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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP2=FULL/STO-3G
Scale factor How many Source
Molecules Vibrations
0.889 ± 0.073 19 103 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 5245 4161 0.793 1 1
LiH Lithium Hydride 1 Σ 1781 1360 0.763 2 2
CH Methylidyne 1 Σ 3114 2733 0.878 3 3
    1 Σ 3577     3 4
N2 Nitrogen diatomic 1 Σg 1669 2330 1.396 4 5
    1 Σg 1207 1733 1.436 4 6
CO Carbon monoxide 1 Σ 2010 2143 1.067 5 7
    1 Σ 1463     5 8
HF Hydrogen fluoride 1 Σ 4145 3961 0.956 6 9
F2 Fluorine diatomic 1 Σg 1464 894 0.611 7 10
HCl Hydrogen chloride 1 Σ 3213 2886 0.898 8 11
H2O Water 1 A1 3799 3657 0.963 9 12
    2 A1 2076 1595 0.768 9 13
    3 B2 4058 3756 0.926 9 14
CO2 Carbon dioxide 1 Σg 1276 1333 1.045 10 15
    2 Σu 2598 2349 0.904 10 16
    3 Πu 478 667 1.395 10 17
SO2 Sulfur dioxide 1 A1 1050 1151 1.097 11 18
    2 A1 443 518 1.169 11 19
    3 B2 2046 1362 0.666 11 20
C2H2 Acetylene 1 Σg 3791 3374 0.890 12 21
    2 Σg 2090 1974 0.945 12 22
    3 Σu 3678 3289 0.894 12 23
    4 Πg 715 612 0.856 12 24
    5 Πu 837 730 0.872 12 25
NH3 Ammonia 1 A1 3539 3337 0.943 13 26
    2 A1 1460 950 0.651 13 27
    3 E 3814 3444 0.903 13 28
    4 E 1991 1627 0.817 13 29
H2CO Formaldehyde 1 A1 3267 2782 0.852 14 30
    2 A1 1800 1746 0.970 14 31
    3 A1 1607 1500 0.933 14 32
    4 B1 1130 1167 1.033 14 33
    5 B2 3400 2843 0.836 14 34
    6 B2 1296 1249 0.963 14 35
CH4 Methane 1 A1 3344 2917 0.872 15 36
    2 E 1810 1534 0.848 15 37
    3 T2 3602 3019 0.838 15 38
    4 T2 1577 1306 0.828 15 39
C2H4 Ethylene 1 Ag 3481 3026 0.869 16 40
    2 Ag 1810 1623 0.897 16 41
    3 Ag 1485 1342 0.904 16 42
    4 Au 1188 1023 0.861 16 43
    5 B1u 3451 2989 0.866 16 44
    6 B1u 1633 1444 0.884 16 45
    7 B2g 1000 940 0.939 16 46
    8 B2u 3625 3105 0.857 16 47
    9 B2u 880 826 0.938 16 48
    10 B3g 3612 3086 0.854 16 49
    11 B3g 1356 1217 0.898 16 50
    12 B3u 1039 949 0.913 16 51
C3H2N2 Malononitrile 1 A1 3393 2935 0.865 17 52
    2 A1 2103 2275 1.082 17 53
    3 A1 1648 1395 0.847 17 54
    4 A1 918 890 0.969 17 55
    5 A1 577 582 1.009 17 56
    6 A1 141 167 1.182 17 57
    7 A2 1347 1220 0.906 17 58
    8 A2 343 367 1.069 17 59
    9 B1 3497 2968 0.849 17 60
    10 B1 1038 933 0.899 17 61
    11 B1 324 337 1.040 17 62
    12 B2 2110 2275 1.078 17 63
    13 B2 1460 1318 0.903 17 64
    14 B2 997 982 0.985 17 65
    15 B2 353 366 1.036 17 66
C3H6 Cyclopropane 1 A1' 3472 3038 0.875 18 67
    2 A1' 1695 1479 0.872 18 68
    3 A1' 1335 1188 0.890 18 69
    4 A1" 1302 1126 0.865 18 70
    5 A2' 1245 1070 0.860 18 71
    6 A2" 3619 3103 0.857 18 72
    7 A2" 903 854 0.946 18 73
    8 E' 3457 3025 0.875 18 74
    9 E' 1644 1438 0.875 18 75
    10 E' 1269 1029 0.811 18 76
    11 E' 1030 866 0.841 18 77
    12 E" 3613 3082 0.853 18 78
    13 E" 1340 1188 0.886 18 79
    14 E" 826 739 0.895 18 80
C6H6 Fulvene 1 A1 3560 3088 0.868 19 81
    2 A1 3531 3051 0.864 19 82
    3 A1 3444 3008 0.873 19 83
    4 A1 1792 1632 0.911 19 84
    5 A1 1653 1486 0.899 19 85
    6 A1 1586 1449 0.913 19 86
    7 A1 1486 1342 0.903 19 87
    8 A1 1182 1082 0.916 19 88
    9 A1 1062 986 0.929 19 89
    10 A1 948 894 0.943 19 90
    11 A1 701 641 0.914 19 91
    12 A2 999     19 92
    13 A2 858     19 93
    14 A2 769 666 0.866 19 94
    15 A2 524 494 0.943 19 95
    16 B1 1014 926 0.913 19 96
    17 B1 974 907 0.931 19 97
    18 B1 836 769 0.920 19 98
    19 B1 641 613 0.956 19 99
    20 B1 201     19 100
    21 B2 3600     19 101
    22 B2 3552 3104 0.874 19 102
    23 B2 3525 3075 0.872 19 103
    24 B2 1714 1550 0.905 19 104
    25 B2 1456 1314 0.902 19 105
    26 B2 1347 1232 0.914 19 106
    27 B2 1183 1077 0.910 19 107
    28 B2 1035 952 0.920 19 108
    29 B2 852 795 0.933 19 109
    30 B2 350 350 1.000 19 110

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 35 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 25 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 15 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 5 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