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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at MP3/cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.948 ± 0.027 42 206 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4447 4161 0.936 1 1
LiH Lithium Hydride 1 Σ 1393 1360 0.976 2 2
Na2 Sodium diatomic 1 Σg 154 158 1.022 3 3
BeH beryllium monohydride 1 Σ 2080 1987 0.955 4 4
C2 Carbon diatomic 1 Σg 1941 1827 0.941 5 5
Si2 Silicon diatomic 1 Σg 503 507 1.008 6 6
CN Cyano radical 1 Σ 2661 2042 0.768 7 7
N2 Nitrogen diatomic 1 Σg 2529 2330 0.921 8 8
P2 Phosphorus diatomic 1 Σg 825 775 0.939 9 9
OH Hydroxyl radical 1 Σ 3778 3570 0.945 10 10
CO Carbon monoxide 1 Σ 2300 2143 0.932 11 11
HS Mercapto radical 1 Σ 2741 2599 0.948 12 12
SO Sulfur monoxide 1 Σ 1157 1138 0.984 13 13
HF Hydrogen fluoride 1 Σ 4215 3961 0.940 14 14
F2 Fluorine diatomic 1 Σg 934 894 0.957 15 15
SF Monosulfur monofluoride 1 Σ 830 829 0.999 16 16
HCl Hydrogen chloride 1 Σ 3059 2886 0.943 17 17
NaCl Sodium Chloride 1 Σ 353 361 1.023 18 18
AlCl Aluminum monochloride 1 Σ 477 478 1.000 19 19
SCl sulfur monochloride 1 Σ 552 577 1.045 20 20
Cl2 Chlorine diatomic 1 Σg 531 554 1.043 21 21
SiH2 silicon dihydride 1 A1 2097 1996 0.952 22 22
    2 A1 1046 999 0.955 22 23
    3 B2 2093 1993 0.952 22 24
HCN Hydrogen cyanide 1 Σ 3512 3312 0.943 23 25
    2 Σ 2241 2089 0.932 23 26
    3 Π 748 712 0.951 23 27
H2O Water 1 A1 3897 3657 0.938 24 28
    2 A1 1702 1595 0.937 24 29
    3 B2 3994 3756 0.940 24 30
CO2 Carbon dioxide 1 Σg 1428 1333 0.934 25 31
    2 Σu 2487 2349 0.944 25 32
    3 Πu 686 667 0.972 25 33
N2O Nitrous oxide 1 Σ 2461 2224 0.904 26 34
    2 Σ 1399 1285 0.918 26 35
    3 Π 622 589 0.948 26 36
SO2 Sulfur dioxide 1 A1 1205 1151 0.955 27 37
    2 A1 531 518 0.975 27 38
    3 B2 1397 1362 0.975 27 39
C2H2 Acetylene 1 Σg 3554 3374 0.949 28 40
    2 Σg 2080 1974 0.949 28 41
    3 Σu 3457 3289 0.951 28 42
    4 Πg 606 612 1.011 28 43
    5 Πu 772 730 0.946 28 44
NH3 Ammonia 1 A1 3501 3337 0.953 29 45
    2 A1 1177 950 0.807 29 46
    3 E 3624 3444 0.950 29 47
    4 E 1698 1627 0.958 29 48
H2CO Formaldehyde 1 A1 2981 2782 0.933 30 49
    2 A1 1872 1746 0.932 30 50
    3 A1 1563 1500 0.960 30 51
    4 B1 1208 1167 0.966 30 52
    5 B2 3054 2843 0.931 30 53
    6 B2 1291 1249 0.967 30 54
BF3 Borane, trifluoro- 1 A1' 886 888 1.002 31 55
    2 A2" 724 691 0.954 31 56
    3 E' 1494 1449 0.970 31 57
    4 E' 490 480 0.979 31 58
AlF3 Aluminum trifluoride 1 A1' 685 690 1.008 32 59
    2 A2" 299 297 0.994 32 60
    3 E' 961 935 0.973 32 61
    4 E' 239 263 1.101 32 62
CH4 Methane 1 A1 3079 2917 0.947 33 63
    2 E 1562 1534 0.982 33 64
    3 T2 3216 3019 0.939 33 65
    4 T2 1343 1306 0.972 33 66
C2H4 Ethylene 1 Ag 3206 3026 0.944 34 67
    2 Ag 1715 1623 0.946 34 68
    3 Ag 1383 1342 0.970 34 69
    4 Au 1059 1023 0.966 34 70
    5 B1u 3187 2989 0.938 34 71
    6 B1u 1477 1444 0.978 34 72
    7 B2g 947 940 0.993 34 73
    8 B2u 3302 3105 0.940 34 74
    9 B2u 830 826 0.995 34 75
    10 B3g 3276 3086 0.942 34 76
    11 B3g 1245 1217 0.978 34 77
    12 B3u 976 949 0.973 34 78
B2Cl4 Diboron tetrachloride 1 A1 1179 1122 0.952 35 79
    2 A1 414 401 0.968 35 80
    3 A1 176 176 0.999 35 81
    5 B2 756 728 0.963 35 82
    6 B2 298 289 0.971 35 83
    7 E 969 917 0.946 35 84
    8 E 509 512 1.007 35 85
    9 E 99 104 1.051 35 86
CH2N4 1H-Tetrazole 1 A' 3739 3447 0.922 36 87
    2 A' 3352 3102 0.925 36 88
    3 A' 1565 1441 0.920 36 89
