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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCD/6-31G(2df,p)
Scale factor How many Source
Molecules Vibrations
0.947 ± 0.018 32 169 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4519 4161 0.921 1 1
LiH Lithium Hydride 1 Σ 1425 1360 0.954 2 2
Li2 Lithium diatomic 1 Σg 347 346 0.999 3 3
Na2 Sodium diatomic 1 Σg 152 158 1.037 4 4
CH Methylidyne 1 Σ 3201     5 5
N2 Nitrogen diatomic 1 Σg 2438 2330 0.956 6 6
PH phosphorus monohydride 1 Σ 2407 2276 0.946 7 7
    1 Σ 2429 2319 0.955 7 8
OH Hydroxyl radical 1 Σ 3809 3570 0.937 8 9
CO Carbon monoxide 1 Σ 2253 2143 0.951 9 10
SO Sulfur monoxide 1 Σ 1204 1138 0.945 10 11
    1 Σ 1154 1054 0.914 10 12
HF Hydrogen fluoride 1 Σ 4243 3961 0.934 11 13
F2 Fluorine diatomic 1 Σg 1043 894 0.857 12 14
HCl Hydrogen chloride 1 Σ 3043 2886 0.949 13 15
AlCl Aluminum monochloride 1 Σ 488 478 0.979 14 16
BeH2 beryllium dihydride 2 Σu 2304 2159 0.937 15 17
    3 Πu 737 698 0.947 15 18
H2O Water 1 A1 3906 3657 0.936 16 19
    2 A1 1717 1595 0.929 16 20
    3 B2 4017 3756 0.935 16 21
CO2 Carbon dioxide 1 Σg 1418 1333 0.940 17 22
    2 Σu 2490 2349 0.943 17 23
    3 Πu 716 667 0.932 17 24
SO2 Sulfur dioxide 1 A1 1240 1151 0.928 18 25
    2 A1 542 518 0.955 18 26
    3 B2 1463 1362 0.931 18 27
C2H2 Acetylene 1 Σg 3587 3374 0.941 19 28
    2 Σg 2078 1974 0.950 19 29
    3 Σu 3485 3289 0.944 19 30
    4 Πg 566 612 1.082 19 31
    5 Πu 795 730 0.918 19 32
NH3 Ammonia 1 A1 3533 3337 0.944 20 33
    2 A1 1148 950 0.828 20 34
    3 E 3664 3444 0.940 20 35
    4 E 1720 1627 0.946 20 36
H2CO Formaldehyde 1 A1 2989 2782 0.931 21 37
    2 A1 1864 1746 0.937 21 38
    3 A1 1576 1500 0.952 21 39
    4 B1 1220 1167 0.956 21 40
    5 B2 3058 2843 0.930 21 41
    6 B2 1302 1249 0.959 21 42
BF3 Borane, trifluoro- 1 A1' 920 888 0.965 22 43
    2 A2" 725 691 0.953 22 44
    3 E' 1534 1449 0.945 22 45
    4 E' 503 480 0.955 22 46
AlF3 Aluminum trifluoride 1 A1' 723 690 0.955 23 47
    2 A2" 311 297 0.954 23 48
    3 E' 1005 935 0.931 23 49
    4 E' 248 263 1.062 23 50
CH4 Methane 1 A1 3092 2917 0.943 24 51
    2 E 1597 1534 0.960 24 52
    3 T2 3222 3019 0.937 24 53
    4 T2 1377 1306 0.948 24 54
C2H4 Ethylene 1 Ag 3215 3026 0.941 25 55
    2 Ag 1716 1623 0.946 25 56
    3 Ag 1401 1342 0.958 25 57
    4 Au 1077 1023 0.949 25 58
    5 B1u 3196 2989 0.935 25 59
    6 B1u 1497 1444 0.965 25 60
    7 B2g 980 940 0.959 25 61
    8 B2u 3303 3105 0.940 25 62
    9 B2u 834 826 0.990 25 63
    10 B3g 3279 3086 0.941 25 64
    11 B3g 1258 1217 0.967 25 65
    12 B3u 997 949 0.952 25 66
C3H2N2 Malononitrile 1 A1 3124 2935 0.940 26 67
    2 A1 2403 2275 0.947 26 68
    3 A1 1483 1395 0.940 26 69
    4 A1 915 890 0.973 26 70
    5 A1 589 582 0.988 26 71
    6 A1 149 167 1.121 26 72
    7 A2 1270 1220 0.961 26 73
    8 A2 376 367 0.975 26 74
    9 B1 3173 2968 0.935 26 75
    10 B1 961 933 0.971 26 76
    11 B1 347 337 0.971 26 77
    12 B2 2402 2275 0.947 26 78
    13 B2 1375 1318 0.958 26 79
