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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(T)/6-31G**
Scale factor How many Source
Molecules Vibrations
0.937 ± 0.113 33 68 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
CH4 Methane 1 A1 3093 2917 0.943 1 1
    2 E 1608 1534 0.954 1 2
    3 T2 3225 3019 0.936 1 3
    4 T2 1397 1306 0.935 1 4
H2 Hydrogen diatomic 1 Σg 4505 4401 0.977 2 5
CS carbon monosulfide 1 Σ 1258 1285 1.022 3 6
HO2 Hydroperoxy radical 1 A' 3688 3436 0.932 4 7
    2 A' 1426 1392 0.976 4 8
    3 A' 1101 1098 0.997 4 9
CH Methylidyne 1 Σ 2848 2861 1.004 5 10
OH Hydroxyl radical 1 Σ 3762 3738 0.993 6 11
LiH Lithium Hydride 1 Σ 1374 1405 1.023 7 12
NaH sodium hydride 1 Σ 1137 1172 1.031 8 13
HCl Hydrogen chloride 1 Σ 3056 2991 0.979 9 14
HF Hydrogen fluoride 1 Σ 4180 4138 0.990 10 15
NH3 Ammonia 1 A1 3511 3337 0.950 11 16
    2 A1 1146 950 0.829 11 17
    3 E 3653 3444 0.943 11 18
    4 E 1724 1627 0.944 11 19
MgH2 magnesium dihydride 2 Σu 1618 1572 0.972 12 20
    3 Πu 445 440 0.989 12 21
H2O Water 1 A1 3869 3657 0.945 13 22
    2 A1 1693 1595 0.942 13 23
    3 B2 3995 3756 0.940 13 24
H2S Hydrogen sulfide 1 A1 2771 2615 0.944 14 25
    2 A1 1259 1183 0.940 14 26
    3 B2 2795 2626 0.940 14 27
AlH3 aluminum trihydride 1 A1' 1960 1900 0.969 15 28
    2 A2" 722 698 0.966 15 29
    3 E' 1975 1883 0.953 15 30
    4 E' 808 783 0.970 15 31
BeH2 beryllium dihydride 2 Σu 2300 2159 0.939 16 32
    3 Πu 723 698 0.966 16 33
PH3 Phosphine 1 A1 2461 2323 0.944 17 34
    2 A1 1065 992 0.932 17 35
    3 E 2476 2328 0.940 17 36
    4 E 1156 1118 0.967 17 37
SiH4 Silane 1 A1 2295 2187 0.953 18 38
    2 E 996 975 0.979 18 39
    3 T2 2307 2191 0.950 18 40
    4 T2 954 914 0.958 18 41
BH3 boron trihydride 2 A2" 1193 1148 0.962 19 42
    3 E' 2773 2602 0.938 19 43
    4 E' 1256 1197 0.953 19 44
BeH beryllium monohydride 1 Σ 2093 2061 0.985 20 45
PH2 Phosphino radical 1 A1 2427 2310 0.952 21 46
    2 A1 1163 1102 0.948 21 47
SiH3 Silyl radical 1 A1 2265 2136 0.943 22 48
    2 A1 797 728 0.913 22 49
    3 E 2303 2185 0.949 22 50
    4 E 963 922 0.958 22 51
BH Boron monohydride 1 Σ 2389 2367 0.991 23 52
NH2 Amino radical 1 A1 3389 3219 0.950 24 53
    2 A1 1591 1497 0.941 24 54
    3 B2 3495 3301 0.944 24 55
NH Imidogen 1 Σ 3274 3283 1.003 25 56
SiH Silylidyne 1 Σ 2068 2043 0.988 26 57
SiH2 silicon dihydride 1 A1 2105 1996 0.948 27 58
    2 A1 1047 999 0.954 27 59
    3 B2 2109 1993 0.945 27 60
SH Mercapto radical 1 Σ 2738 2696 0.985 28 61
PH phosphorus monohydride 1 Σ 2384 2364 0.992 29 62
AlH aluminum monohydride 1 Σ 1710 1682 0.984 30 63
MgH magnesium monohydride 1 Σ 1467 1493 1.018 31 64
BH2 boron dihydride 2 A1 1079 954 0.884 32 65
AlH2 aluminum dihydride 1 A1 1870 1770 0.946 33 66
    2 A1 783 760 0.971 33 67
    3 B2 1910 1807 0.946 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.

45
40
35
30
25
20
15
10
5
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