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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/6-31+G**
Scale factor How many Source
Molecules Vibrations
0.939 ± 0.112 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 1375 1360 0.989 2 2
NaH sodium hydride 1 Σ 1138 1133 0.996 3 3
BeH beryllium monohydride 1 Σ 2092 1987 0.950 4 4
MgH magnesium monohydride 1 Σ 1468 1432 0.976 5 5
BH Boron monohydride 1 Σ 2410 2269 0.942 6 6
AlH aluminum monohydride 1 Σ 1713 1625 0.949 7 7
CH Methylidyne 1 Σ 2874 2733 0.951 8 8
SiH Silylidyne 1 Σ 2071 1971 0.952 9 9
NH Imidogen 1 Σ 3288 3126 0.951 10 10
PH phosphorus monohydride 1 Σ 2383 2276 0.955 11 11
OH Hydroxyl radical 1 Σ 3745 3570 0.953 12 12
HS Mercapto radical 1 Σ 2728 2599 0.953 13 13
CS carbon monosulfide 1 Σ 1263 1272 1.007 14 14
HF Hydrogen fluoride 1 Σ 4122 3961 0.961 15 15
HCl Hydrogen chloride 1 Σ 3048 2886 0.947 16 16
BeH2 beryllium dihydride 2 Σu 2291 2159 0.943 17 17
    3 Πu 715 698 0.975 17 18
MgH2 magnesium dihydride 2 Σu 1617 1572 0.972 18 19
    3 Πu 446 440 0.986 18 20
BH2 boron dihydride 2 A1 1060 954 0.899 19 21
AlH2 aluminum dihydride 1 A1 1873 1770 0.945 20 22
    2 A1 786 760 0.967 20 23
    3 B2 1913 1807 0.945 20 24
SiH2 silicon dihydride 1 A1 2106 1996 0.948 21 25
    2 A1 1046 999 0.955 21 26
    3 B2 2110 1993 0.945 21 27
NH2 Amino radical 1 A1 3396 3219 0.948 22 28
    2 A1 1551 1497 0.965 22 29
    3 B2 3508 3301 0.941 22 30
PH2 Phosphino radical 1 A1 2424 2310 0.953 23 31
    2 A1 1160 1102 0.950 23 32
H2O Water 1 A1 3853 3657 0.949 24 33
    2 A1 1639 1595 0.973 24 34
    3 B2 3985 3756 0.942 24 35
HO2 Hydroperoxy radical 1 A' 3675 3436 0.935 25 36
    2 A' 1417 1392 0.982 25 37
    3 A' 1084 1098 1.012 25 38
H2S Hydrogen sulfide 1 A1 2766 2615 0.946 26 39
    2 A1 1256 1183 0.942 26 40
    3 B2 2789 2626 0.941 26 41
BH3 boron trihydride 2 A2" 1189 1148 0.965 27 42
    3 E' 2762 2602 0.942 27 43
    4 E' 1249 1197 0.958 27 44
AlH3 aluminum trihydride 1 A1' 1966 1900 0.967 28 45
    2 A2" 724 698 0.964 28 46
    3 E' 1979 1883 0.951 28 47
    4 E' 812 783 0.965 28 48
SiH3 Silyl radical 1 A1 2268 2136 0.942 29 49
    2 A1 799 728 0.911 29 50
    3 E 2305 2185 0.948 29 51
    4 E 964 922 0.956 29 52
NH3 Ammonia 1 A1 3524 3337 0.947 30 53
    2 A1 1076 950 0.883 30 54
    3 E 3677 3444 0.937 30 55
    4 E 1705 1627 0.954 30 56
PH3 Phosphine 1 A1 2458 2323 0.945 31 57
    2 A1 1061 992 0.935 31 58
    3 E 2473 2328 0.941 31 59
    4 E 1153 1118 0.970 31 60
CH4 Methane 1 A1 3081 2917 0.947 32 61
    2 E 1585 1534 0.968 32 62
    3 T2 3211 3019 0.940 32 63
    4 T2 1388 1306 0.941 32 64
SiH4 Silane 1 A1 2299 2187 0.951 33 65
    2 E 997 975 0.978 33 66
    3 T2 2309 2191 0.949 33 67
    4 T2 956 914 0.957 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