 21 140
    7 Eg 2217 2155 0.972 21 141
    8 Eg 946 929 0.982 21 142
    9 Eg 634 625 0.985 21 143
    10 Eu 2227 2179 0.978 21 144
    11 Eu 961 940 0.978 21 145
    12 Eu 376 379 1.008 21 146
CH2NH Methanimine 1 A' 3429 3263 0.952 22 147
    2 A' 3105 3024 0.974 22 148
    3 A' 3010 2914 0.968 22 149
    4 A' 1712 1638 0.957 22 150
    5 A' 1493 1452 0.973 22 151
    6 A' 1370 1344 0.981 22 152
    7 A' 1074 1058 0.985 22 153
    8 A" 1166 1127 0.966 22 154
    9 A" 1104 1061 0.961 22 155
CN Cyano radical 1 Σ 2154 2069 0.960 23 156
HCO Formyl radical 1 A' 2640 2434 0.922 24 157
    2 A' 1936 1868 0.965 24 158
    3 A' 1107 1081 0.976 24 159
CS carbon monosulfide 1 Σ 1305 1285 0.984 25 160
HO2 Hydroperoxy radical 1 A' 3599 3436 0.955 26 161
    2 A' 1436 1392 0.969 26 162
    3 A' 1166 1098 0.941 26 163
CH Methylidyne 1 Σ 2826 2861 1.012 27 164
    1 Σ 3048 3145 1.032 27 165
OH Hydroxyl radical 1 Σ 3703 3738 1.009 28 166
CF Fluoromethylidyne 1 Σ 1297 1308 1.009 29 167
CCl carbon monochloride 1 Σ 852 877 1.030 30 168
HCP HCP 1 Σ 3348 3217 0.961 31 169
    2 Σ 1343 1278 0.952 31 170
    3 Π 721 674 0.935 31 171
HNC hydrogen isocyanide 1 Σ 3802 3653 0.961 32 172
    2 Σ 2107 2029 0.963 32 173
    3 Π 473 477 1.009 32 174
LiCl lithium chloride 1 Σ 642 643 1.002 33 175
LiH Lithium Hydride 1 Σ 1407 1405 0.999 34 176
NaH sodium hydride 1 Σ 1158 1172 1.012 35 177
HCl Hydrogen chloride 1 Σ 2934 2991 1.020 36 178
NaCl Sodium Chloride 1 Σ 356 365 1.024 37 179
HF Hydrogen fluoride 1 Σ 4086 4138 1.013 38 180
NH3 Ammonia 1 A1 3471 3337 0.961 39 181
    2 A1 1048 950 0.907 39 182
    3 E 3588 3444 0.960 39 183
    4 E 1670 1627 0.974 39 184
NaF sodium fluoride 1 Σ 524 536 1.021 40 185
MgH2 magnesium dihydride 2 Σu 1638 1572 0.959 41 186
    3 Πu 437 440 1.006 41 187
H2O2 Hydrogen peroxide 1 A 3767 3599 0.955 42 188
    2 A 1439 1402 0.974 42 189
    3 A 951 877 0.922 42 190
    4 A 379 371 0.978 42 191
    5 B 3765 3608 0.958 42 192
    6 B 1327 1266 0.954 42 193
N2 Nitrogen diatomic 1 Σg 2448 2359 0.964 43 194
H2O Water 1 A1 3806 3657 0.961 44 195
    2 A1 1635 1595 0.976 44 196
    3 B2 3906 3756 0.962 44 197
F2 Fluorine diatomic 1 Σg 1045 917 0.877 45 198
Cl2 Chlorine diatomic 1 Σg 539 560 1.039 46 199
H2S Hydrogen sulfide 1 A1 2687 2615 0.973 47 200
    2 A1 1210 1183 0.977 47 201
    3 B2 2700 2626 0.973 47 202
AlH3 aluminum trihydride 1 A1' 1944 1900 0.977 48 203
    2 A2" 712 698 0.981 48 204
    3 E' 1950 1883 0.965 48 205
    4 E' 800 783 0.979 48 206
BeH2 beryllium dihydride 2 Σu 2261 2159 0.955 49 207
    3 Πu 727 698 0.960 49 208
LiF lithium fluoride 1 Σ 911 911 1.000 50 209
ClF Chlorine monofluoride 1 Σ 787 783 0.996 51 210
HOCl hypochlorous acid 1 A' 3771 3609 0.957 52 211
