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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)/3-21G
Scale factor How many Source
Molecules Vibrations
0.991 ± 0.114 48 163 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4383 4161 0.949 1 1
LiH Lithium Hydride 1 Σ 1305 1360 1.042 2 2
Li2 Lithium diatomic 1 Σg 340 346 1.017 3 3
NaH sodium hydride 1 Σ 1039 1133 1.091 4 4
Na2 Sodium diatomic 1 Σg 145 158 1.086 5 5
BH Boron monohydride 1 Σ 2218 2269 1.023 6 6
AlH aluminum monohydride 1 Σ 1549 1625 1.049 7 7
C2 Carbon diatomic 1 Σg 1863 1827 0.981 8 8
N2 Nitrogen diatomic 1 Σg 2138 2330 1.090 9 9
PN Phosphorus mononitride 1 Σ 1153 1323 1.148 10 10
P2 Phosphorus diatomic 1 Σg 612 775 1.267 11 11
CO Carbon monoxide 1 Σ 1995 2143 1.074 12 12
MgO magnesium oxide 1 Σ 670 775 1.156 13 13
SiO Silicon monoxide 1 Σ 1115 1230 1.103 14 14
BeS beryllium sulfide 1 Σ 933 986 1.057 15 15
CS carbon monosulfide 1 Σ 1077 1272 1.182 16 16
MgS magnesium sulfide 1 Σ 475 523 1.102 17 17
SiS silicon monosulfide 1 Σ 613 744 1.215 18 18
HF Hydrogen fluoride 1 Σ 3661 3961 1.082 19 19
LiF lithium fluoride 1 Σ 1052 896 0.852 20 20
F2 Fluorine diatomic 1 Σg 911 894 0.981 21 21
NaF sodium fluoride 1 Σ 579 529 0.913 22 22
AlF Aluminum monofluoride 1 Σ 843 793 0.940 23 23
HCl Hydrogen chloride 1 Σ 2573 2886 1.122 24 24
BCl boron monochloride 1 Σ 627 829 1.323 25 25
ClF Chlorine monofluoride 1 Σ 623 773 1.241 26 26
Cl2 Chlorine diatomic 1 Σg 398 554 1.393 27 27
HCN Hydrogen cyanide 1 Σ 3435 3312 0.964 28 28
    2 Σ 2059 2089 1.014 28 29
    3 Π 818 712 0.870 28 30
H2O Water 1 A1 3411 3657 1.072 29 31
    2 A1 1720 1595 0.927 29 32
    3 B2 3559 3756 1.055 29 33
CO2 Carbon dioxide 1 Σg 1239 1333 1.076 30 34
    2 Σu 2262 2349 1.038 30 35
    3 Πu 547 667 1.218 30 36
H2S Hydrogen sulfide 1 A1 2371 2615 1.103 31 37
    2 A1 1199 1183 0.987 31 38
    3 B2 2397 2626 1.096 31 39
OCS Carbonyl sulfide 1 Σ 1984 2062 1.039 32 40
    2 Σ 762 859 1.127 32 41
    3 Π 501 520 1.038 32 42
SO2 Sulfur dioxide 1 A1 816 1151 1.411 33 43
    2 A1 399 518 1.298 33 44
    3 B2 933 1362 1.460 33 45
CS2 Carbon disulfide 1 Σg 587 658 1.121 34 46
    2 Σu 1425 1535 1.077 34 47
    3 Πu 370 397 1.074 34 48
HOF Hypofluorous acid 1 A' 3310 3578 1.081 35 49
    2 A' 1273 1362 1.070 35 50
    3 A' 898 893 0.995 35 51
HOCl hypochlorous acid 1 A' 3309 3609 1.091 36 52
    2 A' 1221 1239 1.015 36 53
    3 A' 595 724 1.217 36 54
ClCN chlorocyanogen 1 Σ 2193 2216 1.010 37 55
    2 Σ 615 744 1.211 37 56
    3 Π 424 378 0.892 37 57
C2H2 Acetylene 1 Σg 3464 3374 0.974 38 58
H2CO Formaldehyde 1 A1 2912 2782 0.955 39 59
    2 A1 1693 1746 1.031 39 60
    3 A1 1524 1500 0.984 39 61
    4 B1 1178 1167 0.990 39 62
    5 B2 2968 2843 0.958 39 63
    6 B2 1282 1249 0.974 39 64
BF3 Borane, trifluoro- 1 A1' 903 888 0.983 40 65
    2 A2" 659 691 1.048 40 66
    3 E' 1577 1449 0.919 40 67
    4 E' 481 480 0.998 40 68
AlF3 Aluminum trifluoride 1 A1' 720 690 0.958 41 69
    2 A2" 276 297 1.077 41 70
