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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 2880 2733 0.949 5 5
    1 Σ 3146     5 6
PH phosphorus monohydride 1 Σ 2377 2276 0.958 6 7
    1 Σ 2400 2319 0.966 6 8
OH Hydroxyl radical 1 Σ 3783 3570 0.944 7 9
CO Carbon monoxide 1 Σ 2245 2143 0.955 8 10
    1 Σ 2333     8 11
SO Sulfur monoxide 1 Σ 1212 1138 0.939 9 12
    1 Σ 1167 1054 0.903 9 13
HF Hydrogen fluoride 1 Σ 4190 3961 0.945 10 14
F2 Fluorine diatomic 1 Σg 1047 894 0.854 11 15
HCl Hydrogen chloride 1 Σ 3024 2886 0.954 12 16
AlCl Aluminum monochloride 1 Σ 475 478 1.005 13 17
BeH2 beryllium dihydride 2 Σu 2239 2159 0.965 14 18
    3 Πu 711 698 0.981 14 19
HCN Hydrogen cyanide 1 Σ 3472 3312 0.954 15 20
    2 Σ 2192 2089 0.953 15 21
    3 Π 751 712 0.948 15 22
H2O Water 1 A1 3870 3657 0.945 16 23
    2 A1 1661 1595 0.960 16 24
    3 B2 3977 3756 0.944 16 25
CO2 Carbon dioxide 1 Σg 1403 1333 0.950 17 26
    2 Σu 2438 2349 0.963 17 27
    3 Πu 696 667 0.958 17 28
H2S Hydrogen sulfide 1 A1 2741 2615 0.954 18 29
    2 A1 1222 1183 0.968 18 30
    3 B2 2756 2626 0.953 18 31
OCS Carbonyl sulfide 1 Σ 2156 2062 0.956 19 32
    2 Σ 886 859 0.969 19 33
    3 Π 544 520 0.956 19 34
SO2 Sulfur dioxide 1 A1 1229 1151 0.937 20 35
    2 A1 537 518 0.964 20 36
    3 B2 1426 1362 0.955 20 37
C2H2 Acetylene 1 Σg 3536 3374 0.954 21 38
    2 Σg 2058 1974 0.959 21 39
    3 Σu 3420 3289 0.962 21 40
    4 Πg 646 612 0.947 21 41
    5 Πu 774 730 0.943 21 42
NH3 Ammonia 1 A1 3507 3337 0.951 22 43
    2 A1 1065 950 0.892 22 44
    3 E 3637 3444 0.947 22 45
    4 E 1688 1627 0.964 22 46
H2CO Formaldehyde 1 A1 2968 2782 0.937 23 47
    2 A1 1839 1746 0.949 23 48
    3 A1 1554 1500 0.965 23 49
    4 B1 1211 1167 0.963 23 50
    5 B2 3041 2843 0.935 23 51
    6 B2 1284 1249 0.973 23 52
H2CS Thioformaldehyde 1 A1 3114 2971 0.954 24 53
    2 A1 1517 1456 0.960 24 54
    3 A1 1122 1059 0.944 24 55
    4 B1 1024 990 0.967 24 56
    5 B2 3203 3025 0.944 24 57
    6 B2 1015 991 0.977 24 58
BF3 Borane, trifluoro- 1 A1' 908 888 0.978 25 59
    2 A2" 705 691 0.981 25 60
    3 E' 1498 1449 0.967 25 61
    4 E' 485 480 0.990 25 62
NF3 Nitrogen trifluoride 1 A1 1103 1032 0.936 26 63
    2 A1 694 647 0.933 26 64
    3 E 1021 907 0.888 26 65
    4 E 529 492 0.931 26 66
AlF3 Aluminum trifluoride 1 A1' 701 690 0.985 27 67
    2 A2" 302 297 0.982 27 68
    3 E' 966 935 0.968 27 69
    4 E' 247 263 1.064 27 70
CH4 Methane 1 A1 3049 2917 0.957 28 71
    2 E 1586 1534 0.967 28 72
    3 T2 3170 3019 0.952 28 73
    4 T2 1365 1306 0.957 28 74
CH2F2 Methane, difluoro- 1 A1 3105 2948 0.949 29 75
    2 A1 1574 1508 0.958 29 76
    3 A1 1158 1111 0.959 29 77
    4 A1 543 529 0.973 29 78
    5 A2 1303 1262 0.969 29 79
    6 B1 3177 3014 0.949 29 80
    7 B1 1210 1178 0.973 29 81
    8 B2 1493 1435 0.961 29 82
    9 B2 1156 1090 0.943 29 83
CH3Cl Methyl chloride 1 A1 3102 2966 0.956 30 84
    2 A1 1413 1355 0.959 30 85
    3 A1 762 732 0.960 30 86
    4 E 3204 3042 0.950 30 87
    5 E 1515 1455 0.960 30 88
    6 E 1054 1015 0.963 30 89
CF2Cl2 difluorodichloromethane 1 A1 1165 1101 0.945 31 90
    2 A1 688 667 0.970 31 91
    3 A1 471 458 0.973 31 92
    4 A1 268 262 0.976 31 93
    5 A2 330 322 0.975 31 94
