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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD/6-31G**
Scale factor How many Source
Molecules Vibrations
0.933 ± 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 4504 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 2099 1987 0.947 4 4
MgH magnesium monohydride 1 Σ 1472 1432 0.973 5 5
BH Boron monohydride 1 Σ 2396 2269 0.947 6 6
AlH aluminum monohydride 1 Σ 1716 1625 0.947 7 7
CH Methylidyne 1 Σ 2862 2733 0.955 8 8
SiH Silylidyne 1 Σ 2078 1971 0.948 9 9
NH Imidogen 1 Σ 3296 3126 0.948 10 10
PH phosphorus monohydride 1 Σ 2398 2276 0.949 11 11
OH Hydroxyl radical 1 Σ 3781 3570 0.944 12 12
HS Mercapto radical 1 Σ 2746 2599 0.946 13 13
CS carbon monosulfide 1 Σ 1329 1272 0.957 14 14
HF Hydrogen fluoride 1 Σ 4194 3961 0.945 15 15
HCl Hydrogen chloride 1 Σ 3070 2886 0.940 16 16
BeH2 beryllium dihydride 2 Σu 2302 2159 0.938 17 17
    3 Πu 724 698 0.964 17 18
MgH2 magnesium dihydride 2 Σu 1620 1572 0.970 18 19
    3 Πu 446 440 0.986 18 20
BH2 boron dihydride 2 A1 1081 954 0.883 19 21
AlH2 aluminum dihydride 1 A1 1878 1770 0.943 20 22
    2 A1 786 760 0.967 20 23
    3 B2 1917 1807 0.943 20 24
SiH2 silicon dihydride 1 A1 2114 1996 0.944 21 25
    2 A1 1055 999 0.947 21 26
    3 B2 2117 1993 0.941 21 27
PH2 Phosphino radical 1 A1 2441 2310 0.946 22 28
    2 A1 1171 1102 0.941 22 29
H2O Water 1 A1 3892 3657 0.940 23 30
    2 A1 1699 1595 0.939 23 31
    3 B2 4015 3756 0.935 23 32
HO2 Hydroperoxy radical 1 A' 3720 3436 0.924 24 33
    2 A' 1453 1392 0.958 24 34
    3 A' 1142 1098 0.961 24 35
H2S Hydrogen sulfide 1 A1 2781 2615 0.940 25 36
    2 A1 1268 1183 0.933 25 37
    3 B2 2803 2626 0.937 25 38
BH3 boron trihydride 2 A2" 1195 1148 0.960 26 39
    3 E' 2779 2602 0.936 26 40
    4 E' 1260 1197 0.950 26 41
AlH3 aluminum trihydride 1 A1' 1966 1900 0.966 27 42
    2 A2" 724 698 0.963 27 43
    3 E' 1980 1883 0.951 27 44
    4 E' 810 783 0.967 27 45
SiH3 Silyl radical 1 A1 2275 2136 0.939 28 46
    2 A1 802 728 0.908 28 47
    3 E 2311 2185 0.946 28 48
    4 E 967 922 0.953 28 49
NH3 Ammonia 1 A1 3536 3337 0.944 29 50
    2 A1 1143 950 0.831 29 51
    3 E 3676 3444 0.937 29 52
    4 E 1731 1627 0.940 29 53
PH3 Phosphine 1 A1 2473 2323 0.940 30 54
    2 A1 1072 992 0.926 30 55
    3 E 2485 2328 0.937 30 56
    4 E 1166 1118 0.959 30 57
CH4 Methane 1 A1 3108 2917 0.939 31 58
    2 E 1615 1534 0.950 31 59
    3 T2 3237 3019 0.933 31 60
    4 T2 1404 1306 0.930 31 61
SiH4 Silane 1 A1 2304 2187 0.949 32 62
    2 E 1000 975 0.975 32 63
    3 T2 2314 2191 0.947 32 64
    4 T2 959 914 0.953 32 65

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