National Institute of Standards and Technology
Computational Chemistry Comparison and Benchmark DataBase
Release 18October 2016
NIST Standard Reference Database 101
IIntroduction
IIExperimental data
IIICalculated data
IVData comparisons
VCost comparisons
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XOlder CCCBDB versions
XIIGeometries
XIII Vibrations
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XVEntropy data
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XVIIIon data
XVIIIBad calculations
XIXIndex of properties
XXH-bond dimers
XXIOddities

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III.G.7. (XIII.B.3.) (XIII.D.5.)

Compare vibrational frequencies for two calculations for C6H5CH3 (toluene)

A = HF/6-31G*

B = MP2/6-31G*

scale factors=0.8985, 0.943
  symmetry   frequency (cm-1)   reduced mass (amu)   IR Intensity (km mol-1)
mode number A B   A B diff. ratio   A B diff. ratio   A B diff. ratio
1 A' A'   3041 3060 -19.1 0.994   1.099 1.099 -0.000 1.000   22.64 14.74 7.89 1.535
2 A' A'   3020 3041 -20.7 0.993   1.092 1.091 0.002 1.001   14.94 3.64 11.30 4.103
3 A' A'   3006 3026 -20.0 0.993   1.087 1.087 -0.001 0.999   9.73 8.20 1.52 1.186
4 A' A'   2925 2997 -72.3 0.976   1.098 1.102 -0.003 0.997   33.16 15.10 18.06 2.196
5 A' A'   2875 2922 -46.8 0.984   1.040 1.036 0.004 1.004   38.19 21.82 16.37 1.750
6 A' A'   1629 1589 40.3 1.025   5.311 5.829 -0.518 0.911   7.59 3.79 3.81 2.005
7 A' A'   1503 1470 32.8 1.022   2.215 2.315 -0.101 0.957   16.48 14.02 2.46 1.175
8 A' A'   1470 1460 9.6 1.007   1.050 1.049 0.001 1.001   4.40 6.38 -1.98 0.690
9 A' A'   1408 1385 23.2 1.017   1.250 1.258 -0.008 0.994   0.51 0.47 0.04 1.093
10 A' A'   1191 1193 -2.2 0.998   2.671 2.762 -0.091 0.967   0.46 0.14 0.32 3.292
11 A' A'   1170 1165 5.3 1.005   1.200 1.137 0.063 1.056   0.32 0.09 0.22 3.361
12 A' A'   1054 1021 33.0 1.032   1.538 1.424 0.114 1.080   6.63 7.32 -0.69 0.906
scaled by     0.8985 0.943

See section III.C.1 List or set vibrational scaling factors to change the scale factors used here.
See section III.C.2 Calculate a vibrational scaling factor for a given set of molecules to determine the least squares best scaling factor.