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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD/aug-cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.953 ± 0.013 60 125 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4401 4161 0.945 1 1
LiH Lithium Hydride 1 Σ 1389 1360 0.979 2 2
Li2 Lithium diatomic 1 Σg 346 346 1.000 3 3
NaH sodium hydride 1 Σ 1133 1133 1.000 4 4
Na2 Sodium diatomic 1 Σg 152 158 1.039 5 5
BeH beryllium monohydride 1 Σ 2056 1987 0.967 6 6
MgH magnesium monohydride 1 Σ 1492 1432 0.960 7 7
BH Boron monohydride 1 Σ 2367 2269 0.959 8 8
SiH Silylidyne 1 Σ 2056 1971 0.959 9 9
CN Cyano radical 1 Σ 2173 2042 0.940 10 10
N2 Nitrogen diatomic 1 Σg 2376 2330 0.981 11 11
    1 Σg 1795 1733 0.966 11 12
PH phosphorus monohydride 1 Σ 2383 2276 0.955 12 13
P2 Phosphorus diatomic 1 Σg 818 775 0.948 13 14
OH Hydroxyl radical 1 Σ 3778 3570 0.945 14 15
LiO lithium oxide 1 Σ 811 799 0.985 15 16
BeO beryllium oxide 1 Σ 1565 1435 0.917 16 17
BO boron monoxide 1 Σ 1938 1862 0.960 17 18
CO Carbon monoxide 1 Σ 2231 2143 0.961 18 19
NaO sodium monoxide 1 Σ 483     19 20
HS Mercapto radical 1 Σ 2717 2599 0.957 20 21
SO Sulfur monoxide 1 Σ 1197 1138 0.951 21 22
    1 Σ 1164 1054 0.905 21 23
HF Hydrogen fluoride 1 Σ 4187 3961 0.946 22 24
LiF lithium fluoride 1 Σ 905 896 0.990 23 25
CF Fluoromethylidyne 1 Σ 1333 1286 0.965 24 26
F2 Fluorine diatomic 1 Σg 1017 894 0.879 25 27
NaF sodium fluoride 1 Σ 540 529 0.978 26 28
SiF silicon monofluoride 1 Σ 866 848 0.979 27 29
SF Monosulfur monofluoride 1 Σ 860 829 0.964 28 30
HCl Hydrogen chloride 1 Σ 3013 2886 0.958 29 31
LiCl lithium chloride 1 Σ 636 634 0.997 30 32
ClF Chlorine monofluoride 1 Σ 817 773 0.946 31 33
NaCl Sodium Chloride 1 Σ 353 361 1.023 32 34
AlCl Aluminum monochloride 1 Σ 480 478 0.995 33 35
SCl sulfur monochloride 1 Σ 583 577 0.989 34 36
Cl2 Chlorine diatomic 1 Σg 570 554 0.972 35 37
BeH2 beryllium dihydride 2 Σu 2250 2159 0.960 36 38
    3 Πu 715 698 0.976 36 39
MgH2 magnesium dihydride 2 Σu 1627 1572 0.966 37 40
    3 Πu 440 440 0.999 37 41
SiH2 silicon dihydride 1 A1 2086 1996 0.957 38 42
    2 A1 1031 999 0.969 38 43
    3 B2 2083 1993 0.957 38 44
HCN Hydrogen cyanide 1 Σ 3464 3312 0.956 39 45
    2 Σ 2186 2089 0.956 39 46
    3 Π 749 712 0.951 39 47
H2O Water 1 A1 3875 3657 0.944 40 48
    2 A1 1664 1595 0.959 40 49
    3 B2 3981 3756 0.943 40 50
HBO Boron hydride oxide 1 Σ 2904 2850 0.981 41 51
    2 Σ 1879 1826 0.972 41 52
    3 Π 781 756 0.969 41 53
HO2 Hydroperoxy radical 1 A' 3718 3436 0.924 42 54
    2 A' 1472 1392 0.945 42 55
