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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.956 ± 0.023 62 258 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4409 4161 0.944 1 1
LiH Lithium Hydride 1 Σ 1395 1360 0.975 2 2
NaH sodium hydride 1 Σ 1132 1133 1.001 3 3
CH Methylidyne 1 Σ 2852 2733 0.958 4 4
    1 Σ 3134     4 5
CN Cyano radical 1 Σ 2177 2042 0.938 5 6
N2 Nitrogen diatomic 1 Σg 2141 2330 1.088 6 7
OH Hydroxyl radical 1 Σ 3772 3570 0.946 7 8
BeO beryllium oxide 1 Σ 1434 1435 1.001 8 9
CO Carbon monoxide 1 Σ 2187 2143 0.980 9 10
MgO magnesium oxide 1 Σ 719 775 1.078 10 11
CS carbon monosulfide 1 Σ 1288 1272 0.988 11 12
HF Hydrogen fluoride 1 Σ 4204 3961 0.942 12 13
CF Fluoromethylidyne 1 Σ 1328 1286 0.968 13 14
F2 Fluorine diatomic 1 Σg 1009 894 0.886 14 15
NaF sodium fluoride 1 Σ 550 529 0.962 15 16
HCl Hydrogen chloride 1 Σ 3016 2886 0.957 16 17
LiCl lithium chloride 1 Σ 639 634 0.992 17 18
CCl carbon monochloride 1 Σ 869 866 0.997 18 19
NaCl Sodium Chloride 1 Σ 354 361 1.021 19 20
Cl2 Chlorine diatomic 1 Σg 562 554 0.987 20 21
MgH2 magnesium dihydride 2 Σu 1636 1572 0.961 21 22
    3 Πu 441 440 0.998 21 23
HCN Hydrogen cyanide 1 Σ 3467 3312 0.955 22 24
    2 Σ 2162 2089 0.966 22 25
    3 Π 741 712 0.960 22 26
HNC hydrogen isocyanide 1 Σ 3861 3653 0.946 23 27
    2 Σ 2088 2029 0.972 23 28
    3 Π 481 477 0.992 23 29
H2O Water 1 A1 3869 3657 0.945 24 30
    2 A1 1679 1595 0.950 24 31
    3 B2 3972 3756 0.946 24 32
LiOH lithium hydroxide 1 Σ 4050 3688 0.910 25 33
    2 Σ 959 871 0.907 25 34
    3 Π 323 257 0.793 25 35
HCO Formyl radical 1 A' 2725 2434 0.893 26 36
    2 A' 1911 1868 0.978 26 37
    3 A' 1141 1081 0.947 26 38
HO2 Hydroperoxy radical 1 A' 3719 3436 0.924 27 39
    2 A' 1451 1392 0.959 27 40
    3 A' 1130 1098 0.971 27 41
CO2 Carbon dioxide 1 Σg 1372 1333 0.971 28 42
    2 Σu 2414 2349 0.973 28 43
    3 Πu 678 667 0.984 28 44
NaOH sodium hydroxide 1 Σ 3995 3637 0.910 29 45
    2 Σ 572 540 0.945 29 46
    3 Π 227 300 1.319 29 47
SiO2 silicon dioxide 2 Σu 1449 1416 0.977 30 48
    3 Πu 300 273 0.907 30 49
H2S Hydrogen sulfide 1 A1 2736 2615 0.956 31 50
    2 A1 1219 1183 0.971 31 51
    3 B2 2750 2626 0.955 31 52
OCS Carbonyl sulfide 1 Σ 2118 2062 0.974 32 53
    2 Σ 870 859 0.987 32 54
    3 Π 533 520 0.975 32 55
SO2 Sulfur dioxide 1 A1 1195 1151 0.963 33 56
    2 A1 530 518 0.978 33 57
    3 B2 1394 1362 0.977 33 58
CF2 Difluoromethylene 1 A1 1271 1225 0.964 34 59
    2 A1 682 667 0.978 34 60
    3 B2 1181 1114 0.944 34 61
F2O Difluorine monoxide 1 A1 1008 928 0.921 35 62
    2 A1 494 461 0.934 35 63
    3 B2 951 831 0.873 35 64
ClCN chlorocyanogen 1 Σ 2304 2216 0.962 36 65
    2 Σ 747 744 0.996 36 66
    3 Π 395 378 0.956 36 67
ClNO Nitrosyl chloride 1 A' 1843 1800 0.976 37 68
    2 A' 630 596 0.945 37 69
    3 A' 356 332 0.932 37 70
C2H2 Acetylene 1 Σg 3533 3374 0.955 38 71
    2 Σg 2040 1974 0.968 38 72
    3 Σu 3429 3289 0.959 38 73
    4 Πg 617 612 0.991 38 74
    5 Πu 766 730 0.954 38 75
NH3 Ammonia 1 A1 3499 3337 0.954 39 76
    2 A1 1110 950 0.856 39 77
    3 E 3623 3444 0.951 39 78