    4 A' 1527 1384 0.906 36 90
    5 A' 1359 1259 0.926 36 91
    6 A' 1310 1159 0.885 36 92
    7 A' 1170 1084 0.927 36 93
    8 A' 1124 1015 0.903 36 94
    9 A' 1103 1002 0.909 36 95
    10 A' 1032 969 0.939 36 96
    11 A' 998 925 0.927 36 97
    12 A" 876 906 1.034 36 98
    13 A" 749 663 0.886 36 99
    14 A" 700 658 0.939 36 100
    15 A" 575 578 1.005 36 101
C2H6 Ethane 1 A1g 3088 2954 0.957 37 102
    2 A1g 1440 1388 0.964 37 103
    3 A1g 1037 995 0.959 37 104
    4 A1u 328 289 0.882 37 105
    5 A2u 3084 2896 0.939 37 106
    6 A2u 1407 1379 0.980 37 107
    7 Eg 3158 2969 0.940 37 108
    8 Eg 1505 1468 0.975 37 109
    9 Eg 1228 1190 0.969 37 110
    10 Eu 3179 2985 0.939 37 111
    11 Eu 1507 1469 0.975 37 112
    12 Eu 825 822 0.997 37 113
C3H3NO Oxazole 1 A' 3359 3170 0.944 38 114
    2 A' 3337 3144 0.942 38 115
    3 A' 3325 3141 0.945 38 116
    4 A' 1635 1537 0.940 38 117
    5 A' 1586 1504 0.948 38 118
    6 A' 1395 1324 0.949 38 119
    7 A' 1293 1252 0.968 38 120
    8 A' 1222 1139 0.932 38 121
    9 A' 1149 1086 0.945 38 122
    10 A' 1129 1078 0.955 38 123
    11 A' 1103 1046 0.948 38 124
    12 A' 944 899 0.952 38 125
    13 A' 928 854 0.920 38 126
    14 A" 884 907 1.026 38 127
    15 A" 861 830 0.964 38 128
    16 A" 782 750 0.959 38 129
    17 A" 668 647 0.968 38 130
    18 A" 629 607 0.965 38 131
C3H6 Cyclopropane 1 A1' 3199 3038 0.950 39 132
    2 A1' 1540 1479 0.960 39 133
    3 A1' 1237 1188 0.960 39 134
    4 A1" 1162 1126 0.969 39 135
    5 A2' 1090 1070 0.981 39 136
    6 A2" 3295 3103 0.942 39 137
    7 A2" 859 854 0.994 39 138
    8 E' 3187 3025 0.949 39 139
    9 E' 1474 1438 0.976 39 140
    10 E' 1077 1029 0.956 39 141
    11 E' 914 866 0.948 39 142
    12 E" 3276 3082 0.941 39 143
    13 E" 1219 1188 0.975 39 144
    14 E" 742 739 0.996 39 145
CH2CHCH3 Propene 1 A' 3286 3090 0.940 40 146
    2 A' 3200 3013 0.941 40 147
    3 A' 3187 2991 0.939 40 148
    4 A' 3171 2954 0.932 40 149
    5 A' 3077 2871 0.933 40 150
    6 A' 1748 1650 0.944 40 151
    7 A' 1497 1470 0.982 40 152
    8 A' 1462 1420 0.972 40 153
    9 A' 1413 1378 0.975 40 154
    10 A' 1328 1297 0.977 40 155
    11 A' 1199 1171 0.977 40 156
    12 A' 949 963 1.015 40 157
    13 A' 946 920 0.973 40 158
    14 A' 423 428 1.013 40 159
    15 A" 3149 2954 0.938 40 160
    16 A" 1483 1443 0.973 40 161
    17 A" 1071 1045 0.975 40 162
    18 A" 1027 991 0.965 40 163
    19 A" 936 912 0.974 40 164
    20 A" 586 578 0.986 40 165
    21 A" 202 174 0.861 40 166
CHCCH2CH3 1-Butyne 1 A' 3512 3332 0.949 41 167
    2 A' 3182 2988 0.939 41 168
    3 A' 3098     41 169
    4 A' 3093     41 170
    5 A' 2255 2116 0.938 41 171
    6 A' 1507 1470 0.975 41 172
    7 A' 1484 1446 0.974 41 173
    8 A' 1422 1385 0.974 41 174
    9 A' 1366 1322 0.968 41 175
    10 A' 1104 1070 0.969 41 176
    11 A' 1054 1008 0.956 41 177
    12 A' 863 840 0.974 41 178
    13 A' 654 634 0.970 41 179
    14 A' 514 509 0.991 41 180
    15 A' 198 197 0.991 41 181
    16 A" 3188 2988 0.937 41 182
    17 A" 3140 2939 0.936 41 183
    18 A" 1498 1462 0.976 41 184
    19 A" 1299 1261 0.971 41 185
    20 A" 1117 1090 0.976 41 186
    21 A" 791 782 0.989 41 187
    22 A" 649 630 0.971 41 188
    23 A" 358 344 0.958 41 189
    24 A" 228 213 0.933 41 190

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.

40 140 1 1 1 1 1 1 1 1 1 1 1 1 1 1
40 120 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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