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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at QCISD(T)/aug-cc-pVDZ
Scale factor How many Source
Molecules Vibrations
0.978 ± 0.028 32 157 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4344 4161 0.958 1 1
LiH Lithium Hydride 1 Σ 1344 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
CH Methylidyne 1 Σ 3078     5 5
Si2 Silicon diatomic 1 Σg 522 507 0.970 6 6
N2 Nitrogen diatomic 1 Σg 2313 2330 1.007 7 7
PH phosphorus monohydride 1 Σ 2327 2276 0.978 8 8
    1 Σ 2354 2319 0.985 8 9
OH Hydroxyl radical 1 Σ 3678 3570 0.971 9 10
CO Carbon monoxide 1 Σ 2092 2143 1.024 10 11
SO Sulfur monoxide 1 Σ 1065 1138 1.069 11 12
    1 Σ 1003 1054 1.051 11 13
HF Hydrogen fluoride 1 Σ 4079 3961 0.971 12 14
F2 Fluorine diatomic 1 Σg 831 894 1.076 13 15
HCl Hydrogen chloride 1 Σ 2970 2886 0.972 14 16
BeH2 beryllium dihydride 2 Σu 2229 2159 0.968 15 17
    3 Πu 724 698 0.964 15 18
H2O Water 1 A1 3785 3657 0.966 16 19
    2 A1 1636 1595 0.975 16 20
    3 B2 3904 3756 0.962 16 21
CO2 Carbon dioxide 1 Σg 1307 1333 1.020 17 22
    2 Σu 2328 2349 1.009 17 23
    3 Πu 656 667 1.017 17 24
OCS Carbonyl sulfide 1 Σ 2031 2062 1.015 18 25
    2 Σ 844 859 1.017 18 26
    3 Π 508 520 1.023 18 27
SO2 Sulfur dioxide 1 A1 1032 1151 1.115 19 28
    2 A1 470 518 1.101 19 29
    3 B2 1201 1362 1.134 19 30
C2H2 Acetylene 1 Σg 3479 3374 0.970 20 31
    2 Σg 1967 1974 1.004 20 32
    3 Σu 3385 3289 0.972 20 33
    4 Πg 364 612 1.684 20 34
    5 Πu 690 730 1.058 20 35
NH3 Ammonia 1 A1 3432 3337 0.972 21 36
    2 A1 1070 950 0.888 21 37
    3 E 3570 3444 0.965 21 38
    4 E 1650 1627 0.986 21 39
H2CO Formaldehyde 1 A1 2928 2782 0.950 22 40
    2 A1 1734 1746 1.007 22 41
    3 A1 1514 1500 0.991 22 42
    4 B1 1166 1167 1.001 22 43
    5 B2 3004 2843 0.946 22 44
    6 B2 1243 1249 1.005 22 45
BF3 Borane, trifluoro- 1 A1' 838 888 1.060 23 46
    2 A2" 707 691 0.977 23 47
    3 E' 1400 1449 1.035 23 48
    4 E' 456 480 1.052 23 49
AlF3 Aluminum trifluoride 1 A1' 665 690 1.037 24 50
    2 A2" 293 297 1.014 24 51
    3 E' 924 935 1.012 24 52
    4 E' 245 263 1.075 24 53
CH4 Methane 1 A1 3017 2917 0.967 25 54
    2 E 1535 1534 1.000 25 55
    3 T2 3144 3019 0.960 25 56
    4 T2 1319 1306 0.990 25 57
C2H4 Ethylene 1 Ag 3148 3026 0.961 26 58
    2 Ag 1653 1623 0.982 26 59
    3 Ag 1352 1342 0.993 26 60
    4 Au 1016 1023 1.007 26 61
    5 B1u 3130 2989 0.955 26 62
    6 B1u 1459 1444 0.989 26 63
    7 B2g 927 940 1.014 26 64
    8 B2u 3245 3105 0.957 26 65
    9 B2u 813 826 1.016 26 66
    10 B3g 3217 3086 0.959 26 67
    11 B3g 1223 1217 0.995 26 68
    12 B3u 957 949 0.992 26 69
C2H6 Ethane 1 A1g 3023 2954 0.977 27 70
    2 A1g 1408 1388 0.986 27 71
    3 A1g 1011 995 0.984 27 72
    4 A1u 312 289 0.926 27 73
    5 A2u 3018 2896 0.959 27 74
