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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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 C2H3OC2H5 (Ethene, ethoxy-)

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   3092 3153 -61.4 0.981   1.119 1.119 -0.000 1.000   14.26 4.64 9.63 3.077
2 A A   3018 3059 -40.6 0.987   1.077 1.064 0.013 1.012   4.44 0.34 4.10 13.100
3 A A   2996 3040 -43.7 0.986   1.078 1.105 -0.027 0.975   22.18 18.04 4.14 1.230
4 A A   2961 3028 -67.8 0.978   1.105 1.103 0.002 1.002   47.95 18.41 29.54 2.604
5 A A   2949 3008 -59.1 0.980   1.102 1.089 0.014 1.013   43.49 20.66 22.83 2.105
6 A A   2898 2945 -46.3 0.984   1.108 1.109 -0.001 0.999   54.37 42.42 11.95 1.282
7 A A   2890 2942 -52.3 0.982   1.038 1.036 0.002 1.002   24.99 11.61 13.38 2.152
8 A A   2866 2895 -28.4 0.990   1.057 1.057 -0.000 1.000   53.30 43.77 9.53 1.218
9 A A   1697 1641 56.5 1.034   4.275 4.348 -0.074 0.983   176.37 111.05 65.32 1.588
10 A A   1510 1498 11.7 1.008   1.097 1.097 0.000 1.000   7.72 6.09 1.64 1.269
11 A A   1478 1475 2.7 1.002   1.058 1.049 0.009 1.008   2.40 3.66 -1.26 0.656
12 A A   1463 1460 3.1 1.002   1.041 1.042 -0.001 0.999   3.27 5.45 -2.19 0.599
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.