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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)/6-311G**
Scale factor How many Source
Molecules Vibrations
0.965 ± 0.023 47 148 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1410 1360 0.964 1 1
Li2 Lithium diatomic 1 Σg 348 346 0.996 2 2
NaH sodium hydride 1 Σ 1151 1133 0.985 3 3
Na2 Sodium diatomic 1 Σg 153 158 1.029 4 4
BH Boron monohydride 1 Σ 2343 2269 0.969 5 5
AlH aluminum monohydride 1 Σ 1713 1625 0.949 6 6
C2 Carbon diatomic 1 Σg 1830 1827 0.999 7 7
N2 Nitrogen diatomic 1 Σg 2340 2330 0.996 8 8
PN Phosphorus mononitride 1 Σ 1329 1323 0.995 9 9
P2 Phosphorus diatomic 1 Σg 766 775 1.012 10 10
CO Carbon monoxide 1 Σ 2165 2143 0.990 11 11
MgO magnesium oxide 1 Σ 745 775 1.040 12 12
SiO Silicon monoxide 1 Σ 1227 1230 1.002 13 13
BeS beryllium sulfide 1 Σ 985 986 1.000 14 14
CS carbon monosulfide 1 Σ 1281 1272 0.993 15 15
MgS magnesium sulfide 1 Σ 520 523 1.007 16 16
SiS silicon monosulfide 1 Σ 738 744 1.009 17 17
HF Hydrogen fluoride 1 Σ 4234 3961 0.936 18 18
LiF lithium fluoride 1 Σ 961 896 0.933 19 19
F2 Fluorine diatomic 1 Σg 771 894 1.159 20 20
NaF sodium fluoride 1 Σ 575 529 0.920 21 21
AlF Aluminum monofluoride 1 Σ 816 793 0.971 22 22
HCl Hydrogen chloride 1 Σ 3029 2886 0.953 23 23
BCl boron monochloride 1 Σ 860 829 0.965 24 24
ClF Chlorine monofluoride 1 Σ 687 773 1.126 25 25
Cl2 Chlorine diatomic 1 Σg 503 554 1.103 26 26
HCN Hydrogen cyanide 1 Σ 3460 3312 0.957 27 27
    2 Σ 2104 2089 0.993 27 28
    3 Π 742 712 0.959 27 29
H2O Water 1 A1 3877 3657 0.943 28 30
    2 A1 1682 1595 0.948 28 31
    3 B2 3972 3756 0.946 28 32
CO2 Carbon dioxide 1 Σg 1352 1333 0.986 29 33
    2 Σu 2419 2349 0.971 29 34
    3 Πu 660 667 1.010 29 35
H2S Hydrogen sulfide 1 A1 2749 2615 0.951 30 36
    2 A1 1219 1183 0.970 30 37
    3 B2 2766 2626 0.949 30 38
OCS Carbonyl sulfide 1 Σ 2103 2062 0.981 31 39
    2 Σ 873 859 0.984 31 40
    3 Π 508 520 1.024 31 41
SO2 Sulfur dioxide 1 A1 1116 1151 1.032 32 42
    2 A1 507 518 1.020 32 43
    3 B2 1323 1362 1.029 32 44
HOF Hypofluorous acid 1 A' 3811 3578 0.939 33 45
    2 A' 1384 1362 0.984 33 46
    3 A' 855 893 1.045 33 47
HOCl hypochlorous acid 1 A' 3838 3609 0.941 34 48
    2 A' 1220 1239 1.016 34 49
    3 A' 664 724 1.090 34 50
ClCN chlorocyanogen 1 Σ 2241 2216 0.989 35 51
    2 Σ 737 744 1.009 35 52
    3 Π 359 378 1.053 35 53
C2H2 Acetylene 1 Σg 3518 3374 0.959 36 54
    2 Σg 1988 1974 0.993 36 55
    3 Σu 3423 3289 0.961 36 56
    4 Πg 525 612 1.167 36 57
    5 Πu 754 730 0.968 36 58
NH3 Ammonia 1 A1 3476 3337 0.960 37 59
    2 A1 1147 950 0.828 37 60
    3 E 3605 3444 0.955 37 61
    4 E 1672 1627 0.973 37 62
H2CO Formaldehyde 1 A1 2923 2782 0.952 38 63
    2 A1 1781 1746 0.980 38 64
    3 A1 1555 1500 0.965 38 65
    4 B1 1188 1167 0.982 38 66
    5 B2 2982 2843 0.953 38 67
