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

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