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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/aug-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 2882 2782 0.965 1 1
    2 A1 1816 1746 0.961 1 2
    3 A1 1532 1500 0.979 1 3
    4 B1 1200 1167 0.972 1 4
    5 B2 2938 2843 0.968 1 5
    6 B2 1267 1249 0.986 1 6
CH3OH Methyl alcohol 1 A' 3834 3681 0.960 2 7
    2 A' 3106 3000 0.966 2 8
    3 A' 2991 2844 0.951 2 9
    4 A' 1511 1477 0.978 2 10
    5 A' 1481 1455 0.982 2 11
    6 A' 1367 1345 0.984 2 12
    7 A' 1079 1060 0.982 2 13
    8 A' 1042 1033 0.991 2 14
    9 A" 3037 2960 0.975 2 15
    10 A" 1499 1477 0.985 2 16
    11 A" 1174 1165 0.992 2 17
    12 A" 292 200 0.685 2 18
CH4 Methane 1 A1 3027 2917 0.964 3 19
    2 E 1559 1534 0.984 3 20
    3 T2 3130 3019 0.965 3 21
    4 T2 1342 1306 0.974 3 22
C2H6 Ethane 1 A1g 3025 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 0.954 4 26
    5 A2u 3026 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 3094 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 1689 1623 0.961 5 36
    3 Ag 1381 1342 0.972 5 37
    4 Au 1064 1023 0.962 5 38
    5 B1u 3125 2989 0.956 5 39
    6 B1u 1480 1444 0.975 5 40
    7 B2g 987 940 0.952 5 41
    8 B2u 3222 3105 0.964 5 42
    9 B2u 837 826 0.987 5 43
    10 B3g 3194 3086 0.966 5 44
    11 B3g 1248 1217 0.975 5 45
    12 B3u 979 949 0.969 5 46
C2H2 Acetylene 1 Σg 3509 3374 0.962 6 47
    2 Σg 2067 1974 0.955 6 48
    3 Σu 3410 3289 0.965 6 49
    4 Πg 672 612 0.911 6 50
    5 Πu 767 730 0.952 6 51
CH3Cl Methyl chloride 1 A1 3069 2966 0.967 7 52
    2 A1 1380 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 1028 1015 0.987 7 57
CH3NH2 methyl amine 1 A' 3500 3361 0.960 8 58
    2 A' 3055 2961 0.969 8 59
    3 A' 2966 2820 0.951 8 60
    4 A' 1661 1623 0.977 8 61
    5 A' 1500 1473 0.982 8 62
    6 A' 1462 1430 0.978 8 63
    7 A' 1169 1130 0.967 8 64
    8 A' 1055 1044 0.989 8 65
    9 A' 819 780 0.952 8 66
    10 A" 3575 3427 0.959 8 67
    11 A" 3090 2985 0.966 8 68
    12 A" 1519 1485 0.978 8 69
    13 A" 1345 1335 0.992 8 70
    14 A" 974     8 71
    15 A" 294 268 0.910 8 72
HCN Hydrogen cyanide 1 Σ 3438 3312 0.963 9 73
    2 Σ 2200 2089 0.949 9 74
    3 Π 759 712 0.939 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' 1490 1475 0.990 10 79
    5 A' 1360 1335 0.982 10 80
    6 A' 1097 1074 0.979 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" 1477 1430 0.968 10 85
    11 A" 974 976 1.002 10 86
N2H4 Hydrazine 1 A 3555 3398 0.956 11 87
    2 A 3462 3329 0.962 11 88
    3 A 1686 1642 0.974 11 89
    4 A 1325 1275 0.963 11 90
    5 A 1112 1076 0.968 11 91
    6 A 800 780 0.975 11 92
    7 A 442 377 0.852 11 93
    8 B 3561 3350 0.941 11 94
    9 B 3454 3314 0.959 11 95
    10 B 1674 1628 0.973 11 96
    11 B 1296 1275 0.984 11 97
    12 B 971 966 0.995 11 98
CH3F Methyl fluoride 1 A1 3030 2930 0.967 12 99
    2 A1 1484 1464 0.986 12 100
    3 A1 1043 1049 1.006 12 101
    4 E 3110 3006 0.967 12 102
    5 E 1495 1467 0.981 12 103
