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III.B.3.b. (XIII.C.2.)

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
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
SO2 Sulfur dioxide 1 A1 1050 1151 1.097 1 1
    2 A1 443 518 1.169 1 2
    3 B2 2047 1362 0.665 1 3
HF Hydrogen fluoride 1 Σ 4144 4138 0.999 2 4
HCl Hydrogen chloride 1 Σ 3213 2991 0.931 3 5
LiH Lithium Hydride 1 Σ 1781 1405 0.789 4 6
CO Carbon monoxide 1 Σ 2010 2170 1.080 5 7
C3H6 Cyclopropane 1 A1' 3473 3038 0.875 6 8
N2 Nitrogen diatomic 1 Σg 1669 2359 1.413 7 9
H2O Water 3 B2 4057 3756 0.926 8 10
    2 A1 2076 1595 0.768 8 11
    1 A1 3798 3657 0.963 8 12
F2 Fluorine diatomic 1 Σg 1464 917 0.626 9 13
H2CO Formaldehyde 6 B2 1297 1249 0.963 10 14
    5 B2 3400 2843 0.836 10 15
    4 B1 1130 1167 1.033 10 16
    3 A1 1607 1500 0.933 10 17
    2 A1 1800 1746 0.970 10 18
    1 A1 3267 2782 0.852 10 19
C2H4 Ethylene 12 B3u 1039 949 0.913 11 20
    11 B3g 1356 1217 0.898 11 21
    10 B3g 3612 3086 0.854 11 22
    9 B2u 880 826 0.938 11 23
    8 B2u 3625 3105 0.857 11 24
    7 B2g 1000 940 0.939 11 25
    6 B1u 1633 1444 0.884 11 26
    5 B1u 3451 2989 0.866 11 27
    4 Au 1188 1023 0.861 11 28
    3 Ag 1485 1342 0.904 11 29
    2 Ag 1810 1623 0.897 11 30
    1 Ag 3481 3026 0.869 11 31
C3H6 Cyclopropane 14 E" 826 739 0.895 12 32
    13 E" 1340 1188 0.886 12 33
    12 E" 3613 3082 0.853 12 34
    11 E' 1030 866 0.841 12 35
    10 E' 1269 1029 0.811 12 36
    9 E' 1644 1438 0.875 12 37
    8 E' 3457 3025 0.875 12 38
    7 A2" 902 854 0.946 12 39
    6 A2" 3619 3103 0.857 12 40
    5 A2' 1244 1070 0.860 12 41
    4 A1" 1302 1126 0.865 12 42
    3 A1' 1335 1188 0.890 12 43
    2 A1' 1695 1479 0.872 12 44
CO2 Carbon dioxide 3 Πu 478 667 1.395 13 45
    2 Σu 2598 2349 0.904 13 46
    1 Σg 1276 1333 1.045 13 47
H2 Hydrogen diatomic 1 Σg 5245 4401 0.839 14 48
CH Methylidyne 1 Σ 3577 3145 0.879 15 49
C6H6 Fulvene 30 B2 350 350 1.000 16 50
    29 B2 852 795 0.933 16 51
    28 B2 1035 952 0.920 16 52
    27 B2 1183 1077 0.910 16 53
    26 B2 1347 1232 0.914 16 54
    25 B2 1456 1314 0.902 16 55
    24 B2 1714 1550 0.905 16 56
    23 B2 3525 3075 0.872 16 57
    22 B2 3552 3104 0.874 16 58
    21 B2 3600     16 59
    20 B1 201     16 60
    19 B1 641 613 0.956 16 61
    18 B1 836 769 0.920 16 62
    17 B1 974 907 0.931 16 63
    16 B1 1014 926 0.913 16 64
    15 A2 524 494 0.943 16 65
    14 A2 769 666 0.866 16 66
    13 A2 858     16 67
    12 A2 999     16 68
    11 A1 701 641 0.914 16 69
    10 A1 948 894 0.943 16 70
    9 A1 1062 986 0.929 16 71
    8 A1 1182 1082 0.916 16 72
    7 A1 1486 1342 0.903 16 73
    6 A1 1586 1449 0.913 16 74
    5 A1 1653 1486 0.899 16 75
    4 A1 1792 1632 0.911 16 76
    3 A1 3444 3008 0.873 16 77
    2 A1 3531 3051 0.864 16 78
    1 A1 3560 3088 0.868 16 79
C3H2N2 Malononitrile 15 B2 353 366 1.036 17 80
    14 B2 997 982 0.985 17 81
    13 B2 1460 1318 0.903 17 82
    12 B2 2110 2275 1.078 17 83
    11 B1 324 337 1.040 17 84
    10 B1 1038 933 0.899 17 85
    9 B1 3497 2968 0.849 17 86
    8 A2 343 367 1.069 17 87
    7 A2 1347 1220 0.906 17 88
    6 A1 141 167 1.182 17 89
    5 A1 577 582 1.009 17 90
    4 A1 918 890 0.969 17 91
    3 A1 1648 1395 0.847 17 92
    2 A1 2103 2275 1.082 17 93
    1 A1 3393 2935 0.865 17 94
C2H2 Acetylene 5 Πu 837 730 0.872 18 95
    4 Πg 715 612 0.856 18 96
    3 Σu 3677 3289 0.894 18 97
    2 Σg 2091 1974 0.944 18 98
    1 Σg 3791 3374 0.890 18 99
CH4 Methane 4 T2 1577 1306 0.828 19 100
    3 T2 3602 3019 0.838 19 101
    2 E 1810 1534 0.848 19 102
    1 A1 3344 2917 0.872 19 103
NH3 Ammonia 1 A1 3539 3337 0.943 20 104
    2 A1 1460 950 0.651 20 105
    3 E 3814 3444 0.903 20 106
    4 E 1991 1627 0.817 20 107

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.

35
30
25
20
15
10
5
0
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