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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.969 ± 0.024 30 164 cccbdb
Jump to histogram
Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4349 4161 0.957 1 1
LiH Lithium Hydride 1 Σ 1343 1360 1.012 2 2
Li2 Lithium diatomic 1 Σg 339 346 1.022 3 3
Na2 Sodium diatomic 1 Σg 149 158 1.057 4 4
Si2 Silicon diatomic 1 Σg 508 507 0.998 5 5
N2 Nitrogen diatomic 1 Σg 2513 2330 0.927 6 6
    1 Σg 1745 1733 0.993 6 7
OH Hydroxyl radical 1 Σ 3707 3570 0.963 7 8
CO Carbon monoxide 1 Σ 2130 2143 1.006 8 9
    1 Σ 1769     8 10
HF Hydrogen fluoride 1 Σ 4107 3961 0.965 9 11
F2 Fluorine diatomic 1 Σg 919 894 0.973 10 12
HCl Hydrogen chloride 1 Σ 2988 2886 0.966 11 13
AlCl Aluminum monochloride 1 Σ 445 478 1.073 12 14
BeH2 beryllium dihydride 2 Σu 2232 2159 0.968 13 15
    3 Πu 725 698 0.962 13 16
H2O Water 1 A1 3816 3657 0.958 14 17
    2 A1 1646 1595 0.969 14 18
    3 B2 3932 3756 0.955 14 19
CO2 Carbon dioxide 1 Σg 1338 1333 0.996 15 20
    2 Σu 2353 2349 0.998 15 21
    3 Πu 675 667 0.988 15 22
SO2 Sulfur dioxide 1 A1 1092 1151 1.054 16 23
    2 A1 489 518 1.059 16 24
    3 B2 1252 1362 1.088 16 25
C2H2 Acetylene 1 Σg 3499 3374 0.964 17 26
    2 Σg 2007 1974 0.983 17 27
    3 Σu 3403 3289 0.967 17 28
    4 Πg 434 612 1.411 17 29
    5 Πu 712 730 1.025 17 30
NH3 Ammonia 1 A1 3461 3337 0.964 18 31
    2 A1 1071 950 0.887 18 32
    3 E 3596 3444 0.958 18 33
    4 E 1661 1627 0.979 18 34
H2CO Formaldehyde 1 A1 2952 2782 0.943 19 35
    2 A1 1770 1746 0.986 19 36
    3 A1 1527 1500 0.982 19 37
    4 B1 1187 1167 0.983 19 38
    5 B2 3026 2843 0.939 19 39
    6 B2 1255 1249 0.995 19 40
BF3 Borane, trifluoro- 1 A1' 845 888 1.051 20 41
    2 A2" 712 691 0.971 20 42
    3 E' 1412 1449 1.026 20 43
    4 E' 460 480 1.044 20 44
NF3 Nitrogen trifluoride 1 A1 1037 1032 0.995 21 45
    2 A1 647 647 1.000 21 46
    3 E 937 907 0.968 21 47
    4 E 492 492 1.000 21 48
AlF3 Aluminum trifluoride 1 A1' 670 690 1.030 22 49
    2 A2" 294 297 1.009 22 50
    3 E' 929 935 1.006 22 51
    4 E' 246 263 1.068 22 52
CH4 Methane 1 A1 3030 2917 0.963 23 53
    2 E 1544 1534 0.994 23 54
    3 T2 3156 3019 0.957 23 55
    4 T2 1330 1306 0.982 23 56
CF2Cl2 difluorodichloromethane 1 A1 1110 1101 0.992 24 57
    2 A1 657 667 1.015 24 58
    3 A1 457 458 1.002 24 59
    4 A1 267 262 0.980 24 60
    5 A2 325 322 0.992 24 61
    6 B1 934 902 0.966 24 62
    7 B1 441 437 0.991 24 63
    8 B2 1162 1159 0.998 24 64
    9 B2 440 446 1.014 24 65
C2H4 Ethylene 1 Ag 3167 3026 0.955 25 66
    2 Ag 1681 1623 0.966 25 67
    3 Ag 1370 1342 0.980 25 68
    4 Au 1032 1023 0.992 25 69
    5 B1u 3148 2989 0.949 25 70
    6 B1u 1473 1444 0.980 25 71
    7 B2g 953 940 0.986 25 72
    8 B2u 3262 3105 0.952 25 73
    9 B2u 824 826 1.003 25 74
    10 B3g 3234 3086 0.954 25 75
    11 B3g 1235 1217 0.986 25 76
    12 B3u 975 949 0.974 25 77
C2H6 Ethane 1 A1g 3040 2954 0.972 26 78
    2 A1g 1423 1388 0.975 26 79
    3 A1g 1022 995 0.974 26 80
