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

Vibrational frequency scaling factors

Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/6-31G(2df,p)
Scale factor How many Source
Molecules Vibrations
0.954 ± 0.019 18 77 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2CO Formaldehyde 1 A1 2973 2782 0.936 1 1
    2 A1 1829 1746 0.954 1 2
    3 A1 1566 1500 0.958 1 3
    4 B1 1213 1167 0.962 1 4
    5 B2 3034 2843 0.937 1 5
    6 B2 1293 1249 0.966 1 6
CH4 Methane 1 A1 3081 2917 0.947 2 7
    2 E 1594 1534 0.962 2 8
    3 T2 3207 3019 0.942 2 9
    4 T2 1375 1306 0.950 2 10
C2H4 Ethylene 1 Ag 3205 3026 0.944 3 11
    2 Ag 1703 1623 0.953 3 12
    3 Ag 1395 1342 0.962 3 13
    4 Au 1073 1023 0.954 3 14
    5 B1u 3186 2989 0.938 3 15
    6 B1u 1493 1444 0.967 3 16
    7 B2g 969 940 0.970 3 17
    8 B2u 3292 3105 0.943 3 18
    9 B2u 832 826 0.993 3 19
    10 B3g 3267 3086 0.945 3 20
    11 B3g 1255 1217 0.970 3 21
    12 B3u 991 949 0.957 3 22
C2H2 Acetylene 1 Σg 3577 3374 0.943 4 23
    2 Σg 2056 1974 0.960 4 24
    3 Σu 3478 3289 0.946 4 25
    4 Πg 545 612 1.122 4 26
    5 Πu 788 730 0.926 4 27
C3H6 Cyclopropane 1 A1' 3198 3038 0.950 5 28
    2 A1' 1550 1479 0.954 5 29
    3 A1' 1237 1188 0.961 5 30
    4 A1" 1181 1126 0.954 5 31
    5 A2' 1113 1070 0.961 5 32
    6 A2" 3290 3103 0.943 5 33
    7 A2" 864 854 0.989 5 34
    8 E' 3187 3025 0.949 5 35
    9 E' 1496 1438 0.961 5 36
    10 E' 1088 1029 0.946 5 37
    11 E' 918 866 0.943 5 38
    12 E" 3271 3082 0.942 5 39
    13 E" 1233 1188 0.963 5 40
    14 E" 748 739 0.988 5 41
C3H2N2 Malononitrile 1 A1 3115 2935 0.942 6 42
    2 A1 2371 2275 0.960 6 43
    3 A1 1481 1395 0.942 6 44
    4 A1 908 890 0.980 6 45
    5 A1 584 582 0.996 6 46
    6 A1 148 167 1.128 6 47
    7 A2 1265 1220 0.964 6 48
    8 A2 373 367 0.984 6 49
    9 B1 3164 2968 0.938 6 50
    10 B1 957 933 0.975 6 51
    11 B1 344 337 0.978 6 52
    12 B2 2370 2275 0.960 6 53
    13 B2 1369 1318 0.963 6 54
    14 B2 1000 982 0.982 6 55
    15 B2 372 366 0.985 6 56
CO2 Carbon dioxide 1 Σg 1382 1333 0.965 7 57
    2 Σu 2441 2349 0.962 7 58
    3 Πu 701 667 0.951 7 59
CO Carbon monoxide 1 Σ 2184 2170 0.993 8 60
H2 Hydrogen diatomic 1 Σg 4504 4401 0.977 9 61
CH Methylidyne 1 Σ 3184 3145 0.988 10 62
SO2 Sulfur dioxide 1 A1 1194 1151 0.964 11 63
    2 A1 529 518 0.979 11 64
    3 B2 1410 1362 0.966 11 65
LiH Lithium Hydride 1 Σ 1415 1405 0.993 12 66
HCl Hydrogen chloride 1 Σ 3032 2991 0.986 13 67
HF Hydrogen fluoride 1 Σ 4221 4138 0.980 14 68
NH3 Ammonia 1 A1 3518 3337 0.948 15 69
    2 A1 1149 950 0.827 15 70
    3 E 3646 3444 0.945 15 71
    4 E 1718 1627 0.947 15 72
N2 Nitrogen diatomic 1 Σg 2396 2359 0.984 16 73
H2O Water 1 A1 3889 3657 0.940 17 74
    2 A1 1715 1595 0.930 17 75
    3 B2 4000 3756 0.939 17 76
F2 Fluorine diatomic 1 Σg 1006 917 0.911 18 77

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.

60
50
40
30
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10
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