    6 E 1194 1182 0.990 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 0.983 13 108
    5 A 1328 1238 0.932 13 109
    6 A 1117 1086 0.972 13 110
    7 A 994 977 0.983 13 111
    8 A 738 740 1.002 13 112
    9 A 669 677 1.012 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 228 207 0.908 13 118
CO Carbon monoxide 1 Σ 2212 2170 0.981 14 119
H2CS Thioformaldehyde 1 A1 3060 2971 0.971 15 120
    2 A1 1495 1456 0.973 15 121
    3 A1 1087 1059 0.974 15 122
    4 B1 1031 990 0.960 15 123
    5 B2 3140 3025 0.963 15 124
    6 B2 1005 991 0.986 15 125
BeO beryllium oxide 1 Σ 1550 1457 0.940 16 126
MgO magnesium oxide 1 Σ 821 785 0.957 17 127
LiOH lithium hydroxide 1 Σ 4000 3688 0.922 18 128
    2 Σ 952 871 0.914 18 129
    3 Π 341 257 0.752 18 130
NaOH sodium hydroxide 1 Σ 3951 3637 0.921 19 131
    2 Σ 558 540 0.968 19 132
    3 Π 172 300 1.747 19 133
H2 Hydrogen diatomic 1 Σg 4420 4401 0.996 20 134
Si2H6 disilane 1 A1g 2220 2152 0.969 21 135
    2 A1g 928 909 0.980 21 136
    3 A1g 423 434 1.027 21 137
    4 A1u 137 131 0.954 21 138
    5 A2u 2212 2154 0.974 21 139
    6 A2u 855 844 0.987 21 140
    7 Eg 2217 2155 0.972 21 141
    8 Eg 946 929 0.982 21 142
    9 Eg 634 625 0.986 21 143
    10 Eu 2226 2179 0.979 21 144
    11 Eu 960 940 0.979 21 145
    12 Eu 375 379 1.011 21 146
CH2NH Methanimine 1 A' 3432 3263 0.951 22 147
    2 A' 3108 3024 0.973 22 148
    3 A' 3013 2914 0.967 22 149
    4 A' 1710 1638 0.958 22 150
    5 A' 1492 1452 0.973 22 151
    6 A' 1368 1344 0.983 22 152
    7 A' 1074 1058 0.986 22 153
    8 A" 1163 1127 0.969 22 154
    9 A" 1103 1061 0.962 22 155
CN Cyano radical 1 Σ 2153 2069 0.961 23 156
HCO Formyl radical 1 A' 2649 2434 0.919 24 157
    2 A' 1934 1868 0.966 24 158
    3 A' 1105 1081 0.978 24 159
CS carbon monosulfide 1 Σ 1306 1285 0.984 25 160
HO2 Hydroperoxy radical 1 A' 3595 3436 0.956 26 161
    2 A' 1435 1392 0.970 26 162
    3 A' 1166 1098 0.942 26 163
CH Methylidyne 1 Σ 2830 2861 1.011 27 164
    1 Σ 3047 3145 1.032 27 165
OH Hydroxyl radical 1 Σ 3703 3738 1.009 28 166
CF Fluoromethylidyne 1 Σ 1293 1308 1.011 29 167
CCl carbon monochloride 1 Σ 853 877 1.028 30 168
HCP HCP 1 Σ 3348 3217 0.961 31 169
    2 Σ 1342 1278 0.952 31 170
    3 Π 721 674 0.936 31 171
HNC hydrogen isocyanide 1 Σ 3800 3653 0.961 32 172
    2 Σ 2104 2029 0.964 32 173
    3 Π 468 477 1.019 32 174
LiCl lithium chloride 1 Σ 640 643 1.004 33 175
LiH Lithium Hydride 1 Σ 1420 1405 0.990 34 176
NaH sodium hydride 1 Σ 1181 1172 0.993 35 177
HCl Hydrogen chloride 1 Σ 2932 2991 1.020 36 178
NaCl Sodium Chloride 1 Σ 358 365 1.020 37 179
HF Hydrogen fluoride 1 Σ 4077 4138 1.015 38 180
NH3 Ammonia 1 A1 3472 3337 0.961 39 181
    2 A1 1018 950 0.933 39 182
    3 E 3593 3444 0.959 39 183
    4 E 1663 1627 0.978 39 184
NaF sodium fluoride 1 Σ 525 536 1.021 40 185
MgH2 magnesium dihydride 2 Σu 1633 1572 0.962 41 186
    3 Πu 444 440 0.991 41 187
H2O2 Hydrogen peroxide 1 A 3764 3599 0.956 42 188
    2 A 1438 1402 0.975 42 189
    3 A 949 877 0.924 42 190
    4 A 374 371 0.993 42 191
    5 B 3763 3608 0.959 42 192