    6 A2u 1380 1379 1.000 27 75
    7 Eg 3085 2969 0.963 27 76
    8 Eg 1483 1468 0.990 27 77
    9 Eg 1206 1190 0.987 27 78
    10 Eu 3106 2985 0.961 27 79
    11 Eu 1484 1469 0.990 27 80
    12 Eu 809 822 1.017 27 81
C3H5 Allyl radical 1 A1 3249 3114 0.958 28 82
    2 A1 3156 3048 0.966 28 83
    4 A1 1512 1488 0.984 28 84
    5 A1 1259 1245 0.989 28 85
    6 A1 1025 1066 1.040 28 86
    7 A1 420 427 1.017 28 87
    9 A2 546 549 1.005 28 88
    10 B1 982 968 0.986 28 89
    11 B1 790 802 1.015 28 90
    12 B1 524 518 0.988 28 91
    13 B2 3246 3105 0.957 28 92
    14 B2 3139 3016 0.961 28 93
    15 B2 1504 1463 0.972 28 94
    16 B2 1405 1389 0.989 28 95
    17 B2 1185 1182 0.997 28 96
C3H6 Cyclopropane 1 A1' 3140 3038 0.967 29 97
    2 A1' 1506 1479 0.982 29 98
    3 A1' 1201 1188 0.989 29 99
    4 A1" 1136 1126 0.991 29 100
    5 A2' 1050 1070 1.019 29 101
    6 A2" 3236 3103 0.959 29 102
    7 A2" 837 854 1.020 29 103
    8 E' 3128 3025 0.967 29 104
    9 E' 1453 1438 0.990 29 105
    10 E' 1031 1029 0.998 29 106
    11 E' 876 866 0.989 29 107
    12 E" 3216 3082 0.958 29 108
    13 E" 1193 1188 0.995 29 109
    14 E" 722 739 1.024 29 110
CH2CHCH3 Propene 1 A' 3225 3090 0.958 30 111
    2 A' 3143 3013 0.959 30 112
    3 A' 3127 2991 0.956 30 113
    4 A' 3099 2954 0.953 30 114
    5 A' 3010 2871 0.954 30 115
    6 A' 1679 1650 0.983 30 116
    7 A' 1476 1470 0.996 30 117
    8 A' 1437 1420 0.988 30 118
    9 A' 1384 1378 0.996 30 119
    10 A' 1305 1297 0.994 30 120
    11 A' 1178 1171 0.994 30 121
    12 A' 928 963 1.037 30 122
    13 A' 925 920 0.995 30 123
    14 A' 414 428 1.033 30 124
    15 A" 3076 2954 0.960 30 125
    16 A" 1459 1443 0.989 30 126
    17 A" 1046 1045 0.999 30 127
    18 A" 987 991 1.004 30 128
    19 A" 911 912 1.001 30 129
    20 A" 570 578 1.014 30 130
    21 A" 199 174 0.874 30 131
CH3CHClCH3 Propane, 2-chloro- 1 A' 3124 3005 0.962 31 132
    2 A' 3102 2955 0.953 31 133
    3 A' 3078 2927 0.951 31 134
    4 A' 3019 2878 0.953 31 135
    5 A' 1486 1472 0.991 31 136
    6 A' 1472 1454 0.988 31 137
    7 A' 1399 1390 0.994 31 138
    8 A' 1272 1270 0.999 31 139
    9 A' 1176 1163 0.989 31 140
    10 A' 1065 1065 1.000 31 141
    11 A' 901 888 0.985 31 142
    12 A' 621 633 1.019 31 143
    13 A' 417 418 1.001 31 144
    14 A' 334 336 1.006 31 145
    15 A' 266 253 0.950 31 146
    16 A" 3120 2997 0.961 31 147
    17 A" 3094 2985 0.965 31 148
    18 A" 3015 2947 0.977 31 149
    19 A" 1465 1472 1.004 31 150
    20 A" 1460 1454 0.996 31 151
    21 A" 1390 1377 0.991 31 152
    22 A" 1342 1334 0.994 31 153
    23 A" 1152 1123 0.975 31 154
    24 A" 943 972 1.030 31 155
    25 A" 923 936 1.014 31 156
    26 A" 321 317 0.987 31 157
    27 A" 233 276 1.184 31 158

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