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Vibrational frequency scaling factors


Calculated vibrational frequencies ("theory" in table) are calculated at CCSD(T)=FULL/6-31G*
Scale factor How many Source
Molecules Vibrations
0.971 ± 0.031 30 95 cccbdb
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Formula Name Mode Symmetry Frequency Count
Theory Experiment ratio molecules vibrations
LiH Lithium Hydride 1 Σ 1332 1360 1.021 1 1
CH Methylidyne 1 Σ 2806 2733 0.974 2 2
    1 Σ 3174     2 3
CN Cyano radical 1 Σ 2120 2042 0.963 3 4
N2 Nitrogen diatomic 1 Σg 2345 2330 0.993 4 5
    1 Σg 1743 1733 0.994 4 6
OH Hydroxyl radical 1 Σ 3630 3570 0.983 5 7
CO Carbon monoxide 1 Σ 2159 2143 0.993 6 8
    1 Σ 1760     6 9
MgO magnesium oxide 1 Σ 747 775 1.037 7 10
HF Hydrogen fluoride 1 Σ 4006 3961 0.989 8 11
CF Fluoromethylidyne 1 Σ 1310 1286 0.982 9 12
F2 Fluorine diatomic 1 Σg 890 894 1.005 10 13
HCl Hydrogen chloride 1 Σ 2962 2886 0.974 11 14
Cl2 Chlorine diatomic 1 Σg 503 554 1.101 12 15
MgH2 magnesium dihydride 2 Σu 1583 1572 0.993 13 16
    3 Πu 442 440 0.996 13 17
HCN Hydrogen cyanide 1 Σ 3466 3312 0.955 14 18
    2 Σ 2130 2089 0.981 14 19
    3 Π 714 712 0.998 14 20
H2O Water 1 A1 3727 3657 0.981 15 21
    2 A1 1742 1595 0.916 15 22
    3 B2 3856 3756 0.974 15 23
CO2 Carbon dioxide 1 Σg 1349 1333 0.989 16 24
    2 Σu 2417 2349 0.972 16 25
    3 Πu 645 667 1.035 16 26
H2S Hydrogen sulfide 1 A1 2702 2615 0.968 17 27
    2 A1 1257 1183 0.941 17 28
    3 B2 2726 2626 0.963 17 29
SO2 Sulfur dioxide 1 A1 1111 1151 1.036 18 30
    2 A1 499 518 1.038 18 31
    3 B2 1324 1362 1.028 18 32
ClCN chlorocyanogen 1 Σ 2264 2216 0.979 19 33
    2 Σ 741 744 1.004 19 34
    3 Π 355 378 1.065 19 35
AlH3 aluminum trihydride 1 A1' 1924 1900 0.988 20 36
    2 A2" 702 698 0.994 20 37
    3 E' 1942 1883 0.970 20 38
    4 E' 786 783 0.997 20 39
C2H2 Acetylene 1 Σg 3520 3374 0.959 21 40
    2 Σg 2024 1974 0.976 21 41
    3 Σu 3425 3289 0.960 21 42
    4 Πg 358 612 1.708 21 43
    5 Πu 735 730 0.993 21 44
NH3 Ammonia 1 A1 3435 3337 0.972 22 45
    2 A1 1180 950 0.805 22 46
    3 E 3576 3444 0.963 22 47
    4 E 1747 1627 0.932 22 48
H2CO Formaldehyde 1 A1 2956 2782 0.941 23 49
    2 A1 1795 1746 0.973 23 50
    3 A1 1566 1500 0.958 23 51
    4 B1 1185 1167 0.985 23 52
    5 B2 3021 2843 0.941 23 53
    6 B2 1285 1249 0.972 23 54
H2O2 Hydrogen peroxide 1 A 3698 3599 0.973 24 55
    2 A 1455 1402 0.964 24 56
    3 A 879 877 0.998 24 57
    4 A 326 371 1.137 24 58
    5 B 3701 3608 0.975 24 59
    6 B 1311 1266 0.965 24 60
H2CS Thioformaldehyde 1 A1 3111 2971 0.955 25 61
    2 A1 1544 1456 0.943 25 62
    3 A1 1071 1059 0.989 25 63
    4 B1 1009 990 0.981 25 64
    5 B2 3200 3025 0.945 25 65
    6 B2 1036 991 0.957 25 66
BF3 Borane, trifluoro- 1 A1' 892 888 0.995 26 67
    2 A2" 701 691 0.985 26 68
    3 E' 1505 1449 0.963 26 69
    4 E' 483 480 0.994 26 70
CH4 Methane 1 A1 3246 2917 0.899 27 71
    2 E 1756 1534 0.874 27 72
    3 T2 3480 3019 0.868 27 73
    4 T2 1537 1306 0.850 27 74
HCOOH Formic acid 1 A' 3661 3570 0.975 28 75
    2 A' 3113 2943 0.945 28 76
    3 A' 1846 1770 0.959 28 77
    4 A' 1432 1387 0.968 28 78
    5 A' 1344 1229 0.915 28 79
    6 A' 1153 1105 0.958 28 80
    7 A' 626 625 0.998 28 81
    8 A" 1054 1033 0.980 28 82
    9 A" 701 638 0.911 28 83
C2H6 Ethane 1 A1g 3055 2954 0.967 29 84
    2 A1g 1476 1388 0.940 29 85
    3 A1g 1034 995 0.962 29 86
    4 A1u 322 289 0.899 29 87
    5 A2u 3054 2896 0.948 29 88
    6 A2u 1449 1379 0.952 29 89
    7 Eg 3116 2969 0.953 29 90
    8 Eg 1546 1468 0.950 29 91
    9 Eg 1256 1190 0.948 29 92
    10 Eu 3138 2985 0.951 29 93
    11 Eu 1551 1469 0.947 29 94
    12 Eu 839 822 0.980 29 95

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