    6 B1 952 902 0.948 31 95
    7 B1 449 437 0.973 31 96
    8 B2 1231 1159 0.941 31 97
    9 B2 446 446 1.001 31 98
C2H4 Ethylene 1 Ag 3180 3026 0.952 32 99
    2 Ag 1708 1623 0.950 32 100
    3 Ag 1389 1342 0.966 32 101
    4 Au 1041 1023 0.982 32 102
    5 B1u 3159 2989 0.946 32 103
    6 B1u 1490 1444 0.969 32 104
    7 B2g 967 940 0.972 32 105
    8 B2u 3267 3105 0.951 32 106
    9 B2u 831 826 0.994 32 107
    10 B3g 3239 3086 0.953 32 108
    11 B3g 1256 1217 0.969 32 109
    12 B3u 985 949 0.964 32 110
CH2CF2 Ethene, 1,1-difluoro- 1 A1 3230 3070 0.950 33 111
    2 A1 1822 1728 0.949 33 112
    3 A1 1433 1360 0.949 33 113
    4 A1 960 926 0.964 33 114
    5 A1 561 550 0.980 33 115
    6 A2 735 714 0.972 33 116
    7 B1 851 803 0.943 33 117
    8 B1 639 611 0.956 33 118
    9 B2 3335 3154 0.946 33 119
    10 B2 1368 1302 0.952 33 120
    11 B2 985 955 0.970 33 121
    12 B2 443 438 0.989 33 122
C2H6 Ethane 1 A1g 3058 2954 0.966 34 123
    2 A1g 1448 1388 0.959 34 124
    3 A1g 1023 995 0.972 34 125
    4 A1u 311 289 0.930 34 126
    5 A2u 3058 2896 0.947 34 127
    6 A2u 1430 1379 0.964 34 128
    7 Eg 3119 2969 0.952 34 129
    8 Eg 1529 1468 0.960 34 130
    9 Eg 1241 1190 0.959 34 131
    10 Eu 3141 2985 0.950 34 132
    11 Eu 1531 1469 0.960 34 133
    12 Eu 832 822 0.988 34 134
C3H5 Allyl radical 1 A1 3285 3114 0.948 35 135
    2 A1 3190 3048 0.956 35 136
    4 A1 1550 1488 0.960 35 137
    5 A1 1303 1245 0.955 35 138
    6 A1 1060 1066 1.005 35 139
    7 A1 429 427 0.994 35 140
    9 A2 574 549 0.957 35 141
    10 B1 1043 968 0.928 35 142
    11 B1 848 802 0.945 35 143
    12 B1 548 518 0.945 35 144
    13 B2 3282 3105 0.946 35 145
    14 B2 3178 3016 0.949 35 146
    15 B2 1518 1463 0.964 35 147
    16 B2 1431 1389 0.970 35 148
    17 B2 1146 1182 1.031 35 149
C3H6 Cyclopropane 1 A1' 3179 3038 0.956 36 150
    2 A1' 1549 1479 0.955 36 151
    3 A1' 1231 1188 0.965 36 152
    4 A1" 1168 1126 0.964 36 153
    5 A2' 1102 1070 0.971 36 154
    6 A2" 3270 3103 0.949 36 155
    7 A2" 859 854 0.994 36 156
    8 E' 3168 3025 0.955 36 157
    9 E' 1493 1438 0.963 36 158
    10 E' 1071 1029 0.961 36 159
    11 E' 907 866 0.955 36 160
    12 E" 3250 3082 0.948 36 161
    13 E" 1226 1188 0.969 36 162
    14 E" 745 739 0.992 36 163
CH3CHClCH3 Propane, 2-chloro- 1 A' 3159 3005 0.951 37 164
    2 A' 3140 2955 0.941 37 165
    3 A' 3117 2927 0.939 37 166
    4 A' 3060 2878 0.940 37 167
    5 A' 1532 1472 0.961 37 168
    6 A' 1518 1454 0.958 37 169
    7 A' 1445 1390 0.962 37 170
    8 A' 1319 1270 0.963 37 171
    9 A' 1211 1163 0.960 37 172
    10 A' 1105 1065 0.964 37 173
    11 A' 922 888 0.963 37 174
    12 A' 659 633 0.961 37 175
    13 A' 426 418 0.981 37 176
    14 A' 340 336 0.989 37 177
    15 A' 274 253 0.923 37 178
    16 A" 3154 2997 0.950 37 179
    17 A" 3133 2985 0.953 37 180
    18 A" 3057 2947 0.964 37 181
    19 A" 1511 1472 0.974 37 182
    20 A" 1507 1454 0.965 37 183
    21 A" 1433 1377 0.961 37 184
    22 A" 1386 1334 0.963 37 185
    23 A" 1174 1123 0.957 37 186
    24 A" 974 972 0.997 37 187
    25 A" 955 936 0.980 37 188
    26 A" 328 317 0.968 37 189
    27 A" 243 276 1.135 37 190

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