    4 E 1700 1627 0.957 39 79
H2CO Formaldehyde 1 A1 2951 2782 0.943 40 80
    2 A1 1817 1746 0.961 40 81
    3 A1 1557 1500 0.964 40 82
    4 B1 1213 1167 0.962 40 83
    5 B2 3016 2843 0.943 40 84
    6 B2 1287 1249 0.971 40 85
H2O2 Hydrogen peroxide 1 A 3846 3599 0.936 41 86
    2 A 1465 1402 0.957 41 87
    3 A 969 877 0.905 41 88
    4 A 384 371 0.965 41 89
    5 B 3845 3608 0.938 41 90
    6 B 1354 1266 0.935 41 91
HNCO Isocyanic acid 1 A' 3721 3538 0.951 42 92
    2 A' 2328 2269 0.975 42 93
    3 A' 1329 1327 0.999 42 94
    4 A' 832 777 0.933 42 95
    5 A' 569 577 1.014 42 96
    6 A" 641 656 1.024 42 97
HNO2 Nitrous acid 1 A' 3834 3591 0.937 43 98
    2 A' 1782 1700 0.954 43 99
    3 A' 1348 1263 0.937 43 100
    4 A' 877 790 0.901 43 101
    5 A' 662 596 0.899 43 102
    6 A" 573 543 0.948 43 103
H2CS Thioformaldehyde 1 A1 3105 2971 0.957 44 104
    2 A1 1518 1456 0.959 44 105
    3 A1 1089 1059 0.972 44 106
    4 B1 1032 990 0.960 44 107
    5 B2 3193 3025 0.947 44 108
    6 B2 1014 991 0.977 44 109
SO3 Sulfur trioxide 1 A1' 1096 1065 0.972 45 110
    2 A2" 506 498 0.984 45 111
    3 E' 1428 1391 0.974 45 112
    4 E' 532 530 0.995 45 113
CF2O Carbonic difluoride 1 A1 2007 1928 0.961 46 114
    2 A1 1000 965 0.965 46 115
    3 A1 596 584 0.980 46 116
    4 B1 801 774 0.966 46 117
    5 B2 1318 1249 0.948 46 118
    6 B2 635 626 0.985 46 119
BF3 Borane, trifluoro- 1 A1' 905 888 0.981 47 120
    2 A2" 704 691 0.981 47 121
    3 E' 1503 1449 0.964 47 122
    4 E' 487 480 0.986 47 123
NF3 Nitrogen trifluoride 1 A1 1089 1032 0.948 48 124
    2 A1 680 647 0.951 48 125
    3 E 1002 907 0.905 48 126
    4 E 518 492 0.949 48 127
C2Cl2 dichloroacetylene 4 Πg 369 333 0.904 49 128
    5 Πu 180 172 0.955 49 129
CCl2O Phosgene 1 A1 1883 1827 0.970 50 130
    2 A1 584 567 0.971 50 131
    3 A1 306 285 0.932 50 132
    4 B1 598 580 0.970 50 133
    5 B2 883 849 0.962 50 134
    6 B2 453 440 0.970 50 135
CH4 Methane 1 A1 3047 2917 0.957 51 136
    2 E 1581 1534 0.971 51 137
    3 T2 3164 3019 0.954 51 138
    4 T2 1356 1306 0.963 51 139
HCOOH Formic acid 1 A' 3807 3570 0.938 52 140
    2 A' 3113 2943 0.946 52 141
    3 A' 1850 1770 0.957 52 142
    4 A' 1431 1387 0.969 52 143
    5 A' 1341 1229 0.917 52 144
    6 A' 1156 1105 0.956 52 145
    7 A' 639 625 0.978 52 146
    8 A" 1081 1033 0.956 52 147
    9 A" 677 638 0.943 52 148
CH3Cl Methyl chloride 1 A1 3097 2966 0.958 53 149
    2 A1 1400 1355 0.968 53 150
    3 A1 754 732 0.971 53 151
    4 E 3197 3042 0.952 53 152
    5 E 1506 1455 0.966 53 153
    6 E 1043 1015 0.973 53 154
CF2Cl2 difluorodichloromethane 1 A1 1163 1101 0.947 54 155
    2 A1 684 667 0.975 54 156
    3 A1 468 458 0.979 54 157
    4 A1 266 262 0.985 54 158
    5 A2 328 322 0.981 54 159
    6 B1 943 902 0.956 54 160
    7 B1 447 437 0.978 54 161
    8 B2 1235 1159 0.938 54 162
    9 B2 444 446 1.004 54 163
CCl4 Carbon tetrachloride 1 A1 470 459 0.976 55 164
    2 E 222 217 0.979 55 165
    3 T2 825 776 0.940 55 166
    4 T2 321 314 0.979 55 167
C2H4 Ethylene 1 Ag 3176 3026 0.953 56 168
    2 Ag 1700 1623 0.955 56 169
    3 Ag 1386 1342 0.968 56 170