    4 A1u 316 289 0.915 26 81
    5 A2u 3036 2896 0.954 26 82
    6 A2u 1393 1379 0.990 26 83
    7 Eg 3100 2969 0.958 26 84
    8 Eg 1493 1468 0.983 26 85
    9 Eg 1217 1190 0.977 26 86
    10 Eu 3121 2985 0.956 26 87
    11 Eu 1495 1469 0.983 26 88
    12 Eu 817 822 1.007 26 89
C3H5 Allyl radical 1 A1 3266 3114 0.953 27 90
    2 A1 3176 3048 0.960 27 91
    4 A1 1522 1488 0.978 27 92
    5 A1 1268 1245 0.982 27 93
    6 A1 1032 1066 1.033 27 94
    7 A1 422 427 1.011 27 95
    9 A2 547 549 1.004 27 96
    10 B1 989 968 0.979 27 97
    11 B1 798 802 1.004 27 98
    12 B1 527 518 0.983 27 99
    13 B2 3263 3105 0.952 27 100
    14 B2 3156 3016 0.956 27 101
    15 B2 1513 1463 0.967 27 102
    16 B2 1415 1389 0.981 27 103
    17 B2 1188 1182 0.995 27 104
C3H6 Cyclopropane 1 A1' 3160 3038 0.962 28 105
    2 A1' 1525 1479 0.970 28 106
    3 A1' 1218 1188 0.976 28 107
    4 A1" 1148 1126 0.981 28 108
    5 A2' 1070 1070 1.000 28 109
    6 A2" 3253 3103 0.954 28 110
    7 A2" 846 854 1.009 28 111
    8 E' 3146 3025 0.961 28 112
    9 E' 1468 1438 0.980 28 113
    10 E' 1049 1029 0.981 28 114
    11 E' 890 866 0.972 28 115
    12 E" 3233 3082 0.953 28 116
    13 E" 1206 1188 0.985 28 117
    14 E" 731 739 1.011 28 118
CH2CHCH3 Propene 1 A' 3244 3090 0.953 29 119
    2 A' 3164 3013 0.952 29 120
    3 A' 3148 2991 0.950 29 121
    4 A' 3117 2954 0.948 29 122
    5 A' 3029 2871 0.948 29 123
    6 A' 1711 1650 0.965 29 124
    7 A' 1488 1470 0.988 29 125
    8 A' 1453 1420 0.978 29 126
    9 A' 1400 1378 0.984 29 127
    10 A' 1321 1297 0.982 29 128
    11 A' 1191 1171 0.983 29 129
    12 A' 939 963 1.026 29 130
    13 A' 935 920 0.984 29 131
    14 A' 420 428 1.019 29 132
    15 A" 3093 2954 0.955 29 133
    16 A" 1471 1443 0.981 29 134
    17 A" 1061 1045 0.985 29 135
    18 A" 1004 991 0.987 29 136
    19 A" 935 912 0.976 29 137
    20 A" 580 578 0.997 29 138
    21 A" 200 174 0.871 29 139
CH3CHClCH3 Propane, 2-chloro- 1 A' 3142 3005 0.956 30 140
    2 A' 3122 2955 0.947 30 141
    3 A' 3100 2927 0.944 30 142
    4 A' 3040 2878 0.947 30 143
    5 A' 1498 1472 0.982 30 144
    6 A' 1485 1454 0.979 30 145
    7 A' 1416 1390 0.982 30 146
    8 A' 1290 1270 0.985 30 147
    9 A' 1189 1163 0.978 30 148
    10 A' 1079 1065 0.987 30 149
    11 A' 912 888 0.973 30 150
    12 A' 632 633 1.001 30 151
    13 A' 423 418 0.988 30 152
    14 A' 339 336 0.992 30 153
    15 A' 271 253 0.933 30 154
    16 A" 3137 2997 0.955 30 155
    17 A" 3113 2985 0.959 30 156
    18 A" 3036 2947 0.971 30 157
    19 A" 1478 1472 0.996 30 158
    20 A" 1473 1454 0.987 30 159
    21 A" 1407 1377 0.979 30 160
    22 A" 1357 1334 0.983 30 161
    23 A" 1163 1123 0.965 30 162
    24 A" 955 972 1.018 30 163
    25 A" 934 936 1.003 30 164
    26 A" 327 317 0.969 30 165
    27 A" 238 276 1.160 30 166

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 90 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 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