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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCD/aug-cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.957 ± 0.017 39 208 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4413 4161 0.943 1 1
LiH Lithium Hydride 1 Σ 1391 1360 0.977 2 2
Li2 Lithium diatomic 1 Σg 346 346 1.001 3 3
Na2 Sodium diatomic 1 Σg 153 158 1.034 4 4
CH Methylidyne 1 Σ 3146     5 5
PH phosphorus monohydride 1 Σ 2377 2276 0.958 6 6
    1 Σ 2400 2319 0.966 6 7
OH Hydroxyl radical 1 Σ 3783 3570 0.944 7 8
CO Carbon monoxide 1 Σ 2245 2143 0.955 8 9
SO Sulfur monoxide 1 Σ 1212 1138 0.939 9 10
    1 Σ 1167 1054 0.903 9 11
HF Hydrogen fluoride 1 Σ 4190 3961 0.945 10 12
F2 Fluorine diatomic 1 Σg 1047 894 0.854 11 13
HCl Hydrogen chloride 1 Σ 3024 2886 0.954 12 14
AlCl Aluminum monochloride 1 Σ 475 478 1.005 13 15
BeH2 beryllium dihydride 2 Σu 2239 2159 0.965 14 16
    3 Πu 711 698 0.981 14 17
HCN Hydrogen cyanide 1 Σ 3472 3312 0.954 15 18
    2 Σ 2192 2089 0.953 15 19
    3 Π 751 712 0.948 15 20
H2O Water 1 A1 3870 3657 0.945 16 21
    2 A1 1661 1595 0.960 16 22
    3 B2 3977 3756 0.944 16 23
CO2 Carbon dioxide 1 Σg 1403 1333 0.950 17 24
    2 Σu 2438 2349 0.963 17 25
    3 Πu 696 667 0.958 17 26
H2S Hydrogen sulfide 1 A1 2741 2615 0.954 18 27
    2 A1 1222 1183 0.968 18 28
    3 B2 2756 2626 0.953 18 29
OCS Carbonyl sulfide 1 Σ 2156 2062 0.956 19 30
    2 Σ 886 859 0.969 19 31
    3 Π 544 520 0.956 19 32
SO2 Sulfur dioxide 1 A1 1229 1151 0.937 20 33
    2 A1 537 518 0.964 20 34
    3 B2 1426 1362 0.955 20 35
C2H2 Acetylene 1 Σg 3536 3374 0.954 21 36
    2 Σg 2058 1974 0.959 21 37
    3 Σu 3420 3289 0.962 21 38
    4 Πg 646 612 0.947 21 39
    5 Πu 774 730 0.943 21 40
NH3 Ammonia 1 A1 3507 3337 0.951 22 41
    2 A1 1065 950 0.892 22 42
    3 E 3637 3444 0.947 22 43
    4 E 1688 1627 0.964 22 44
H2CO Formaldehyde 1 A1 2967 2782 0.938 23 45
    2 A1 1840 1746 0.949 23 46
    3 A1 1554 1500 0.965 23 47
    4 B1 1212 1167 0.963 23 48
    5 B2 3039 2843 0.935 23 49
    6 B2 1284 1249 0.973 23 50
H2CS Thioformaldehyde 1 A1 3114 2971 0.954 24 51
    2 A1 1517 1456 0.960 24 52
    3 A1 1122 1059 0.944 24 53
    4 B1 1024 990 0.967 24 54
    5 B2 3203 3025 0.944 24 55
    6 B2 1015 991 0.977 24 56
BF3 Borane, trifluoro- 1 A1' 908 888 0.978 25 57
    2 A2" 705 691 0.981 25 58
    3 E' 1498 1449 0.967 25 59
    4 E' 485 480 0.990 25 60
NF3 Nitrogen trifluoride 1 A1 1103 1032 0.936 26 61
    2 A1 694 647 0.933 26 62
    3 E 1021 907 0.888 26 63
    4 E 529 492 0.931 26 64
AlF3 Aluminum trifluoride 1 A1' 701 690 0.985 27 65
    2 A2" 302 297 0.982 27 66
    3 E' 966 935 0.968 27 67
    4 E' 247 263 1.064 27 68
CH4 Methane 1 A1 3049 2917 0.957 28 69
    2 E 1586 1534 0.967 28 70
    3 T2 3170 3019 0.952 28 71
    4 T2 1365 1306 0.957 28 72
CH2F2 Methane, difluoro- 1 A1 3105 2948 0.949 29 73
    2 A1 1574 1508 0.958 29 74
    3 A1 1158 1111 0.959 29 75
    4 A1 543 529 0.973 29 76
    5 A2 1303 1262 0.969 29 77
    6 B1 3177 3014 0.949 29 78
    7 B1 1210 1178 0.973 29 79
    8 B2 1493 1435 0.961 29 80
    9 B2 1156 1090 0.943 29 81
CH3Cl Methyl chloride 1 A1 3102 2966 0.956 30 82
    2 A1 1413 1355 0.959 30 83
    3 A1 762 732 0.960 30 84
    4 E 3204 3042 0.950 30 85
    5 E 1515 1455 0.960 30 86
    6 E 1054 1015 0.963 30 87
CF2Cl2 difluorodichloromethane 1 A1 1165 1101 0.945 31 88
    2 A1 688 667 0.970 31 89
