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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
    1 Σg 1768 1733 0.981 6 8
OH Hydroxyl radical 1 Σ 3772 3570 0.946 7 9
BeO beryllium oxide 1 Σ 1434 1435 1.001 8 10
CO Carbon monoxide 1 Σ 2187 2143 0.980 9 11
    1 Σ 1821     9 12
MgO magnesium oxide 1 Σ 719 775 1.078 10 13
CS carbon monosulfide 1 Σ 1288 1272 0.988 11 14
HF Hydrogen fluoride 1 Σ 4204 3961 0.942 12 15
CF Fluoromethylidyne 1 Σ 1328 1286 0.968 13 16
F2 Fluorine diatomic 1 Σg 1009 894 0.886 14 17
NaF sodium fluoride 1 Σ 550 529 0.962 15 18
HCl Hydrogen chloride 1 Σ 3016 2886 0.957 16 19
LiCl lithium chloride 1 Σ 639 634 0.992 17 20
CCl carbon monochloride 1 Σ 869 866 0.997 18 21
NaCl Sodium Chloride 1 Σ 354 361 1.021 19 22
Cl2 Chlorine diatomic 1 Σg 562 554 0.987 20 23
MgH2 magnesium dihydride 2 Σu 1636 1572 0.961 21 24
    3 Πu 441 440 0.998 21 25
HCN Hydrogen cyanide 1 Σ 3467 3312 0.955 22 26
    2 Σ 2162 2089 0.966 22 27
    3 Π 741 712 0.960 22 28
HNC hydrogen isocyanide 1 Σ 3861 3653 0.946 23 29
    2 Σ 2088 2029 0.972 23 30
    3 Π 481 477 0.992 23 31
H2O Water 1 A1 3869 3657 0.945 24 32
    2 A1 1679 1595 0.950 24 33
    3 B2 3972 3756 0.946 24 34
LiOH lithium hydroxide 1 Σ 4050 3688 0.910 25 35
    2 Σ 959 871 0.907 25 36
    3 Π 323 257 0.793 25 37
HCO Formyl radical 1 A' 2725 2434 0.893 26 38
    2 A' 1911 1868 0.978 26 39
    3 A' 1141 1081 0.947 26 40
HO2 Hydroperoxy radical 1 A' 3719 3436 0.924 27 41
    2 A' 1451 1392 0.959 27 42
    3 A' 1130 1098 0.971 27 43
CO2 Carbon dioxide 1 Σg 1372 1333 0.971 28 44
    2 Σu 2414 2349 0.973 28 45
    3 Πu 678 667 0.984 28 46
NaOH sodium hydroxide 1 Σ 3995 3637 0.910 29 47
    2 Σ 572 540 0.945 29 48
    3 Π 227 300 1.319 29 49
SiO2 silicon dioxide 2 Σu 1449 1416 0.977 30 50
    3 Πu 300 273 0.907 30 51
H2S Hydrogen sulfide 1 A1 2736 2615 0.956 31 52
    2 A1 1219 1183 0.971 31 53
    3 B2 2750 2626 0.955 31 54
OCS Carbonyl sulfide 1 Σ 2118 2062 0.974 32 55
    2 Σ 870 859 0.987 32 56
    3 Π 533 520 0.975 32 57
SO2 Sulfur dioxide 1 A1 1195 1151 0.963 33 58
    2 A1 530 518 0.978 33 59
    3 B2 1394 1362 0.977 33 60
CF2 Difluoromethylene 1 A1 1271 1225 0.964 34 61
    2 A1 682 667 0.978 34 62
    3 B2 1181 1114 0.944 34 63
F2O Difluorine monoxide 1 A1 1008 928 0.921 35 64
    2 A1 494 461 0.934 35 65
    3 B2 951 831 0.873 35 66
ClCN chlorocyanogen 1 Σ 2304 2216 0.962 36 67
    2 Σ 747 744 0.996 36 68
    3 Π 395 378 0.956 36 69
ClNO Nitrosyl chloride 1 A' 1843 1800 0.976 37 70
    2 A' 630 596 0.945 37 71
    3 A' 356 332 0.932 37 72
C2H2 Acetylene 1 Σg 3533 3374 0.955 38 73
    2 Σg 2040 1974 0.968 38 74
    3 Σu 3429 3289 0.959 38 75
    4 Πg 617 612 0.991 38 76
    5 Πu 766 730 0.954 38 77
NH3 Ammonia 1 A1 3499 3337 0.954 39 78
    2 A1 1110 950 0.856 39 79
    3 E 3623 3444 0.951 39 80
    4 E 1700 1627 0.957 39 81
H2CO Formaldehyde 1 A1 2953 2782 0.942 40 82
