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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP4/6-311G**
Scale factor How many Source
Molecules Vibrations
0.970 ± 0.033 17 62 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4456 4161 0.934 1 1
LiH Lithium Hydride 1 Σ 1425 1360 0.954 2 2
CH Methylidyne 1 Σ 3156     3 3
N2 Nitrogen diatomic 1 Σg 2184 2330 1.067 4 4
CO Carbon monoxide 1 Σ 2010 2143 1.066 5 5
    1 Σ 2373     5 6
HF Hydrogen fluoride 1 Σ 4238 3961 0.935 6 7
F2 Fluorine diatomic 1 Σg 791 894 1.129 7 8
HCl Hydrogen chloride 1 Σ 3047 2886 0.947 8 9
H2O Water 1 A1 3880 3657 0.943 9 10
    2 A1 1680 1595 0.950 9 11
    3 B2 3978 3756 0.944 9 12
CO2 Carbon dioxide 1 Σg 1271 1333 1.049 10 13
    2 Σu 2368 2349 0.992 10 14
    3 Πu 635 667 1.050 10 15
SO2 Sulfur dioxide 1 A1 974 1151 1.182 11 16
    2 A1 472 518 1.097 11 17
    3 B2 1198 1362 1.136 11 18
C2H2 Acetylene 1 Σg 3522 3374 0.958 12 19
    2 Σg 1954 1974 1.010 12 20
    3 Σu 3431 3289 0.959 12 21
    4 Πg 514 612 1.190 12 22
    5 Πu 754 730 0.968 12 23
NH3 Ammonia 1 A1 3481 3337 0.959 13 24
    2 A1 1147 950 0.828 13 25
    3 E 3614 3444 0.953 13 26
    4 E 1672 1627 0.973 13 27
H2CO Formaldehyde 1 A1 2914 2782 0.955 14 28
    2 A1 1750 1746 0.998 14 29
    3 A1 1545 1500 0.971 14 30
    4 B1 1188 1167 0.983 14 31
    5 B2 2969 2843 0.957 14 32
    6 B2 1273 1249 0.981 14 33
CH4 Methane 1 A1 3042 2917 0.959 15 34
    2 E 1566 1534 0.980 15 35
    3 T2 3168 3019 0.953 15 36
    4 T2 1359 1306 0.961 15 37
C2H4 Ethylene 1 Ag 3160 3026 0.958 16 38
    2 Ag 1662 1623 0.976 16 39
    3 Ag 1367 1342 0.982 16 40
    4 Au 1048 1023 0.976 16 41
    5 B1u 3142 2989 0.951 16 42
    6 B1u 1474 1444 0.979 16 43
    7 B2g 892 940 1.053 16 44
    8 B2u 3253 3105 0.955 16 45
    9 B2u 820 826 1.007 16 46
    10 B3g 3226 3086 0.957 16 47
    11 B3g 1229 1217 0.990 16 48
    12 B3u 954 949 0.996 16 49
C3H6 Cyclopropane 1 A1' 3156 3038 0.962 17 50
    2 A1' 1536 1479 0.963 17 51
    3 A1' 1220 1188 0.974 17 52
    4 A1" 1173 1126 0.960 17 53
    5 A2' 1093 1070 0.979 17 54
    6 A2" 3253 3103 0.954 17 55
    7 A2" 865 854 0.987 17 56
    8 E' 3146 3025 0.961 17 57
    9 E' 1484 1438 0.969 17 58
    10 E' 1085 1029 0.948 17 59
    11 E' 896 866 0.966 17 60
    12 E" 3233 3082 0.953 17 61
    13 E" 1227 1188 0.968 17 62
    14 E" 754 739 0.980 17 63

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