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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/cc-pVTZ
Scale factor How many Source
Molecules Vibrations
0.949 ± 0.118 27 60 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4410 4161 0.944 1 1
BH Boron monohydride 1 Σ 2350 2269 0.966 2 2
AlH aluminum monohydride 1 Σ 1681 1625 0.967 3 3
CH Methylidyne 1 Σ 2834 2733 0.964 4 4
    1 Σ 3109     4 5
SiH Silylidyne 1 Σ 2031 1971 0.970 5 6
NH Imidogen 1 Σ 3264 3126 0.958 6 7
PH phosphorus monohydride 1 Σ 2352 2276 0.968 7 8
    1 Σ 2372 2319 0.978 7 9
OH Hydroxyl radical 1 Σ 3738 3570 0.955 8 10
HS Mercapto radical 1 Σ 2687 2599 0.967 9 11
CS carbon monosulfide 1 Σ 1253 1272 1.015 10 12
HF Hydrogen fluoride 1 Σ 4178 3961 0.948 11 13
HCl Hydrogen chloride 1 Σ 3000 2886 0.962 12 14
BH2 boron dihydride 2 A1 1018 954 0.937 13 15
AlH2 aluminum dihydride 1 A1 1847 1770 0.958 14 16
    2 A1 765 760 0.993 14 17
    3 B2 1883 1807 0.960 14 18
SiH2 silicon dihydride 1 A1 2062 1996 0.968 15 19
    2 A1 1020 999 0.980 15 20
    3 B2 2060 1993 0.967 15 21
PH2 Phosphino radical 1 A1 2385 2310 0.968 16 22
    2 A1 1124 1102 0.980 16 23
H2O Water 1 A1 3838 3657 0.953 17 24
    2 A1 1668 1595 0.956 17 25
    3 B2 3943 3756 0.953 17 26
HO2 Hydroperoxy radical 1 A' 3676 3436 0.935 18 27
    2 A' 1430 1392 0.974 18 28
    3 A' 1116 1098 0.984 18 29
H2S Hydrogen sulfide 1 A1 2717 2615 0.963 19 30
    2 A1 1204 1183 0.983 19 31
    3 B2 2733 2626 0.961 19 32
BH3 boron trihydride 2 A2" 1160 1148 0.989 20 33
    3 E' 2697 2602 0.964 20 34
    4 E' 1223 1197 0.979 20 35
AlH3 aluminum trihydride 1 A1' 1940 1900 0.980 21 36
    2 A2" 717 698 0.973 21 37
    3 E' 1946 1883 0.967 21 38
    4 E' 792 783 0.990 21 39
SiH3 Silyl radical 1 A1 2217 2136 0.963 22 40
    2 A1 774 728 0.941 22 41
    3 E 2253 2185 0.970 22 42
    4 E 940 922 0.981 22 43
NH3 Ammonia 1 A1 3469 3337 0.962 23 44
    2 A1 1112 950 0.854 23 45
    3 E 3594 3444 0.958 23 46
    4 E 1688 1627 0.964 23 47
PH3 Phosphine 1 A1 2411 2323 0.963 24 48
    2 A1 1018 992 0.974 24 49
    3 E 2420 2328 0.962 24 50
    4 E 1142 1118 0.979 24 51
CH4 Methane 1 A1 3035 2917 0.961 25 52
    2 E 1570 1534 0.977 25 53
    3 T2 3154 3019 0.957 25 54
    4 T2 1343 1306 0.972 25 55
SiH4 Silane 1 A1 2251 2187 0.972 26 56
    2 E 986 975 0.989 26 57
    3 T2 2259 2191 0.970 26 58
    4 T2 932 914 0.980 26 59

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 45 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 40 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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