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

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