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III.B.3.b. (XIII.C.2.)

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
CH4 Methane 1 A1 3108 2917 0.939 1 1
    2 E 1615 1534 0.950 1 2
    3 T2 3237 3019 0.933 1 3
    4 T2 1404 1306 0.930 1 4
H2 Hydrogen diatomic 1 Σg 4504 4401 0.977 2 5
CS carbon monosulfide 1 Σ 1329 1285 0.967 3 6
HO2 Hydroperoxy radical 1 A' 3720 3436 0.924 4 7
    2 A' 1453 1392 0.958 4 8
    3 A' 1143 1098 0.961 4 9
CH Methylidyne 1 Σ 2862 2861 0.999 5 10
OH Hydroxyl radical 1 Σ 3781 3738 0.989 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 3070 2991 0.974 9 14
HF Hydrogen fluoride 1 Σ 4197 4138 0.986 10 15
NH3 Ammonia 1 A1 3536 3337 0.944 11 16
    2 A1 1143 950 0.831 11 17
    3 E 3676 3444 0.937 11 18
    4 E 1731 1627 0.940 11 19
MgH2 magnesium dihydride 2 Σu 1620 1572 0.970 12 20
    3 Πu 446 440 0.986 12 21
H2O Water 1 A1 3891 3657 0.940 13 22
    2 A1 1699 1595 0.939 13 23
    3 B2 4015 3756 0.936 13 24
H2S Hydrogen sulfide 1 A1 2781 2615 0.940 14 25
    2 A1 1268 1183 0.933 14 26
    3 B2 2803 2626 0.937 14 27
AlH3 aluminum trihydride 1 A1' 1965 1900 0.967 15 28
    2 A2" 725 698 0.963 15 29
    3 E' 1979 1883 0.951 15 30
    4 E' 810 783 0.967 15 31
BeH2 beryllium dihydride 2 Σu 2302 2159 0.938 16 32
    3 Πu 724 698 0.964 16 33
PH3 Phosphine 1 A1 2473 2323 0.940 17 34
    2 A1 1072 992 0.926 17 35
    3 E 2485 2328 0.937 17 36
    4 E 1166 1118 0.959 17 37
SiH4 Silane 1 A1 2303 2187 0.950 18 38
    2 E 1000 975 0.975 18 39
    3 T2 2314 2191 0.947 18 40
    4 T2 959 914 0.953 18 41
BH3 boron trihydride 2 A2" 1195 1148 0.960 19 42
    3 E' 2779 2602 0.936 19 43
    4 E' 1260 1197 0.950 19 44
BeH beryllium monohydride 1 Σ 2099 2061 0.982 20 45
PH2 Phosphino radical 1 A1 2441 2310 0.946 21 46
    2 A1 1171 1102 0.941 21 47
SiH3 Silyl radical 1 A1 2275 2136 0.939 22 48
    2 A1 802 728 0.908 22 49
    3 E 2311 2185 0.946 22 50
    4 E 967 922 0.953 22 51
BH Boron monohydride 1 Σ 2400 2367 0.986 23 52
NH2 Amino radical 1 A1 3413 3219 0.943 24 53
    2 A1 1597 1497 0.938 24 54
    3 B2 3517 3301 0.939 24 55
NH Imidogen 1 Σ 3296 3283 0.996 25 56
SiH Silylidyne 1 Σ 2078 2043 0.983 26 57
SiH2 silicon dihydride 1 A1 2114 1996 0.944 27 58
    2 A1 1055 999 0.947 27 59
    3 B2 2117 1993 0.941 27 60
SH Mercapto radical 1 Σ 2746 2696 0.982 28 61
PH phosphorus monohydride 1 Σ 2399 2364 0.985 29 62
AlH aluminum monohydride 1 Σ 1716 1682 0.980 30 63
MgH magnesium monohydride 1 Σ 1472 1493 1.014 31 64
BH2 boron dihydride 2 A1 1081 954 0.883 32 65
AlH2 aluminum dihydride 1 A1 1878 1770 0.943 33 66
    2 A1 786 760 0.967 33 67
    3 B2 1917 1807 0.943 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.

50
40
30
20
10
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