    2 A1 1816 1746 0.961 40 83
    3 A1 1557 1500 0.964 40 84
    4 B1 1213 1167 0.962 40 85
    5 B2 3018 2843 0.942 40 86
    6 B2 1287 1249 0.971 40 87
H2O2 Hydrogen peroxide 1 A 3846 3599 0.936 41 88
    2 A 1465 1402 0.957 41 89
    3 A 969 877 0.905 41 90
    4 A 384 371 0.965 41 91
    5 B 3845 3608 0.938 41 92
    6 B 1354 1266 0.935 41 93
HNCO Isocyanic acid 1 A' 3721 3538 0.951 42 94
    2 A' 2328 2269 0.975 42 95
    3 A' 1329 1327 0.999 42 96
    4 A' 832 777 0.933 42 97
    5 A' 569 577 1.014 42 98
    6 A" 641 656 1.024 42 99
HNO2 Nitrous acid 1 A' 3834 3591 0.937 43 100
    2 A' 1782 1700 0.954 43 101
    3 A' 1348 1263 0.937 43 102
    4 A' 877 790 0.901 43 103
    5 A' 662 596 0.899 43 104
    6 A" 573 543 0.948 43 105
H2CS Thioformaldehyde 1 A1 3105 2971 0.957 44 106
    2 A1 1518 1456 0.959 44 107
    3 A1 1089 1059 0.972 44 108
    4 B1 1032 990 0.960 44 109
    5 B2 3193 3025 0.947 44 110
    6 B2 1014 991 0.977 44 111
SO3 Sulfur trioxide 1 A1' 1096 1065 0.972 45 112
    2 A2" 506 498 0.984 45 113
    3 E' 1428 1391 0.974 45 114
    4 E' 532 530 0.995 45 115
CF2O Carbonic difluoride 1 A1 2007 1928 0.961 46 116
    2 A1 1000 965 0.965 46 117
    3 A1 596 584 0.980 46 118
    4 B1 801 774 0.966 46 119
    5 B2 1318 1249 0.948 46 120
    6 B2 635 626 0.985 46 121
BF3 Borane, trifluoro- 1 A1' 905 888 0.981 47 122
    2 A2" 704 691 0.981 47 123
    3 E' 1503 1449 0.964 47 124
    4 E' 487 480 0.986 47 125
NF3 Nitrogen trifluoride 1 A1 1089 1032 0.948 48 126
    2 A1 680 647 0.951 48 127
    3 E 1002 907 0.905 48 128
    4 E 518 492 0.949 48 129
C2Cl2 dichloroacetylene 4 Πg 369 333 0.904 49 130
    5 Πu 180 172 0.955 49 131
CCl2O Phosgene 1 A1 1883 1827 0.970 50 132
    2 A1 584 567 0.971 50 133
    3 A1 306 285 0.932 50 134
    4 B1 598 580 0.970 50 135
    5 B2 883 849 0.962 50 136
    6 B2 453 440 0.970 50 137
CH4 Methane 1 A1 3047 2917 0.957 51 138
    2 E 1581 1534 0.971 51 139
    3 T2 3164 3019 0.954 51 140
    4 T2 1356 1306 0.963 51 141
HCOOH Formic acid 1 A' 3807 3570 0.938 52 142
    2 A' 3113 2943 0.946 52 143
    3 A' 1850 1770 0.957 52 144
    4 A' 1431 1387 0.969 52 145
    5 A' 1341 1229 0.917 52 146
    6 A' 1156 1105 0.956 52 147
    7 A' 639 625 0.978 52 148
    8 A" 1081 1033 0.956 52 149
    9 A" 677 638 0.943 52 150
CH3Cl Methyl chloride 1 A1 3097 2966 0.958 53 151
    2 A1 1400 1355 0.968 53 152
    3 A1 754 732 0.971 53 153
    4 E 3197 3042 0.952 53 154
    5 E 1506 1455 0.966 53 155
    6 E 1043 1015 0.973 53 156
CF2Cl2 difluorodichloromethane 1 A1 1162 1101 0.947 54 157
    2 A1 684 667 0.975 54 158
    3 A1 468 458 0.979 54 159
    4 A1 266 262 0.985 54 160
    5 A2 329 322 0.980 54 161
    6 B1 944 902 0.955 54 162
    7 B1 447 437 0.978 54 163
    8 B2 1233 1159 0.940 54 164
    9 B2 445 446 1.003 54 165
CCl4 Carbon tetrachloride 1 A1 470 459 0.976 55 166
    2 E 222 217 0.979 55 167
    3 T2 825 776 0.940 55 168