    6 B 1326 1266 0.955 42 193
N2 Nitrogen diatomic 1 Σg 2448 2359 0.964 43 194
H2O Water 1 A1 3804 3657 0.961 44 195
    2 A1 1629 1595 0.979 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 1.038 46 199
H2S Hydrogen sulfide 1 A1 2686 2615 0.974 47 200
    2 A1 1210 1183 0.978 47 201
    3 B2 2700 2626 0.973 47 202
AlH3 aluminum trihydride 1 A1' 1943 1900 0.978 48 203
    2 A2" 712 698 0.980 48 204
    3 E' 1949 1883 0.966 48 205
    4 E' 799 783 0.981 48 206
BeH2 beryllium dihydride 2 Σu 2260 2159 0.955 49 207
    3 Πu 727 698 0.960 49 208
LiF lithium fluoride 1 Σ 905 911 1.006 50 209
ClF Chlorine monofluoride 1 Σ 786 783 0.996 51 210
HOCl hypochlorous acid 1 A' 3770 3609 0.958 52 211
    2 A' 1260 1239 0.983 52 212
    3 A' 739 724 0.981 52 213
NH2OH hydroxylamine 1 A' 3811 3650 0.958 53 214
    2 A' 3441 3294 0.957 53 215
    3 A' 1666 1605 0.963 53 216
    4 A' 1394 1353 0.971 53 217
    5 A' 1142 1115 0.977 53 218
    6 A' 929 895 0.963 53 219
    7 A" 3518 3359 0.955 53 220
    8 A" 1328 1295 0.975 53 221
    9 A" 417 386 0.925 53 222
PH3 Phosphine 1 A1 2387 2323 0.973 54 223
    2 A1 1018 992 0.975 54 224
    3 E 2393 2328 0.973 54 225
    4 E 1139 1118 0.982 54 226
SiH4 Silane 1 A1 2238 2187 0.977 55 227
    2 E 979 975 0.996 55 228
    3 T2 2240 2191 0.978 55 229
    4 T2 923 914 0.991 55 230
SiO Silicon monoxide 1 Σ 1257 1242 0.988 56 231
SiF silicon monofluoride 1 Σ 824 857 1.040 57 232
MgS magnesium sulfide 1 Σ 526 529 1.005 58 233
SiN Silicon nitride 1 Σ 1184 1151 0.973 59 234
C2 Carbon diatomic 1 Σg 1874 1855 0.990 60 235
LiO lithium oxide 1 Σ 814 815 1.001 61 236
P2 Phosphorus diatomic 1 Σg 808 781 0.967 62 237
BS boron sulfide 1 Σ 1180 1180 1.000 63 238
AlS Aluminum sulfide 1 Σ 594 617 1.038 64 239
CP Carbon monophosphide 1 Σ 1281 1240 0.968 65 240
NaO sodium monoxide 1 Σ 481 492 1.024 66 241
SiS silicon monosulfide 1 Σ 744 750 1.008 67 242
BO boron monoxide 1 Σ 1919 1885 0.982 68 243
Si2 Silicon diatomic 1 Σg 548 511 0.933 69 244
BH3 boron trihydride 2 A2" 1161 1148 0.989 70 245
    3 E' 2690 2602 0.967 70 246
    4 E' 1206 1197 0.992 70 247
HCF Fluoromethylene 1 A' 2762 2643 0.957 71 248
    2 A' 1438 1403 0.976 71 249
    3 A' 1198 1189 0.993 71 250
H2S2 HSSH 1 A 2620 2556 0.976 72 251
    2 A 889 882 0.993 72 252
    3 A 500 515 1.029 72 253
    4 A 428 417 0.976 72 254
    5 B 2622 2559 0.976 72 255
    6 B 889 878 0.987 72 256
SiH3Cl chlorosilane 1 A1 2250 2201 0.978 73 257
    2 A1 954 949 0.995 73 258
    3 A1 532 551 1.036 73 259
    4 E 2259 2195 0.972 73 260
    5 E 959 954 0.994 73 261
    6 E 661 664 1.004 73 262
SiH3F monofluorosilane 1 A1 2253 2206 0.979 74 263
    2 A1 992 990 0.998 74 264
    3 A1 857 872 1.017 74 265
    4 E 2256 2196 0.973 74 266
    5 E 967 956 0.989 74 267
    6 E 724 728 1.005 74 268
AlCl Aluminum monochloride 1 Σ 454 482 1.062 75 269
AlF Aluminum monofluoride 1 Σ 770 802 1.041 76 270
BeF Beryllium monofluoride 1 Σ 1255 1247 0.994 77 271
BeH beryllium monohydride 1 Σ 2063 2061 0.999 78 272
BeS beryllium sulfide 1 Σ 1011 998 0.987 79 273
