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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/6-31+G**
Scale factor How many Source
Molecules Vibrations
0.934 ± 0.113 32 67 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
CH4 Methane 1 A1 3097 2917 0.942 1 1
    2 E 1593 1534 0.963 1 2
    3 T2 3225 3019 0.936 1 3
    4 T2 1396 1306 0.936 1 4
H2 Hydrogen diatomic 1 Σg 4504 4401 0.977 2 5
CS carbon monosulfide 1 Σ 1335 1285 0.963 3 6
HO2 Hydroperoxy radical 1 A' 3713 3436 0.925 4 7
    2 A' 1447 1392 0.962 4 8
    3 A' 1130 1098 0.971 4 9
CH Methylidyne 1 Σ 2889 2861 0.990 5 10
OH Hydroxyl radical 1 Σ 3769 3738 0.992 6 11
LiH Lithium Hydride 1 Σ 1375 1405 1.022 7 12
NaH sodium hydride 1 Σ 1138 1172 1.030 8 13
HCl Hydrogen chloride 1 Σ 3064 2991 0.976 9 14
HF Hydrogen fluoride 1 Σ 4151 4138 0.997 10 15
NH3 Ammonia 1 A1 3549 3337 0.940 11 16
    2 A1 1072 950 0.886 11 17
    3 E 3700 3444 0.931 11 18
    4 E 1713 1627 0.950 11 19
MgH2 magnesium dihydride 2 Σu 1619 1572 0.971 12 20
    3 Πu 447 440 0.984 12 21
H2O Water 1 A1 3880 3657 0.943 13 22
    2 A1 1647 1595 0.969 13 23
    3 B2 4009 3756 0.937 13 24
H2S Hydrogen sulfide 1 A1 2782 2615 0.940 14 25
    2 A1 1265 1183 0.935 14 26
    3 B2 2804 2626 0.936 14 27
AlH3 aluminum trihydride 1 A1' 1971 1900 0.964 15 28
    2 A2" 727 698 0.960 15 29
    3 E' 1984 1883 0.949 15 30
    4 E' 815 783 0.962 15 31
BeH2 beryllium dihydride 2 Σu 2293 2159 0.942 16 32
    3 Πu 717 698 0.973 16 33
PH3 Phosphine 1 A1 2470 2323 0.941 17 34
    2 A1 1068 992 0.929 17 35
    3 E 2483 2328 0.938 17 36
    4 E 1163 1118 0.961 17 37
SiH4 Silane 1 A1 2308 2187 0.948 18 38
    2 E 1002 975 0.973 18 39
    3 T2 2317 2191 0.946 18 40
    4 T2 961 914 0.951 18 41
BH3 boron trihydride 2 A2" 1192 1148 0.963 19 42
    3 E' 2769 2602 0.940 19 43
    4 E' 1253 1197 0.955 19 44
BeH beryllium monohydride 1 Σ 2098 2061 0.983 20 45
PH2 Phosphino radical 1 A1 2439 2310 0.947 21 46
    2 A1 1169 1102 0.943 21 47
SiH3 Silyl radical 1 A1 2278 2136 0.938 22 48
    2 A1 804 728 0.905 22 49
    3 E 2313 2185 0.945 22 50
    4 E 969 922 0.952 22 51
BH Boron monohydride 1 Σ 2418 2367 0.979 23 52
NH2 Amino radical 1 A1 3420 3219 0.941 24 53
    2 A1 1559 1497 0.961 24 54
    3 B2 3530 3301 0.935 24 55
NH Imidogen 1 Σ 3311 3283 0.992 25 56
SiH Silylidyne 1 Σ 2081 2043 0.981 26 57
SiH2 silicon dihydride 1 A1 2116 1996 0.943 27 58
    2 A1 1054 999 0.948 27 59
    3 B2 2118 1993 0.941 27 60
SH Mercapto radical 1 Σ 2744 2696 0.983 28 61
PH phosphorus monohydride 1 Σ 2398 2364 0.986 29 62
AlH aluminum monohydride 1 Σ 1719 1682 0.979 30 63
MgH magnesium monohydride 1 Σ 1473 1493 1.013 31 64
AlH2 aluminum dihydride 1 A1 1882 1770 0.940 32 65
    2 A1 790 760 0.962 32 66
    3 B2 1921 1807 0.940 32 67

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