    4 Au 1063 1023 0.962 56 171
    5 B1u 3156 2989 0.947 56 172
    6 B1u 1493 1444 0.967 56 173
    7 B2g 969 940 0.969 56 174
    8 B2u 3262 3105 0.952 56 175
    9 B2u 832 826 0.992 56 176
    10 B3g 3236 3086 0.954 56 177
    11 B3g 1255 1217 0.970 56 178
    12 B3u 986 949 0.963 56 179
CH3OH Methyl alcohol 1 A' 3900 3681 0.944 57 180
    2 A' 3142 3000 0.955 57 181
    3 A' 3026 2844 0.940 57 182
    4 A' 1536 1477 0.962 57 183
    5 A' 1503 1455 0.968 57 184
    6 A' 1405 1345 0.957 57 185
    7 A' 1109 1060 0.956 57 186
    8 A' 1080 1033 0.956 57 187
    9 A" 3080 2960 0.961 57 188
    10 A" 1520 1477 0.971 57 189
    11 A" 1193 1165 0.977 57 190
    12 A" 309 200 0.647 57 191
CH2CCH2 allene 1 A1 3166 3015 0.952 58 192
    2 A1 1507 1443 0.958 58 193
    3 A1 1100 1073 0.975 58 194
    4 B1 884 865 0.978 58 195
    5 B2 3165 3007 0.950 58 196
    6 B2 2050 1957 0.954 58 197
    7 B2 1453 1398 0.962 58 198
    8 E 3247 3086 0.950 58 199
    9 E 1031 999 0.969 58 200
    10 E 882 841 0.954 58 201
    11 E 361 355 0.985 58 202
CH3NH2 methyl amine 1 A' 3529 3361 0.953 59 203
    2 A' 3094 2961 0.957 59 204
    3 A' 3013 2820 0.936 59 205
    4 A' 1684 1623 0.964 59 206
    5 A' 1521 1473 0.968 59 207
    6 A' 1474 1430 0.970 59 208
    7 A' 1198 1130 0.943 59 209
    8 A' 1081 1044 0.966 59 210
    9 A' 884 780 0.883 59 211
    10 A" 3608 3427 0.950 59 212
    11 A" 3128 2985 0.954 59 213
    12 A" 1540 1485 0.964 59 214
    13 A" 1371 1335 0.974 59 215
    14 A" 985     59 216
    15 A" 309 268 0.867 59 217
C3H6 Cyclopropane 1 A1' 3175 3038 0.957 60 218
    2 A1' 1547 1479 0.956 60 219
    3 A1' 1230 1188 0.966 60 220
    4 A1" 1174 1126 0.959 60 221
    5 A2' 1109 1070 0.965 60 222
    6 A2" 3264 3103 0.951 60 223
    7 A2" 865 854 0.987 60 224
    8 E' 3163 3025 0.956 60 225
    9 E' 1493 1438 0.963 60 226
    10 E' 1078 1029 0.954 60 227
    11 E' 906 866 0.956 60 228
    12 E" 3244 3082 0.950 60 229
    13 E" 1231 1188 0.965 60 230
    14 E" 750 739 0.986 60 231
CH2CHCH3 Propene 1 A' 3248 3090 0.951 61 232
    2 A' 3171 3013 0.950 61 233
    3 A' 3157 2991 0.947 61 234
    4 A' 3129 2954 0.944 61 235
    5 A' 3047 2871 0.942 61 236
    6 A' 1728 1650 0.955 61 237
    7 A' 1515 1470 0.970 61 238
    8 A' 1472 1420 0.965 61 239
    9 A' 1425 1378 0.967 61 240
    10 A' 1337 1297 0.970 61 241
    11 A' 1205 1171 0.972 61 242
    12 A' 953 963 1.010 61 243
    13 A' 940 920 0.978 61 244
    14 A' 424 428 1.010 61 245
    15 A" 3105 2954 0.951 61 246
    16 A" 1502 1443 0.961 61 247
    17 A" 1084 1045 0.964 61 248
    18 A" 1032 991 0.960 61 249
    19 A" 949 912 0.961 61 250
    20 A" 594 578 0.973 61 251
    21 A" 202 174 0.860 61 252

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.

40 180 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 160 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 140 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 80 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 60 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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