    3 E' 1034 935 0.904 41 71
    4 E' 276 263 0.951 41 72
CH4 Methane 1 A1 3012 2917 0.968 42 73
    2 E 1634 1534 0.939 42 74
    3 T2 3111 3019 0.970 42 75
    4 T2 1429 1306 0.914 42 76
CH3Cl Methyl chloride 1 A1 3086 2966 0.961 43 77
    2 A1 1386 1355 0.978 43 78
    3 A1 611 732 1.198 43 79
    4 E 3198 3042 0.951 43 80
    5 E 1541 1455 0.944 43 81
    6 E 1002 1015 1.013 43 82
C2H4 Ethylene 1 Ag 3118 3026 0.971 44 83
    2 Ag 1665 1623 0.975 44 84
    3 Ag 1398 1342 0.960 44 85
    4 Au 1042 1023 0.982 44 86
    5 B1u 3098 2989 0.965 44 87
    6 B1u 1542 1444 0.936 44 88
    7 B2g 942 940 0.998 44 89
    8 B2u 3196 3105 0.971 44 90
    9 B2u 876 826 0.943 44 91
    10 B3g 3167 3086 0.974 44 92
    11 B3g 1280 1217 0.951 44 93
    12 B3u 967 949 0.982 44 94
B2H6 Diborane 1 Ag 2624 2530 0.964 45 95
    2 Ag 2164 2088 0.965 45 96
    3 Ag 1208 1183 0.979 45 97
    4 Ag 802 790 0.985 45 98
    5 Au 867 833 0.961 45 99
    6 B1g 2715 2596 0.956 45 100
    7 B1g 913 915 1.003 45 101
    8 B1u 1928 1930 1.001 45 102
    9 B1u 971 973 1.002 45 103
    10 B2g 1867 1760 0.943 45 104
    11 B2g 794 860 1.083 45 105
    12 B2u 2724 2609 0.958 45 106
    13 B2u 1013 949 0.937 45 107
    14 B2u 405 369 0.910 45 108
    15 B3g 1085 1020 0.940 45 109
    16 B3u 2613 2520 0.964 45 110
    17 B3u 1760 1603 0.911 45 111
    18 B3u 1208 1172 0.970 45 112
C2H6 Ethane 1 A1g 3016 2954 0.979 46 113
    2 A1g 1471 1388 0.944 46 114
    3 A1g 948 995 1.050 46 115
    4 A1u 311 289 0.930 46 116
    5 A2u 3015 2896 0.960 46 117
    6 A2u 1476 1379 0.934 46 118
    7 Eg 3066 2969 0.968 46 119
    8 Eg 1577 1468 0.931 46 120
    9 Eg 1270 1190 0.937 46 121
    10 Eu 3089 2985 0.966 46 122
    11 Eu 1580 1469 0.930 46 123
    12 Eu 857 822 0.959 46 124
C3H6 Cyclopropane 1 A1' 3144 3038 0.966 47 125
    2 A1' 1552 1479 0.953 47 126
    3 A1' 1115 1188 1.065 47 127
    4 A1" 1186 1126 0.949 47 128
    5 A2' 1145 1070 0.934 47 129
    6 A2" 3235 3103 0.959 47 130
    7 A2" 862 854 0.990 47 131
    8 E' 3133 3025 0.966 47 132
    9 E' 1530 1438 0.940 47 133
    10 E' 1122 1029 0.917 47 134
    11 E' 826 866 1.048 47 135
    12 E" 3213 3082 0.959 47 136
    13 E" 1233 1188 0.963 47 137
    14 E" 775 739 0.953 47 138
CH2CHCH3 Propene 1 A' 3179 3090 0.972 48 139
    2 A' 3108 3013 0.969 48 140
    3 A' 3097 2991 0.966 48 141
    4 A' 3072 2954 0.962 48 142
    5 A' 3003 2871 0.956 48 143
    6 A' 1673 1650 0.986 48 144
    7 A' 1570 1470 0.936 48 145
    8 A' 1501 1420 0.946 48 146
    9 A' 1468 1378 0.939 48 147
    10 A' 1357 1297 0.955 48 148
    11 A' 1212 1171 0.966 48 149
    12 A' 992 963 0.971 48 150
    13 A' 887 920 1.038 48 151
    14 A' 435 428 0.984 48 152
    15 A" 3056 2954 0.967 48 153
    16 A" 1558 1443 0.926 48 154
    17 A" 1110 1045 0.942 48 155
    18 A" 1012 991 0.980 48 156
    19 A" 928 912 0.983 48 157
    20 A" 579 578 0.999 48 158
    21 A" 181 174 0.959 48 159

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