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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at HF/6-311+G(3df,2pd)
Scale factor How many Source
Molecules Vibrations
0.906 ± 0.024 24 114 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4586 4161 0.907 1 1
LiH Lithium Hydride 1 Σ 1429 1360 0.952 2 2
Na2 Sodium diatomic 1 Σg 156 158 1.012 3 3
N2 Nitrogen diatomic 1 Σg 2727 2330 0.855 4 4
OH Hydroxyl radical 1 Σ 4059 3570 0.879 5 5
CO Carbon monoxide 1 Σ 2430 2143 0.882 6 6
HF Hydrogen fluoride 1 Σ 4491 3961 0.882 7 7
F2 Fluorine diatomic 1 Σg 1266 894 0.706 8 8
HCl Hydrogen chloride 1 Σ 3143 2886 0.918 9 9
Cl2 Chlorine diatomic 1 Σg 616 554 0.899 10 10
H2O Water 1 A1 4147 3657 0.882 11 11
    2 A1 1745 1595 0.914 11 12
    3 B2 4247 3756 0.884 11 13
CO2 Carbon dioxide 1 Σg 1514 1333 0.881 12 14
    2 Σu 2560 2349 0.917 12 15
    3 Πu 780 667 0.855 12 16
SO2 Sulfur dioxide 1 A1 1387 1151 0.830 13 17
    2 A1 610 518 0.848 13 18
    3 B2 1593 1362 0.855 13 19
C2H2 Acetylene 1 Σg 3662 3374 0.921 14 20
    2 Σg 2208 1974 0.894 14 21
    3 Σu 3551 3289 0.926 14 22
    4 Πg 807 612 0.758 14 23
    5 Πu 865 730 0.844 14 24
NH3 Ammonia 1 A1 3695 3337 0.903 15 25
    2 A1 1096 950 0.866 15 26
    3 E 3820 3444 0.902 15 27
    4 E 1786 1627 0.911 15 28
H2CO Formaldehyde 1 A1 3085 2782 0.902 16 29
    2 A1 1998 1746 0.874 16 30
    3 A1 1649 1500 0.910 16 31
    4 B1 1337 1167 0.873 16 32
    5 B2 3155 2843 0.901 16 33
    6 B2 1369 1249 0.913 16 34
BF3 Borane, trifluoro- 1 A1' 951 888 0.934 17 35
    2 A2" 743 691 0.930 17 36
    3 E' 1558 1449 0.930 17 37
    4 E' 514 480 0.934 17 38
AlF3 Aluminum trifluoride 1 A1' 730 690 0.945 18 39
    2 A2" 312 297 0.953 18 40
    3 E' 1003 935 0.933 18 41
    4 E' 253 263 1.041 18 42
CH4 Methane 1 A1 3147 2917 0.927 19 43
    2 E 1667 1534 0.920 19 44
    3 T2 3245 3019 0.930 19 45
    4 T2 1455 1306 0.898 19 46
HCOOH Formic acid 1 A' 4106 3570 0.869 20 47
    2 A' 3239 2943 0.908 20 48
    3 A' 1995 1770 0.887 20 49
    4 A' 1533 1387 0.905 20 50
    5 A' 1419 1229 0.866 20 51
    6 A' 1258 1105 0.879 20 52
    7 A' 696 625 0.898 20 53
    8 A" 1192 1033 0.866 20 54
    9 A" 691 638 0.923 20 55
C2H4 Ethylene 1 Ag 3289 3026 0.920 21 56
    2 Ag 1815 1623 0.894 21 57
    3 Ag 1474 1342 0.911 21 58
    4 Au 1139 1023 0.898 21 59
    5 B1u 3268 2989 0.914 21 60
    6 B1u 1590 1444 0.908 21 61
    7 B2g 1105 940 0.850 21 62
    8 B2u 3370 3105 0.921 21 63
    9 B2u 891 826 0.927 21 64
    10 B3g 3342 3086 0.923 21 65
    11 B3g 1343 1217 0.906 21 66
    12 B3u 1085 949 0.875 21 67
C2H6 Ethane 1 A1g 3156 2954 0.936 22 68
    2 A1g 1549 1388 0.896 22 69
    3 A1g 1049 995 0.948 22 70
    4 A1u 328 289 0.881 22 71
    5 A2u 3149 2896 0.920 22 72
    6 A2u 1522 1379 0.906 22 73
    7 Eg 3193 2969 0.930 22 74
    8 Eg 1615 1468 0.909 22 75
    9 Eg 1323 1190 0.899 22 76
    10 Eu 3221 2985 0.927 22 77
    11 Eu 1619 1469 0.907 22 78
    12 Eu 881 822 0.933 22 79
C3H6 Cyclopropane 1 A1' 3274 3038 0.928 23 80
    2 A1' 1652 1479 0.895 23 81
    3 A1' 1282 1188 0.927 23 82
    4 A1" 1254 1126 0.898 23 83
    5 A2' 1212 1070 0.883 23 84
    6 A2" 3358 3103 0.924 23 85
    7 A2" 914 854 0.934 23 86
    8 E' 3260 3025 0.928 23 87
    9 E' 1594 1438 0.902 23 88
    10 E' 1169 1029 0.880 23 89
    11 E' 941 866 0.920 23 90
    12 E" 3334 3082 0.924 23 91
    13 E" 1314 1188 0.904 23 92
    14 E" 795 739 0.930 23 93
CH2CHCH3 Propene 1 A' 3353 3090 0.921 24 94
    2 A' 3280 3013 0.918 24 95
    3 A' 3269 2991 0.915 24 96
    4 A' 3226 2954 0.916 24 97
    5 A' 3151 2871 0.911 24 98
    6 A' 1840 1650 0.897 24 99
    7 A' 1611 1470 0.912 24 100
    8 A' 1571 1420 0.904 24 101
    9 A' 1529 1378 0.901 24 102
    10 A' 1429 1297 0.908 24 103
    11 A' 1285 1171 0.911 24 104
    12 A' 1021 963 0.944 24 105
    13 A' 974 920 0.945 24 106
    14 A' 454 428 0.942 24 107
    15 A" 3194 2954 0.925 24 108
    16 A" 1598 1443 0.903 24 109
    17 A" 1178 1045 0.887 24 110
    18 A" 1115 991 0.889 24 111
    19 A" 1064 912 0.858 24 112
    20 A" 641 578 0.901 24 113
    21 A" 219 174 0.793 24 114

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 70 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 50 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 30 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 10 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