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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)/6-31+G**
Scale factor How many Source
Molecules Vibrations
0.939 ± 0.112 33 68 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
CH4 Methane 1 A1 3081 2917 0.947 1 1
    2 E 1585 1534 0.968 1 2
    3 T2 3211 3019 0.940 1 3
    4 T2 1388 1306 0.941 1 4
H2 Hydrogen diatomic 1 Σg 4505 4401 0.977 2 5
CS carbon monosulfide 1 Σ 1263 1285 1.017 3 6
HO2 Hydroperoxy radical 1 A' 3676 3436 0.935 4 7
    2 A' 1417 1392 0.982 4 8
    3 A' 1084 1098 1.012 4 9
CH Methylidyne 1 Σ 2874 2861 0.995 5 10
OH Hydroxyl radical 1 Σ 3745 3738 0.998 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 3048 2991 0.981 9 14
HF Hydrogen fluoride 1 Σ 4122 4138 1.004 10 15
NH3 Ammonia 1 A1 3524 3337 0.947 11 16
    2 A1 1076 950 0.883 11 17
    3 E 3677 3444 0.937 11 18
    4 E 1705 1627 0.954 11 19
MgH2 magnesium dihydride 2 Σu 1617 1572 0.972 12 20
    3 Πu 446 440 0.986 12 21
H2O Water 1 A1 3853 3657 0.949 13 22
    2 A1 1639 1595 0.973 13 23
    3 B2 3985 3756 0.942 13 24
H2S Hydrogen sulfide 1 A1 2766 2615 0.946 14 25
    2 A1 1256 1183 0.942 14 26
    3 B2 2789 2626 0.941 14 27
AlH3 aluminum trihydride 1 A1' 1965 1900 0.967 15 28
    2 A2" 724 698 0.964 15 29
    3 E' 1979 1883 0.951 15 30
    4 E' 812 783 0.965 15 31
BeH2 beryllium dihydride 2 Σu 2291 2159 0.943 16 32
    3 Πu 715 698 0.975 16 33
PH3 Phosphine 1 A1 2458 2323 0.945 17 34
    2 A1 1061 992 0.935 17 35
    3 E 2473 2328 0.941 17 36
    4 E 1153 1118 0.970 17 37
SiH4 Silane 1 A1 2299 2187 0.951 18 38
    2 E 997 975 0.978 18 39
    3 T2 2309 2191 0.949 18 40
    4 T2 956 914 0.957 18 41
BH3 boron trihydride 2 A2" 1189 1148 0.965 19 42
    3 E' 2762 2602 0.942 19 43
    4 E' 1249 1197 0.958 19 44
BeH beryllium monohydride 1 Σ 2092 2061 0.985 20 45
PH2 Phosphino radical 1 A1 2424 2310 0.953 21 46
    2 A1 1160 1102 0.950 21 47
SiH3 Silyl radical 1 A1 2268 2136 0.942 22 48
    2 A1 799 728 0.911 22 49
    3 E 2305 2185 0.948 22 50
    4 E 964 922 0.956 22 51
BH Boron monohydride 1 Σ 2410 2367 0.982 23 52
NH2 Amino radical 1 A1 3396 3219 0.948 24 53
    2 A1 1551 1497 0.965 24 54
    3 B2 3508 3301 0.941 24 55
NH Imidogen 1 Σ 3288 3283 0.998 25 56
SiH Silylidyne 1 Σ 2071 2043 0.986 26 57
SiH2 silicon dihydride 1 A1 2106 1996 0.948 27 58
    2 A1 1046 999 0.955 27 59
    3 B2 2110 1993 0.945 27 60
SH Mercapto radical 1 Σ 2728 2696 0.988 28 61
PH phosphorus monohydride 1 Σ 2383 2364 0.992 29 62
AlH aluminum monohydride 1 Σ 1713 1682 0.982 30 63
MgH magnesium monohydride 1 Σ 1468 1493 1.017 31 64
BH2 boron dihydride 2 A1 1060 954 0.899 32 65
AlH2 aluminum dihydride 1 A1 1873 1770 0.945 33 66
    2 A1 786 760 0.967 33 67
    3 B2 1913 1807 0.945 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