    3 A1 471 458 0.973 31 90
    4 A1 268 262 0.976 31 91
    5 A2 330 322 0.975 31 92
    6 B1 952 902 0.948 31 93
    7 B1 449 437 0.973 31 94
    8 B2 1231 1159 0.941 31 95
    9 B2 446 446 1.001 31 96
C2H4 Ethylene 1 Ag 3180 3026 0.952 32 97
    2 Ag 1708 1623 0.950 32 98
    3 Ag 1389 1342 0.966 32 99
    4 Au 1041 1023 0.982 32 100
    5 B1u 3159 2989 0.946 32 101
    6 B1u 1490 1444 0.969 32 102
    7 B2g 967 940 0.972 32 103
    8 B2u 3267 3105 0.951 32 104
    9 B2u 831 826 0.994 32 105
    10 B3g 3239 3086 0.953 32 106
    11 B3g 1256 1217 0.969 32 107
    12 B3u 985 949 0.964 32 108
CH2CF2 Ethene, 1,1-difluoro- 1 A1 3230 3070 0.950 33 109
    2 A1 1822 1728 0.949 33 110
    3 A1 1433 1360 0.949 33 111
    4 A1 960 926 0.964 33 112
    5 A1 561 550 0.980 33 113
    6 A2 735 714 0.972 33 114
    7 B1 851 803 0.943 33 115
    8 B1 639 611 0.956 33 116
    9 B2 3335 3154 0.946 33 117
    10 B2 1368 1302 0.952 33 118
    11 B2 985 955 0.970 33 119
    12 B2 443 438 0.989 33 120
C2H6 Ethane 1 A1g 3058 2954 0.966 34 121
    2 A1g 1448 1388 0.959 34 122
    3 A1g 1023 995 0.972 34 123
    4 A1u 311 289 0.930 34 124
    5 A2u 3058 2896 0.947 34 125
    6 A2u 1430 1379 0.964 34 126
    7 Eg 3119 2969 0.952 34 127
    8 Eg 1529 1468 0.960 34 128
    9 Eg 1241 1190 0.959 34 129
    10 Eu 3141 2985 0.950 34 130
    11 Eu 1531 1469 0.960 34 131
    12 Eu 832 822 0.988 34 132
C3H5 Allyl radical 1 A1 3285 3114 0.948 35 133
    2 A1 3190 3048 0.956 35 134
    4 A1 1550 1488 0.960 35 135
    5 A1 1303 1245 0.955 35 136
    6 A1 1060 1066 1.005 35 137
    7 A1 429 427 0.994 35 138
    9 A2 574 549 0.957 35 139
    10 B1 1043 968 0.928 35 140
    11 B1 848 802 0.945 35 141
    12 B1 548 518 0.945 35 142
    13 B2 3282 3105 0.946 35 143
    14 B2 3178 3016 0.949 35 144
    15 B2 1518 1463 0.964 35 145
    16 B2 1431 1389 0.970 35 146
    17 B2 1146 1182 1.031 35 147
C3H6 Cyclopropane 1 A1' 3179 3038 0.956 36 148
    2 A1' 1549 1479 0.955 36 149
    3 A1' 1231 1188 0.965 36 150
    4 A1" 1168 1126 0.964 36 151
    5 A2' 1102 1070 0.971 36 152
    6 A2" 3270 3103 0.949 36 153
    7 A2" 859 854 0.994 36 154
    8 E' 3168 3025 0.955 36 155
    9 E' 1493 1438 0.963 36 156
    10 E' 1071 1029 0.961 36 157
    11 E' 907 866 0.955 36 158
    12 E" 3250 3082 0.948 36 159
    13 E" 1226 1188 0.969 36 160
    14 E" 745 739 0.992 36 161
CH3CHClCH3 Propane, 2-chloro- 1 A' 3159 3005 0.951 37 162
    2 A' 3140 2955 0.941 37 163
    3 A' 3117 2927 0.939 37 164
    4 A' 3060 2878 0.940 37 165
    5 A' 1532 1472 0.961 37 166
    6 A' 1518 1454 0.958 37 167
    7 A' 1445 1390 0.962 37 168
    8 A' 1319 1270 0.963 37 169
    9 A' 1211 1163 0.960 37 170
    10 A' 1105 1065 0.964 37 171
    11 A' 922 888 0.963 37 172
    12 A' 659 633 0.961 37 173
    13 A' 426 418 0.981 37 174
    14 A' 340 336 0.989 37 175
    15 A' 274 253 0.923 37 176
    16 A" 3154 2997 0.950 37 177
    17 A" 3133 2985 0.953 37 178
    18 A" 3057 2947 0.964 37 179
    19 A" 1511 1472 0.974 37 180
    20 A" 1507 1454 0.965 37 181
    21 A" 1433 1377 0.961 37 182
    22 A" 1386 1334 0.963 37 183
    23 A" 1174 1123 0.957 37 184
    24 A" 974 972 0.997 37 185
    25 A" 955 936 0.980 37 186
    26 A" 328 317 0.968 37 187
    27 A" 243 276 1.135 37 188

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.

40 160 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