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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at B2PLYP/cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.957 ± 0.014 16 42 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4462 4161 0.933 1 1
LiH Lithium Hydride 1 Σ 1422 1360 0.957 2 2
Na2 Sodium diatomic 1 Σg 159 158 0.989 3 3
N2 Nitrogen diatomic 1 Σg 2347 2330 0.993 4 4
OH Hydroxyl radical 1 Σ 3752 3570 0.951 5 5
CO Carbon monoxide 1 Σ 2164 2143 0.990 6 6
HF Hydrogen fluoride 1 Σ 4118 3961 0.962 7 7
F2 Fluorine diatomic 1 Σg 1013 894 0.883 8 8
HCl Hydrogen chloride 1 Σ 2985 2886 0.967 9 9
Cl2 Chlorine diatomic 1 Σg 555 554 0.998 10 10
H2O Water 1 A1 3829 3657 0.955 11 11
    2 A1 1645 1595 0.970 11 12
    3 B2 3938 3756 0.954 11 13
CO2 Carbon dioxide 1 Σg 1346 1333 0.991 12 14
    2 Σu 2396 2349 0.980 12 15
    3 Πu 669 667 0.998 12 16
NH3 Ammonia 1 A1 3491 3337 0.956 13 17
    2 A1 1065 950 0.892 13 18
    3 E 3617 3444 0.952 13 19
    4 E 1681 1627 0.968 13 20
H2CO Formaldehyde 1 A1 2926 2782 0.951 14 21
    2 A1 1792 1746 0.974 14 22
    3 A1 1543 1500 0.972 14 23
    4 B1 1208 1167 0.966 14 24
    5 B2 2988 2843 0.951 14 25
    6 B2 1275 1249 0.980 14 26
CH4 Methane 1 A1 3052 2917 0.956 15 27
    2 E 1576 1534 0.974 15 28
    3 T2 3165 3019 0.954 15 29
    4 T2 1353 1306 0.965 15 30
C2H4 Ethylene 1 Ag 3168 3026 0.955 16 31
    2 Ag 1688 1623 0.962 16 32
    3 Ag 1385 1342 0.969 16 33
    4 Au 1072 1023 0.955 16 34
    5 B1u 3154 2989 0.948 16 35
    6 B1u 1488 1444 0.970 16 36
    7 B2g 982 940 0.957 16 37
    8 B2u 3257 3105 0.953 16 38
    9 B2u 836 826 0.988 16 39
    10 B3g 3230 3086 0.955 16 40
    11 B3g 1253 1217 0.971 16 41
    12 B3u 984 949 0.965 16 42

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