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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 2909 2733 0.940 5 5
    1 Σ 3201     5 6
N2 Nitrogen diatomic 1 Σg 2438 2330 0.956 6 7
    1 Σg 1824 1733 0.950 6 8
PH phosphorus monohydride 1 Σ 2407 2276 0.946 7 9
    1 Σ 2429 2319 0.955 7 10
OH Hydroxyl radical 1 Σ 3809 3570 0.937 8 11
CO Carbon monoxide 1 Σ 2253 2143 0.951 9 12
    1 Σ 2360     9 13
SO Sulfur monoxide 1 Σ 1204 1138 0.945 10 14
    1 Σ 1154 1054 0.914 10 15
HF Hydrogen fluoride 1 Σ 4243 3961 0.934 11 16
F2 Fluorine diatomic 1 Σg 1043 894 0.857 12 17
HCl Hydrogen chloride 1 Σ 3043 2886 0.949 13 18
AlCl Aluminum monochloride 1 Σ 488 478 0.979 14 19
BeH2 beryllium dihydride 2 Σu 2304 2159 0.937 15 20
    3 Πu 737 698 0.947 15 21
H2O Water 1 A1 3906 3657 0.936 16 22
    2 A1 1717 1595 0.929 16 23
    3 B2 4017 3756 0.935 16 24
CO2 Carbon dioxide 1 Σg 1418 1333 0.940 17 25
    2 Σu 2490 2349 0.943 17 26
    3 Πu 716 667 0.932 17 27
SO2 Sulfur dioxide 1 A1 1240 1151 0.928 18 28
    2 A1 542 518 0.955 18 29
    3 B2 1463 1362 0.931 18 30
C2H2 Acetylene 1 Σg 3587 3374 0.941 19 31
    2 Σg 2078 1974 0.950 19 32
    3 Σu 3485 3289 0.944 19 33
    4 Πg 566 612 1.082 19 34
    5 Πu 795 730 0.918 19 35
NH3 Ammonia 1 A1 3533 3337 0.944 20 36
    2 A1 1148 950 0.828 20 37
    3 E 3664 3444 0.940 20 38
    4 E 1720 1627 0.946 20 39
H2CO Formaldehyde 1 A1 2989 2782 0.931 21 40
    2 A1 1863 1746 0.937 21 41
    3 A1 1575 1500 0.952 21 42
    4 B1 1220 1167 0.956 21 43
    5 B2 3059 2843 0.929 21 44
    6 B2 1302 1249 0.959 21 45
BF3 Borane, trifluoro- 1 A1' 920 888 0.965 22 46
    2 A2" 725 691 0.953 22 47
    3 E' 1534 1449 0.945 22 48
    4 E' 503 480 0.955 22 49
AlF3 Aluminum trifluoride 1 A1' 723 690 0.955 23 50
    2 A2" 311 297 0.954 23 51
    3 E' 1005 935 0.931 23 52
    4 E' 248 263 1.062 23 53
CH4 Methane 1 A1 3092 2917 0.943 24 54
    2 E 1597 1534 0.960 24 55
    3 T2 3222 3019 0.937 24 56
    4 T2 1377 1306 0.948 24 57
C2H4 Ethylene 1 Ag 3215 3026 0.941 25 58
    2 Ag 1716 1623 0.946 25 59
    3 Ag 1401 1342 0.958 25 60
    4 Au 1077 1023 0.949 25 61
    5 B1u 3196 2989 0.935 25 62
    6 B1u 1497 1444 0.965 25 63
    7 B2g 980 940 0.959 25 64
    8 B2u 3303 3105 0.940 25 65
    9 B2u 834 826 0.990 25 66
    10 B3g 3279 3086 0.941 25 67
    11 B3g 1258 1217 0.967 25 68
    12 B3u 997 949 0.952 25 69
C3H2N2 Malononitrile 1 A1 3124 2935 0.940 26 70
    2 A1 2403 2275 0.947 26 71
    3 A1 1483 1395 0.940 26 72
    4 A1 915 890 0.973 26 73
    5 A1 589 582 0.988 26 74
    6 A1 149 167 1.121 26 75
    7 A2 1270 1220 0.961 26 76
    8 A2 376 367 0.975 26 77
    9 B1 3173 2968 0.935 26 78
    10 B1 961 933 0.971 26 79
    11 B1 347 337 0.971 26 80
    12 B2 2402 2275 0.947 26 81
    13 B2 1375 1318 0.958 26 82
    14 B2 1008 982 0.974 26 83
    15 B2 376 366 0.974 26 84
C2H6 Ethane 1 A1g 3099 2954 0.953 27 85
    2 A1g 1461 1388 0.950 27 86