    6 B2 1280 1249 0.976 38 68
BF3 Borane, trifluoro- 1 A1' 883 888 1.006 39 69
    2 A2" 708 691 0.977 39 70
    3 E' 1466 1449 0.988 39 71
    4 E' 485 480 0.990 39 72
AlF3 Aluminum trifluoride 1 A1' 700 690 0.986 40 73
    2 A2" 303 297 0.981 40 74
    3 E' 983 935 0.952 40 75
    4 E' 247 263 1.066 40 76
CH4 Methane 1 A1 3034 2917 0.961 41 77
    2 E 1564 1534 0.981 41 78
    3 T2 3155 3019 0.957 41 79
    4 T2 1358 1306 0.962 41 80
CH3Cl Methyl chloride 1 A1 3082 2966 0.962 42 81
    2 A1 1427 1355 0.950 42 82
    3 A1 755 732 0.970 42 83
    4 E 3181 3042 0.956 42 84
    5 E 1485 1455 0.980 42 85
    6 E 1051 1015 0.966 42 86
C2H4 Ethylene 1 Ag 3153 3026 0.960 43 87
    2 Ag 1664 1623 0.975 43 88
    3 Ag 1365 1342 0.983 43 89
    4 Au 1038 1023 0.986 43 90
    5 B1u 3136 2989 0.953 43 91
    6 B1u 1473 1444 0.980 43 92
    7 B2g 890 940 1.056 43 93
    8 B2u 3243 3105 0.957 43 94
    9 B2u 821 826 1.006 43 95
    10 B3g 3217 3086 0.959 43 96
    11 B3g 1230 1217 0.990 43 97
    12 B3u 949 949 1.001 43 98
C2H6 Ethane 1 A1g 3040 2954 0.972 44 99
    2 A1g 1444 1388 0.961 44 100
    3 A1g 1017 995 0.979 44 101
    4 A1u 325 289 0.890 44 102
    5 A2u 3037 2896 0.954 44 103
    6 A2u 1415 1379 0.974 44 104
    7 Eg 3099 2969 0.958 44 105
    8 Eg 1511 1468 0.971 44 106
    9 Eg 1235 1190 0.964 44 107
    10 Eu 3122 2985 0.956 44 108
    11 Eu 1516 1469 0.969 44 109
    12 Eu 826 822 0.996 44 110
C3H6 Cyclopropane 1 A1' 3151 3038 0.964 45 111
    2 A1' 1536 1479 0.963 45 112
    3 A1' 1219 1188 0.975 45 113
    4 A1" 1172 1126 0.961 45 114
    5 A2' 1094 1070 0.978 45 115
    6 A2" 3245 3103 0.956 45 116
    7 A2" 864 854 0.989 45 117
    8 E' 3140 3025 0.963 45 118
    9 E' 1483 1438 0.970 45 119
    10 E' 1086 1029 0.947 45 120
    11 E' 895 866 0.967 45 121
    12 E" 3225 3082 0.956 45 122
    13 E" 1226 1188 0.969 45 123
    14 E" 754 739 0.981 45 124
CH2CHCH3 Propene 1 A' 3227 3090 0.957 46 125
    2 A' 3146 3013 0.958 46 126
    3 A' 3134 2991 0.954 46 127
    4 A' 3113 2954 0.949 46 128
    5 A' 3028 2871 0.948 46 129
    6 A' 1690 1650 0.976 46 130
    7 A' 1507 1470 0.976 46 131
    8 A' 1456 1420 0.975 46 132
    9 A' 1416 1378 0.973 46 133
    10 A' 1314 1297 0.987 46 134
    11 A' 1191 1171 0.983 46 135
    12 A' 943 963 1.021 46 136
    13 A' 929 920 0.990 46 137
    14 A' 418 428 1.023 46 138
    15 A" 3091 2954 0.956 46 139
    16 A" 1490 1443 0.969 46 140
    17 A" 1067 1045 0.980 46 141
    18 A" 1000 991 0.991 46 142
    19 A" 888 912 1.027 46 143
    20 A" 570 578 1.014 46 144
    21 A" 193 174 0.901 46 145

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 70 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 50 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 30 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 10 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