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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)/cc-pVQZ
Scale factor How many Source
Molecules Vibrations
0.970 ± 0.020 26 88 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
H2 Hydrogen diatomic 1 Σg 4404 4161 0.945 1 1
LiH Lithium Hydride 1 Σ 1393 1360 0.976 2 2
Li2 Lithium diatomic 1 Σg 347 346 0.999 3 3
Na2 Sodium diatomic 1 Σg 152 158 1.039 4 4
N2 Nitrogen diatomic 1 Σg 2357 2330 0.989 5 5
PH phosphorus monohydride 1 Σ 2366 2276 0.962 6 6
    1 Σ 2385 2319 0.972 6 7
OH Hydroxyl radical 1 Σ 3745 3570 0.953 7 8
CO Carbon monoxide 1 Σ 2165 2143 0.990 8 9
SO Sulfur monoxide 1 Σ 1153 1138 0.987 9 10
    1 Σ 1095 1054 0.963 9 11
HF Hydrogen fluoride 1 Σ 4163 3961 0.952 10 12
F2 Fluorine diatomic 1 Σg 921 894 0.971 11 13
HCl Hydrogen chloride 1 Σ 2998 2886 0.963 12 14
AlCl Aluminum monochloride 1 Σ 481 478 0.992 13 15
BeH2 beryllium dihydride 2 Σu 2250 2159 0.960 14 16
    3 Πu 714 698 0.977 14 17
H2O Water 1 A1 3845 3657 0.951 15 18
    2 A1 1659 1595 0.961 15 19
    3 B2 3952 3756 0.950 15 20
CO2 Carbon dioxide 1 Σg 1352 1333 0.986 16 21
    2 Σu 2396 2349 0.980 16 22
    3 Πu 671 667 0.994 16 23
C2H2 Acetylene 1 Σg 3503 3374 0.963 17 24
    2 Σg 2006 1974 0.984 17 25
    3 Σu 3411 3289 0.964 17 26
    4 Πg 595 612 1.029 17 27
    5 Πu 746 730 0.979 17 28
NH3 Ammonia 1 A1 3481 3337 0.959 18 29
    2 A1 1083 950 0.877 18 30
    3 E 3610 3444 0.954 18 31
    4 E 1680 1627 0.969 18 32
H2CO Formaldehyde 1 A1 2934 2782 0.948 19 33
    2 A1 1781 1746 0.980 19 34
    3 A1 1538 1500 0.976 19 35
    4 B1 1190 1167 0.981 19 36
    5 B2 3004 2843 0.946 19 37
    6 B2 1272 1249 0.982 19 38
BF3 Borane, trifluoro- 1 A1' 897 888 0.991 20 39
    2 A2" 697 691 0.992 20 40
    3 E' 1481 1449 0.979 20 41
    4 E' 482 480 0.997 20 42
AlF3 Aluminum trifluoride 1 A1' 702 690 0.983 21 43
    2 A2" 297 297 1.000 21 44
    3 E' 970 935 0.964 21 45
    4 E' 248 263 1.062 21 46
CH4 Methane 1 A1 3037 2917 0.960 22 47
    2 E 1570 1534 0.977 22 48
    3 T2 3158 3019 0.956 22 49
    4 T2 1345 1306 0.971 22 50
C2H4 Ethylene 1 Ag 3157 3026 0.959 23 51
    2 Ag 1671 1623 0.971 23 52
    3 Ag 1367 1342 0.982 23 53
    4 Au 1049 1023 0.976 23 54
    5 B1u 3142 2989 0.951 23 55
    6 B1u 1475 1444 0.979 23 56
    7 B2g 948 940 0.992 23 57
    8 B2u 3249 3105 0.956 23 58
    9 B2u 821 826 1.006 23 59
    10 B3g 3223 3086 0.957 23 60
    11 B3g 1243 1217 0.979 23 61
    12 B3u 966 949 0.983 23 62
C2H6 Ethane 1 A1g 3040 2954 0.972 24 63
    2 A1g 1428 1388 0.972 24 64
    3 A1g 1014 995 0.981 24 65
    4 A1u 303 289 0.953 24 66
    5 A2u 3039 2896 0.953 24 67
    6 A2u 1408 1379 0.979 24 68
    7 Eg 3100 2969 0.958 24 69
    8 Eg 1510 1468 0.972 24 70
    9 Eg 1225 1190 0.972 24 71
    10 Eu 3123 2985 0.956 24 72
    11 Eu 1512 1469 0.972 24 73
    12 Eu 821 822 1.001 24 74
C3H5 Allyl radical 1 A1 3255 3114 0.957 25 75
    2 A1 3155 3048 0.966 25 76
    4 A1 1511 1488 0.985 25 77
    5 A1 1271 1245 0.979 25 78
    6 A1 1034 1066 1.031 25 79
    7 A1 410 427 1.043 25 80
    9 A2 510 549 1.077 25 81
    10 B1 998 968 0.970 25 82
    11 B1 805 802 0.996 25 83
    12 B1 499 518 1.038 25 84
    13 B2 3254 3105 0.954 25 85
    14 B2 3143 3016 0.960 25 86
    15 B2 1509 1463 0.970 25 87
    16 B2 1415 1389 0.982 25 88
    17 B2 1176 1182 1.005 25 89

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 45 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 35 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 25 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 15 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 5 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