PH2 Phosphino radical 1 A1 2365 2310 0.977 80 274
    2 A1 1126 1102 0.978 80 275
SiH3 Silyl radical 1 A1 2190 2136 0.975 81 276
    2 A1 770 728 0.945 81 277
    3 E 2227 2185 0.981 81 278
    4 E 938 922 0.983 81 279
BH Boron monohydride 1 Σ 2354 2367 1.005 82 280
NH2 Amino radical 1 A1 3355 3219 0.960 83 281
    2 A1 1531 1497 0.978 83 282
    3 B2 3444 3301 0.958 83 283
NH Imidogen 1 Σ 3262 3283 1.006 84 284
    1 Σ 3303 3314 1.003 84 285
SiH Silylidyne 1 Σ 2021 2043 1.011 85 286
BeCl beryllium chloride 1 Σ 832 847 1.018 86 287
HPO HPO 1 A' 2090 2095 1.003 87 288
    2 A' 1220 1188 0.974 87 289
    3 A' 1002 986 0.984 87 290
SiH2 silicon dihydride 1 A1 2042 1996 0.977 88 291
    2 A1 1022 999 0.977 88 292
    3 B2 2041 1993 0.976 88 293
SO Sulfur monoxide 1 Σ 1152 1151 0.999 89 294
    1 Σ 1152 1069 0.927 89 295
SH Mercapto radical 1 Σ 2666 2696 1.012 90 296
SiCl Clorosilylidyne 1 Σ 507 536 1.056 91 297
NF nitrogen fluoride 1 Σ 1150 1141 0.993 92 298
PH phosphorus monohydride 1 Σ 2337 2364 1.011 93 299
    1 Σ 2356 2415 1.025 93 300
AlH aluminum monohydride 1 Σ 1644 1682 1.023 94 301
HOF Hypofluorous acid 1 A' 3727 3537 0.949 95 302
    2 A' 1409 1393 0.989 95 303
    3 A' 981 886 0.903 95 304
HNO Nitrosyl hydride 1 A' 2856 2684 0.940 96 305
    2 A' 1668 1565 0.939 96 306
    3 A' 1562 1501 0.961 96 307
MgH magnesium monohydride 1 Σ 1463 1493 1.021 97 308
Li2 Lithium diatomic 1 Σg 342 351 1.027 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 772 760 0.985 100 312
    3 B2 1864 1807 0.969 100 313
HBS hydrogen boron sulfide 1 Σ 2838 2736 0.964 101 314
    2 Σ 1187 1172 0.988 101 315
MgF Magnesium monofluoride 1 Σ 695 712 1.024 102 316
MgCl magnesium monochloride 1 Σ 444 462 1.040 103 317
ClO Monochlorine monoxide 1 Σ 855 854 0.999 104 318
SCl sulfur monochloride 1 Σ 559 575 1.027 105 319
PF phosphorus monofluoride 1 Σ 820 847 1.032 106 320
SF Monosulfur monofluoride 1 Σ 820 838 1.021 107 321
PCl phosphorus chloride 1 Σ 528 577 1.092 108 322
PN Phosphorus mononitride 1 Σ 1403 1337 0.953 109 323
B2H6 Diborane 1 Ag 2619 2524 0.964 110 324
    2 Ag 2176 2104 0.967 110 325
    3 Ag 1207 1180 0.978 110 326
    4 Ag 801 794 0.992 110 327
    5 Au 852 833 0.978 110 328
    6 B1g 2693 2591 0.962 110 329
    7 B1g 942 915 0.972 110 330
    8 B1u 1993 1915 0.961 110 331
    9 B1u 992 973 0.980 110 332
    10 B2g 1859 1768 0.951 110 333
    11 B2g 895 850 0.950 110 334
    12 B2u 2707 2612 0.965 110 335
    13 B2u 956 950 0.994 110 336
    14 B2u 365 368 1.009 110 337
    15 B3g 1024 1012 0.989 110 338
    16 B3u 2606 2525 0.969 110 339
    17 B3u 1716 1602 0.933 110 340
    18 B3u 1200 1177 0.981 110 341
BCl boron monochloride 1 Σ 819 840 1.026 111 342
HBO Boron hydride oxide 1 Σ 2892 2850 0.986 112 343
    2 Σ 1867 1826 0.978 112 344
    3 Π 775 756 0.975 112 345
BeOH beryllium hydroxide 2 A' 1281 1246 0.972 113 346
S2 Sulfur diatomic 1 Σg 713 726 1.017 114 347
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.

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