    2 A' 1264 1239 0.980 52 212
    3 A' 738 724 0.982 52 213
NH2OH hydroxylamine 1 A' 3814 3650 0.957 53 214
    2 A' 3439 3294 0.958 53 215
    3 A' 1667 1605 0.963 53 216
    4 A' 1398 1353 0.968 53 217
    5 A' 1148 1115 0.972 53 218
    6 A' 930 895 0.963 53 219
    7 A" 3515 3359 0.956 53 220
    8 A" 1329 1295 0.974 53 221
    9 A" 414 386 0.933 53 222
PH3 Phosphine 1 A1 2387 2323 0.973 54 223
    2 A1 1018 992 0.974 54 224
    3 E 2393 2328 0.973 54 225
    4 E 1139 1118 0.981 54 226
SiH4 Silane 1 A1 2238 2187 0.977 55 227
    2 E 979 975 0.996 55 228
    3 T2 2242 2191 0.977 55 229
    4 T2 923 914 0.991 55 230
SiO Silicon monoxide 1 Σ 1260 1242 0.986 56 231
SiF silicon monofluoride 1 Σ 829 857 1.034 57 232
MgS magnesium sulfide 1 Σ 527 529 1.003 58 233
SiN Silicon nitride 1 Σ 1185 1151 0.971 59 234
C2 Carbon diatomic 1 Σg 1875 1855 0.989 60 235
LiO lithium oxide 1 Σ 821 815 0.993 61 236
P2 Phosphorus diatomic 1 Σg 808 781 0.967 62 237
BS boron sulfide 1 Σ 1181 1180 0.999 63 238
AlS Aluminum sulfide 1 Σ 595 617 1.037 64 239
CP Carbon monophosphide 1 Σ 1281 1240 0.968 65 240
NaO sodium monoxide 1 Σ 481 492 1.023 66 241
SiS silicon monosulfide 1 Σ 744 750 1.007 67 242
BO boron monoxide 1 Σ 1921 1885 0.981 68 243
Si2 Silicon diatomic 1 Σg 498 511 1.026 69 244
BH3 boron trihydride 2 A2" 1161 1148 0.988 70 245
    3 E' 2690 2602 0.967 70 246
    4 E' 1206 1197 0.992 70 247
HCF Fluoromethylene 1 A' 2761 2643 0.957 71 248
    2 A' 1440 1403 0.974 71 249
    3 A' 1200 1189 0.990 71 250
H2S2 HSSH 1 A 2620 2556 0.976 72 251
    2 A 888 882 0.993 72 252
    3 A 500 515 1.028 72 253
    4 A 430 417 0.972 72 254
    5 B 2622 2559 0.976 72 255
    6 B 889 878 0.987 72 256
SiH3Cl chlorosilane 1 A1 2253 2201 0.977 73 257
    2 A1 954 949 0.995 73 258
    3 A1 532 551 1.036 73 259
    4 E 2263 2195 0.970 73 260
    5 E 960 954 0.994 73 261
    6 E 660 664 1.006 73 262
SiH3F monofluorosilane 1 A1 2253 2206 0.979 74 263
    2 A1 996 990 0.994 74 264
    3 A1 861 872 1.012 74 265
    4 E 2257 2196 0.973 74 266
    5 E 967 956 0.988 74 267
    6 E 727 728 1.001 74 268
AlCl Aluminum monochloride 1 Σ 455 482 1.060 75 269
AlF Aluminum monofluoride 1 Σ 777 802 1.032 76 270
BeF Beryllium monofluoride 1 Σ 1261 1247 0.989 77 271
BeH beryllium monohydride 1 Σ 2066 2061 0.998 78 272
BeS beryllium sulfide 1 Σ 1012 998 0.986 79 273
PH2 Phosphino radical 1 A1 2364 2310 0.977 80 274
    2 A1 1127 1102 0.978 80 275
SiH3 Silyl radical 1 A1 2191 2136 0.975 81 276
    2 A1 771 728 0.945 81 277
    3 E 2229 2185 0.981 81 278
    4 E 938 922 0.982 81 279
BH Boron monohydride 1 Σ 2353 2367 1.006 82 280
NH2 Amino radical 1 A1 3350 3219 0.961 83 281
    2 A1 1536 1497 0.975 83 282
    3 B2 3438 3301 0.960 83 283