    4 T2 321 314 0.979 55 169
C2H4 Ethylene 1 Ag 3176 3026 0.953 56 170
    2 Ag 1700 1623 0.955 56 171
    3 Ag 1386 1342 0.968 56 172
    4 Au 1063 1023 0.962 56 173
    5 B1u 3156 2989 0.947 56 174
    6 B1u 1493 1444 0.967 56 175
    7 B2g 969 940 0.969 56 176
    8 B2u 3262 3105 0.952 56 177
    9 B2u 832 826 0.992 56 178
    10 B3g 3236 3086 0.954 56 179
    11 B3g 1255 1217 0.970 56 180
    12 B3u 986 949 0.963 56 181
CH3OH Methyl alcohol 1 A' 3900 3681 0.944 57 182
    2 A' 3142 3000 0.955 57 183
    3 A' 3026 2844 0.940 57 184
    4 A' 1536 1477 0.962 57 185
    5 A' 1503 1455 0.968 57 186
    6 A' 1405 1345 0.957 57 187
    7 A' 1109 1060 0.956 57 188
    8 A' 1080 1033 0.956 57 189
    9 A" 3080 2960 0.961 57 190
    10 A" 1520 1477 0.971 57 191
    11 A" 1193 1165 0.977 57 192
    12 A" 309 200 0.647 57 193
CH2CCH2 allene 1 A1 3166 3015 0.952 58 194
    2 A1 1507 1443 0.958 58 195
    3 A1 1100 1073 0.975 58 196
    4 B1 884 865 0.978 58 197
    5 B2 3165 3007 0.950 58 198
    6 B2 2050 1957 0.954 58 199
    7 B2 1453 1398 0.962 58 200
    8 E 3247 3086 0.950 58 201
    9 E 1031 999 0.969 58 202
    10 E 882 841 0.954 58 203
    11 E 361 355 0.985 58 204
CH3NH2 methyl amine 1 A' 3529 3361 0.953 59 205
    2 A' 3094 2961 0.957 59 206
    3 A' 3013 2820 0.936 59 207
    4 A' 1684 1623 0.964 59 208
    5 A' 1521 1473 0.968 59 209
    6 A' 1474 1430 0.970 59 210
    7 A' 1198 1130 0.943 59 211
    8 A' 1081 1044 0.966 59 212
    9 A' 884 780 0.883 59 213
    10 A" 3608 3427 0.950 59 214
    11 A" 3128 2985 0.954 59 215
    12 A" 1540 1485 0.964 59 216
    13 A" 1371 1335 0.974 59 217
    14 A" 985     59 218
    15 A" 309 268 0.867 59 219
C3H6 Cyclopropane 1 A1' 3175 3038 0.957 60 220
    2 A1' 1547 1479 0.956 60 221
    3 A1' 1230 1188 0.966 60 222
    4 A1" 1174 1126 0.959 60 223
    5 A2' 1109 1070 0.965 60 224
    6 A2" 3264 3103 0.951 60 225
    7 A2" 865 854 0.987 60 226
    8 E' 3163 3025 0.956 60 227
    9 E' 1493 1438 0.963 60 228
    10 E' 1078 1029 0.954 60 229
    11 E' 906 866 0.956 60 230
    12 E" 3244 3082 0.950 60 231
    13 E" 1231 1188 0.965 60 232
    14 E" 750 739 0.986 60 233
CH2CHCH3 Propene 1 A' 3248 3090 0.951 61 234
    2 A' 3171 3013 0.950 61 235
    3 A' 3157 2991 0.947 61 236
    4 A' 3129 2954 0.944 61 237
    5 A' 3047 2871 0.942 61 238
    6 A' 1728 1650 0.955 61 239
    7 A' 1515 1470 0.970 61 240
    8 A' 1472 1420 0.965 61 241
    9 A' 1425 1378 0.967 61 242
    10 A' 1337 1297 0.970 61 243
    11 A' 1205 1171 0.972 61 244
    12 A' 953 963 1.010 61 245
    13 A' 940 920 0.978 61 246
    14 A' 424 428 1.010 61 247
    15 A" 3105 2954 0.951 61 248
    16 A" 1502 1443 0.961 61 249
    17 A" 1084 1045 0.964 61 250
    18 A" 1032 991 0.960 61 251
    19 A" 949 912 0.961 61 252
    20 A" 594 578 0.973 61 253
    21 A" 202 174 0.860 61 254

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