    3 A' 1183 1098 0.928 42 56
CO2 Carbon dioxide 1 Σg 1394 1333 0.956 43 57
    2 Σu 2430 2349 0.967 43 58
    3 Πu 695 667 0.960 43 59
N2O Nitrous oxide 1 Σ 2365 2224 0.940 44 60
    2 Σ 1330 1285 0.966 44 61
    3 Π 626 589 0.941 44 62
H2S Hydrogen sulfide 1 A1 2737 2615 0.955 45 63
    2 A1 1225 1183 0.966 45 64
    3 B2 2752 2626 0.954 45 65
OCS Carbonyl sulfide 1 Σ 2143 2062 0.962 46 66
    2 Σ 883 859 0.973 46 67
    3 Π 541 520 0.962 46 68
CF2 Difluoromethylene 1 A1 1276 1225 0.960 47 69
    2 A1 688 667 0.970 47 70
    3 B2 1174 1114 0.949 47 71
HOCl hypochlorous acid 1 A' 3851 3609 0.937 48 72
    2 A' 1294 1239 0.957 48 73
    3 A' 774 724 0.935 48 74
BH3 boron trihydride 2 A2" 1162 1148 0.987 49 75
    3 E' 2706 2602 0.961 49 76
    4 E' 1225 1197 0.977 49 77
AlH3 aluminum trihydride 1 A1' 1956 1900 0.972 50 78
    2 A2" 717 698 0.974 50 79
    3 E' 1959 1883 0.961 50 80
    4 E' 802 783 0.977 50 81
C2H2 Acetylene 1 Σg 3525 3374 0.957 51 82
    2 Σg 2052 1974 0.962 51 83
    3 Σu 3428 3289 0.960 51 84
    4 Πg 649 612 0.943 51 85
    5 Πu 768 730 0.950 51 86
SiH3 Silyl radical 1 A1 2239 2136 0.954 52 87
    2 A1 779 728 0.934 52 88
    3 E 2269 2185 0.963 52 89
    4 E 947 922 0.973 52 90
NH3 Ammonia 1 A1 3509 3337 0.951 53 91
    2 A1 1065 950 0.892 53 92
    3 E 3637 3444 0.947 53 93
    4 E 1688 1627 0.964 53 94
PH3 Phosphine 1 A1 2434 2323 0.955 54 95
    2 A1 1025 992 0.968 54 96
    3 E 2440 2328 0.954 54 97
    4 E 1154 1118 0.968 54 98
H2CS Thioformaldehyde 1 A1 3112 2971 0.955 55 99
    2 A1 1516 1456 0.960 55 100
    3 A1 1105 1059 0.958 55 101
    4 B1 1029 990 0.962 55 102
    5 B2 3202 3025 0.945 55 103
    6 B2 1014 991 0.978 55 104
H2S2 Disulfane 1 A 2702 2556 0.946 56 105
    2 A 918 882 0.961 56 106
    3 A 534 515 0.963 56 107
    4 A 439 417 0.951 56 108
    5 B 2704 2559 0.946 56 109
    6 B 917 878 0.957 56 110
AlF3 Aluminum trifluoride 1 A1' 707 690 0.976 57 111
    2 A2" 300 297 0.991 57 112
    3 E' 975 935 0.959 57 113
    4 E' 250 263 1.054 57 114
CH4 Methane 1 A1 3049 2917 0.957 58 115
    2 E 1581 1534 0.970 58 116
    3 T2 3168 3019 0.953 58 117
    4 T2 1358 1306 0.962 58 118
SiH4 Silane 1 A1 2269 2187 0.964 59 119
    2 E 987 975 0.988 59 120
    3 T2 2270 2191 0.965 59 121
    4 T2 937 914 0.975 59 122

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.

40 100 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 80 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 60 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 20 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