    3 A1g 1029 995 0.967 27 87
    4 A1u 314 289 0.921 27 88
    5 A2u 3100 2896 0.934 27 89
    6 A2u 1439 1379 0.958 27 90
    7 Eg 3167 2969 0.937 27 91
    8 Eg 1539 1468 0.954 27 92
    9 Eg 1246 1190 0.955 27 93
    10 Eu 3189 2985 0.936 27 94
    11 Eu 1543 1469 0.952 27 95
    12 Eu 834 822 0.986 27 96
C3H5 Allyl radical 1 A1 3320 3114 0.938 28 97
    2 A1 3223 3048 0.946 28 98
    4 A1 1555 1488 0.957 28 99
    5 A1 1308 1245 0.952 28 100
    6 A1 1067 1066 0.999 28 101
    7 A1 431 427 0.991 28 102
    9 A2 592 549 0.928 28 103
    10 B1 1069 968 0.906 28 104
    11 B1 847 802 0.946 28 105
    12 B1 563 518 0.920 28 106
    13 B2 3317 3105 0.936 28 107
    14 B2 3213 3016 0.939 28 108
    15 B2 1518 1463 0.964 28 109
    16 B2 1437 1389 0.967 28 110
    17 B2 1157 1182 1.021 28 111
C3H6 Cyclopropane 1 A1' 3209 3038 0.947 29 112
    2 A1' 1555 1479 0.951 29 113
    3 A1' 1243 1188 0.955 29 114
    4 A1" 1184 1126 0.951 29 115
    5 A2' 1118 1070 0.957 29 116
    6 A2" 3303 3103 0.939 29 117
    7 A2" 866 854 0.986 29 118
    8 E' 3199 3025 0.946 29 119
    9 E' 1500 1438 0.959 29 120
    10 E' 1093 1029 0.941 29 121
    11 E' 925 866 0.936 29 122
    12 E" 3285 3082 0.938 29 123
    13 E" 1237 1188 0.961 29 124
    14 E" 751 739 0.984 29 125
CH2CHCH3 Propene 1 A' 3289 3090 0.940 30 126
    2 A' 3209 3013 0.939 30 127
    3 A' 3196 2991 0.936 30 128
    4 A' 3178 2954 0.930 30 129
    5 A' 3087 2871 0.930 30 130
    6 A' 1748 1650 0.944 30 131
    7 A' 1530 1470 0.961 30 132
    8 A' 1481 1420 0.959 30 133
    9 A' 1439 1378 0.957 30 134
    10 A' 1348 1297 0.962 30 135
    11 A' 1212 1171 0.966 30 136
    12 A' 958 963 1.005 30 137
    13 A' 945 920 0.973 30 138
    14 A' 425 428 1.007 30 139
    15 A" 3154 2954 0.937 30 140
    16 A" 1517 1443 0.951 30 141
    17 A" 1090 1045 0.959 30 142
    18 A" 1046 991 0.947 30 143
    19 A" 964 912 0.946 30 144
    20 A" 597 578 0.969 30 145
    21 A" 203 174 0.858 30 146
CH3CHClCH3 Propane, 2-chloro- 1 A' 3202 3005 0.939 31 147
    2 A' 3184 2955 0.928 31 148
    3 A' 3151 2927 0.929 31 149
    4 A' 3099 2878 0.929 31 150
    5 A' 1540 1472 0.956 31 151
    6 A' 1527 1454 0.952 31 152
    7 A' 1454 1390 0.956 31 153
    8 A' 1326 1270 0.958 31 154
    9 A' 1213 1163 0.959 31 155
    10 A' 1106 1065 0.963 31 156
    11 A' 927 888 0.958 31 157
    12 A' 669 633 0.946 31 158
    13 A' 427 418 0.979 31 159
    14 A' 342 336 0.984 31 160
    15 A' 279 253 0.908 31 161
    16 A" 3198 2997 0.937 31 162
    17 A" 3178 2985 0.939 31 163
    18 A" 3096 2947 0.952 31 164
    19 A" 1519 1472 0.969 31 165
    20 A" 1515 1454 0.960 31 166
    21 A" 1441 1377 0.956 31 167
    22 A" 1388 1334 0.961 31 168
    23 A" 1176 1123 0.955 31 169
    24 A" 974 972 0.998 31 170
    25 A" 954 936 0.981 31 171
    26 A" 329 317 0.962 31 172
    27 A" 248 276 1.114 31 173

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