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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/6-31G**
Scale factor How many Source
Molecules Vibrations
0.937 ± 0.113 33 68 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4505 4161 0.924 1 1
LiH Lithium Hydride 1 Σ 1374 1360 0.990 2 2
NaH sodium hydride 1 Σ 1137 1133 0.997 3 3
BeH beryllium monohydride 1 Σ 2093 1987 0.949 4 4
MgH magnesium monohydride 1 Σ 1467 1432 0.976 5 5
BH Boron monohydride 1 Σ 2389 2269 0.950 6 6
AlH aluminum monohydride 1 Σ 1710 1625 0.950 7 7
CH Methylidyne 1 Σ 2848 2733 0.960 8 8
SiH Silylidyne 1 Σ 2068 1971 0.953 9 9
NH Imidogen 1 Σ 3274 3126 0.955 10 10
PH phosphorus monohydride 1 Σ 2384 2276 0.955 11 11
OH Hydroxyl radical 1 Σ 3762 3570 0.949 12 12
HS Mercapto radical 1 Σ 2738 2599 0.949 13 13
CS carbon monosulfide 1 Σ 1258 1272 1.011 14 14
HF Hydrogen fluoride 1 Σ 4180 3961 0.948 15 15
HCl Hydrogen chloride 1 Σ 3056 2886 0.945 16 16
BeH2 beryllium dihydride 2 Σu 2300 2159 0.939 17 17
    3 Πu 723 698 0.966 17 18
MgH2 magnesium dihydride 2 Σu 1618 1572 0.972 18 19
    3 Πu 445 440 0.989 18 20
BH2 boron dihydride 2 A1 1079 954 0.884 19 21
AlH2 aluminum dihydride 1 A1 1870 1770 0.946 20 22
    2 A1 783 760 0.971 20 23
    3 B2 1910 1807 0.946 20 24
SiH2 silicon dihydride 1 A1 2105 1996 0.948 21 25
    2 A1 1047 999 0.954 21 26
    3 B2 2109 1993 0.945 21 27
NH2 Amino radical 1 A1 3389 3219 0.950 22 28
    2 A1 1591 1497 0.941 22 29
    3 B2 3495 3301 0.944 22 30
PH2 Phosphino radical 1 A1 2427 2310 0.952 23 31
    2 A1 1163 1102 0.948 23 32
H2O Water 1 A1 3869 3657 0.945 24 33
    2 A1 1693 1595 0.942 24 34
    3 B2 3995 3756 0.940 24 35
HO2 Hydroperoxy radical 1 A' 3688 3436 0.932 25 36
    2 A' 1426 1392 0.976 25 37
    3 A' 1101 1098 0.997 25 38
H2S Hydrogen sulfide 1 A1 2771 2615 0.944 26 39
    2 A1 1259 1183 0.940 26 40
    3 B2 2795 2626 0.940 26 41
BH3 boron trihydride 2 A2" 1193 1148 0.962 27 42
    3 E' 2773 2602 0.938 27 43
    4 E' 1256 1197 0.953 27 44
AlH3 aluminum trihydride 1 A1' 1960 1900 0.969 28 45
    2 A2" 722 698 0.966 28 46
    3 E' 1975 1883 0.953 28 47
    4 E' 808 783 0.970 28 48
SiH3 Silyl radical 1 A1 2265 2136 0.943 29 49
    2 A1 797 728 0.913 29 50
    3 E 2303 2185 0.949 29 51
    4 E 963 922 0.958 29 52
NH3 Ammonia 1 A1 3511 3337 0.950 30 53
    2 A1 1146 950 0.829 30 54
    3 E 3653 3444 0.943 30 55
    4 E 1724 1627 0.944 30 56
PH3 Phosphine 1 A1 2461 2323 0.944 31 57
    2 A1 1065 992 0.932 31 58
    3 E 2476 2328 0.940 31 59
    4 E 1156 1118 0.967 31 60
CH4 Methane 1 A1 3093 2917 0.943 32 61
    2 E 1608 1534 0.954 32 62
    3 T2 3225 3019 0.936 32 63
    4 T2 1397 1306 0.935 32 64
SiH4 Silane 1 A1 2295 2187 0.953 33 65
    2 E 996 975 0.979 33 66
    3 T2 2307 2191 0.950 33 67
    4 T2 954 914 0.958 33 68

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 60 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 50 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 30 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 10 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