NH Imidogen 1 Σ 3257 3283 1.008 84 284
    1 Σ 3298 3314 1.005 84 285
SiH Silylidyne 1 Σ 2021 2043 1.011 85 286
BeCl beryllium chloride 1 Σ 833 847 1.017 86 287
HPO HPO 1 A' 2085 2095 1.005 87 288
    2 A' 1223 1188 0.971 87 289
    3 A' 1004 986 0.982 87 290
SiH2 silicon dihydride 1 A1 2043 1996 0.977 88 291
    2 A1 1023 999 0.977 88 292
    3 B2 2043 1993 0.976 88 293
SO Sulfur monoxide 1 Σ 1153 1151 0.998 89 294
    1 Σ 1152 1069 0.928 89 295
SH Mercapto radical 1 Σ 2665 2696 1.012 90 296
SiCl Clorosilylidyne 1 Σ 508 536 1.055 91 297
NF nitrogen fluoride 1 Σ 1153 1141 0.990 92 298
PH phosphorus monohydride 1 Σ 2336 2364 1.012 93 299
    1 Σ 2354 2415 1.026 93 300
AlH aluminum monohydride 1 Σ 1645 1682 1.023 94 301
HOF Hypofluorous acid 1 A' 3731 3537 0.948 95 302
    2 A' 1409 1393 0.988 95 303
    3 A' 983 886 0.902 95 304
HNO Nitrosyl hydride 1 A' 2846 2684 0.943 96 305
    2 A' 1667 1565 0.939 96 306
    3 A' 1566 1501 0.958 96 307
MgH magnesium monohydride 1 Σ 1463 1493 1.020 97 308
Li2 Lithium diatomic 1 Σg 346 351 1.017 98 309
BH2 boron dihydride 2 A1 986 954 0.967 99 310
AlH2 aluminum dihydride 1 A1 1823 1770 0.971 100 311
    2 A1 773 760 0.983 100 312
    3 B2 1865 1807 0.969 100 313
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 101 314
    2 Σ 1188 1172 0.987 101 315
MgF Magnesium monofluoride 1 Σ 705 712 1.009 102 316
MgCl magnesium monochloride 1 Σ 446 462 1.036 103 317
ClO Monochlorine monoxide 1 Σ 852 854 1.002 104 318
SCl sulfur monochloride 1 Σ 560 575 1.026 105 319
PF phosphorus monofluoride 1 Σ 825 847 1.026 106 320
SF Monosulfur monofluoride 1 Σ 823 838 1.017 107 321
PCl phosphorus chloride 1 Σ 529 577 1.090 108 322
PN Phosphorus mononitride 1 Σ 1404 1337 0.952 109 323
B2H6 Diborane 1 Ag 2619 2524 0.964 110 324
    2 Ag 2176 2104 0.967 110 325
    3 Ag 1206 1180 0.978 110 326
    4 Ag 801 794 0.992 110 327
    5 Au 851 833 0.979 110 328
    6 B1g 2692 2591 0.962 110 329
    7 B1g 942 915 0.972 110 330
    8 B1u 1992 1915 0.961 110 331
    9 B1u 992 973 0.981 110 332
    10 B2g 1859 1768 0.951 110 333
    11 B2g 894 850 0.951 110 334
    12 B2u 2707 2612 0.965 110 335
    13 B2u 956 950 0.994 110 336
    14 B2u 364 368 1.010 110 337
    15 B3g 1022 1012 0.991 110 338
    16 B3u 2606 2525 0.969 110 339
    17 B3u 1716 1602 0.933 110 340
    18 B3u 1199 1177 0.982 110 341
BCl boron monochloride 1 Σ 818 840 1.027 111 342
HBO Boron hydride oxide 1 Σ 2893 2850 0.985 112 343
    2 Σ 1869 1826 0.977 112 344
    3 Π 776 756 0.975 112 345
BeOH beryllium hydroxide 2 A' 1294 1246 0.962 113 346
S2 Sulfur diatomic 1 Σg 713 726 1.018 114 347
Na2 Sodium diatomic 1 Σg 161 159 0.991 115 348

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