    14 B2 1008 982 0.974 26 80
    15 B2 376 366 0.974 26 81
C2H6 Ethane 1 A1g 3099 2954 0.953 27 82
    2 A1g 1461 1388 0.950 27 83
    3 A1g 1029 995 0.967 27 84
    4 A1u 314 289 0.921 27 85
    5 A2u 3100 2896 0.934 27 86
    6 A2u 1439 1379 0.958 27 87
    7 Eg 3167 2969 0.937 27 88
    8 Eg 1539 1468 0.954 27 89
    9 Eg 1246 1190 0.955 27 90
    10 Eu 3189 2985 0.936 27 91
    11 Eu 1543 1469 0.952 27 92
    12 Eu 834 822 0.986 27 93
C3H5 Allyl radical 1 A1 3320 3114 0.938 28 94
    2 A1 3223 3048 0.946 28 95
    4 A1 1555 1488 0.957 28 96
    5 A1 1308 1245 0.952 28 97
    6 A1 1067 1066 0.999 28 98
    7 A1 431 427 0.991 28 99
    9 A2 592 549 0.928 28 100
    10 B1 1069 968 0.906 28 101
    11 B1 847 802 0.946 28 102
    12 B1 563 518 0.920 28 103
    13 B2 3317 3105 0.936 28 104
    14 B2 3213 3016 0.939 28 105
    15 B2 1518 1463 0.964 28 106
    16 B2 1437 1389 0.967 28 107
    17 B2 1157 1182 1.021 28 108
C3H6 Cyclopropane 1 A1' 3209 3038 0.947 29 109
    2 A1' 1555 1479 0.951 29 110
    3 A1' 1243 1188 0.955 29 111
    4 A1" 1184 1126 0.951 29 112
    5 A2' 1118 1070 0.957 29 113
    6 A2" 3303 3103 0.939 29 114
    7 A2" 866 854 0.986 29 115
    8 E' 3199 3025 0.946 29 116
    9 E' 1500 1438 0.959 29 117
    10 E' 1093 1029 0.941 29 118
    11 E' 925 866 0.936 29 119
    12 E" 3285 3082 0.938 29 120
    13 E" 1237 1188 0.961 29 121
    14 E" 751 739 0.984 29 122
CH2CHCH3 Propene 1 A' 3289 3090 0.940 30 123
    2 A' 3209 3013 0.939 30 124
    3 A' 3196 2991 0.936 30 125
    4 A' 3178 2954 0.930 30 126
    5 A' 3087 2871 0.930 30 127
    6 A' 1748 1650 0.944 30 128
    7 A' 1530 1470 0.961 30 129
    8 A' 1481 1420 0.959 30 130
    9 A' 1439 1378 0.957 30 131
    10 A' 1348 1297 0.962 30 132
    11 A' 1212 1171 0.966 30 133
    12 A' 958 963 1.005 30 134
    13 A' 945 920 0.973 30 135
    14 A' 425 428 1.007 30 136
    15 A" 3154 2954 0.937 30 137
    16 A" 1517 1443 0.951 30 138
    17 A" 1090 1045 0.959 30 139
    18 A" 1046 991 0.947 30 140
    19 A" 964 912 0.946 30 141
    20 A" 597 578 0.969 30 142
    21 A" 203 174 0.858 30 143
CH3CHClCH3 Propane, 2-chloro- 1 A' 3202 3005 0.939 31 144
    2 A' 3184 2955 0.928 31 145
    3 A' 3151 2927 0.929 31 146
    4 A' 3099 2878 0.929 31 147
    5 A' 1540 1472 0.956 31 148
    6 A' 1527 1454 0.952 31 149
    7 A' 1454 1390 0.956 31 150
    8 A' 1326 1270 0.958 31 151
    9 A' 1213 1163 0.959 31 152
    10 A' 1106 1065 0.963 31 153
    11 A' 927 888 0.958 31 154
    12 A' 669 633 0.946 31 155
    13 A' 427 418 0.979 31 156
    14 A' 342 336 0.984 31 157
    15 A' 279 253 0.908 31 158
    16 A" 3198 2997 0.937 31 159
    17 A" 3178 2985 0.939 31 160
    18 A" 3096 2947 0.952 31 161
    19 A" 1519 1472 0.969 31 162
    20 A" 1515 1454 0.960 31 163
    21 A" 1441 1377 0.956 31 164
    22 A" 1388 1334 0.961 31 165
    23 A" 1176 1123 0.955 31 166
    24 A" 974 972 0.998 31 167
    25 A" 954 936 0.981 31 168
    26 A" 329 317 0.962 31 169
    27 A" 248 276 1.114 31 170

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