(maintained
by J. Zheng, B. J. Lynch, Y. Zhao, and D. G. Truhlar)
http://comp.chem.umn.edu/database/freq_scale.htm
Date of last update: April 2, 2009
When vibrational frequencies are calculated by electronic structure theory, they can often be improved by scaling, and it is useful to have general scaling factors for doing this. Such factors depend on the level of electronic structure theory and the one-electron basis set. As explained in Ref. 1, frequencies may be scaled in various ways. For example, one may scale them to try to reproduce the true harmonic frequencies, the true fundamental frequencies, or the zero point energy. Most scaling factors in this database are scaled to to try to reproduce accurate zero point energies, although they could also be used for other purposes. The property that the scaling factory should be used to reproduce is listed in the column labeled "property". There are two references for each method; the first reference (labeled "Reference") is the reference where the scale factor is obtained. The second reference (labeled "Method") gives the method and data set that was used to get the scale factor.
|
Level/Basis |
Scale Factor |
Property |
Reference |
Method |
|
HF/6-31G(d) |
0.9135 |
ZPE |
1 |
1 |
|
MP2(FULL)/6-31G(d) |
0.9646 |
ZPE |
1 |
1 |
|
AM1 |
0.9532 |
Fundamentals |
2 |
2 |
|
PM3 |
0.9761 |
Fundamentals |
2 |
2 |
|
HF/3-21G |
0.9207 |
ZPE |
2 |
2 |
|
HF/6-31G(d) |
0.9135 |
ZPE |
2 |
2 |
|
HF/6-31+G(d) |
0.9163 |
ZPE |
2 |
2 |
|
HF/6-31G(d,p) |
0.9181 |
ZPE |
2 |
2 |
|
HF/6-311G(d,p) |
0.9248 |
ZPE |
2 |
2 |
|
HF/6-311G(df,p) |
0.9247 |
ZPE |
2 |
2 |
|
MP2(FC)/6-31G(d) |
0.9670 |
ZPE |
2 |
2 |
|
MP2(FC)/6-31G(d,p) |
0.9608 |
ZPE |
2 |
2 |
|
MP2(FC)/6-311G(d,p) |
0.9748 |
ZPE |
2 |
2 |
|
QCISD(FC)/6-31G(d) |
0.9776 |
ZPE |
2 |
2 |
|
BLYP/6-31G(d) |
1.0126 |
ZPE |
2 |
2 |
|
BLYP/6-311G(df,p) |
1.0167 |
ZPE |
2 |
2 |
|
BP86/6-31G(d) |
1.0108 |
ZPE |
2 |
2 |
|
B3LYP/6-31G(d) |
0.9806 |
ZPE |
2 |
2 |
|
B3P86/6-31G(d) |
0.9759 |
ZPE |
2 |
2 |
|
B3PW91/6-31G(d) |
0.9772 |
ZPE |
2 |
2 |
|
MP2/cc-pVDZ |
0.9790 |
ZPE |
3 |
3 |
|
MPW1K/6-31+G(d,p) |
0.9515 |
ZPE |
4 |
3 |
|
MPW1K/MG3S |
0.9581 |
ZPE |
6 |
3 |
|
MPW1K/MG3 |
0.9552 |
ZPE |
4 |
3 |
|
MPW74/6-311+G(d,p) |
0.9147 |
ZPE |
5 |
3 |
|
G96LYP80/6-311+G(d,p) |
0.9135 |
ZPE |
5 |
3 |
|
BPW60/6-311+G(d,p) |
0.9363 |
ZPE |
5 |
3 |
|
MPW76/MG3S |
0.9117 |
ZPE |
5 |
3 |
|
G96LYP82/MG3S |
0.9094 |
ZPE |
5 |
3 |
|
BPW63/MG3S |
0.9252 |
ZPE |
5 |
3 |
|
MC-QCISD/3 |
0.9940 |
ZPE |
7 |
3 |
|
HF/6-31+G(d,p) |
0.9173 |
ZPE |
6 |
3 |
|
HF/MG3S |
0.9210 |
ZPE |
6 |
3 |
|
BB1K/6-31+G(d,p) |
0.9561 |
ZPE |
6 |
3 |
|
BB1K/MG3S |
0.9590 |
ZPE |
6 |
3 |
|
B1B95/6-31+G(d,p) |
0.9735 |
ZPE |
6 |
3 |
|
B1B95/MG3S |
0.9758 |
ZPE |
6 |
3 |
|
BB95/6-31+G(d,p) |
1.0139 |
ZPE |
6 |
3 |
|
BB95/MG3S |
1.0144 |
ZPE |
6 |
3 |
|
MC3BB |
0.9675 |
ZPE |
7 |
3 |
|
MC3MPW |
0.9669 |
ZPE |
7 |
3 |
|
MP2/6-31+G(d,p) |
0.9700 |
ZPE |
7 |
3 |
|
MPW3LYP/6-31+G(d,p) |
0.9825 |
ZPE |
8 |
3 |
|
MPW3LYP/MG3S |
0.9846 |
ZPE |
8 |
3 |
|
X1B95/6-31+G(d,p) |
0.9709 |
ZPE |
8 |
3 |
|
X1B95/MG3S |
0.9733 |
ZPE |
8 |
3 |
|
XB1K/6-31+G(d,p) |
0.9549 |
ZPE |
8 |
3 |
|
XB1K/MG3S |
0.9579 |
ZPE |
8 |
3 |
|
MPW1B95/6-31+G(d,p) |
0.9721 |
ZPE |
8 |
3 |
|
MPW1B95/MG3S |
0.9746 |
ZPE |
8 |
3 |
|
MPWB1K/6-31+G(d,p) |
0.9537 |
ZPE |
8 |
3 |
|
MPWB1K/MG3S |
0.9567 |
ZPE |
8 |
3 |
|
B3LYP/6-31(2df,2p) |
0.983 |
ZPE |
9 |
3 |
|
PBE1KCIS/MG3 |
0.9833 |
ZPE |
10 |
3 |
|
PBE1KCIS/MG3S |
0.9832 |
ZPE |
10 |
3 |
|
MPW1B95/MG3 |
0.9722 |
ZPE |
10 |
3 |
|
PW6B95/6-31+G(d,p) |
0.9720 |
ZPE |
10 |
3 |
|
VSXC/MG3S |
0.9885 |
ZPE |
11 |
3 |
|
PBE/MG3S |
1.0122 |
ZPE |
11 |
3 |
|
B98/MG3S |
0.9844 |
ZPE |
11 |
3 |
|
TPSSh/MG3S |
0.9864 |
ZPE |
11 |
3 |
|
BLYP/MG3S |
1.0156 |
ZPE |
11 |
3 |
|
B3LYP/MG3S |
0.9853 |
ZPE |
11 |
3 |
|
B97-3/MG3S |
0.9743 |
ZPE |
11 |
3 |
|
M06-L/MG3S |
0.9800 |
ZPE |
11 |
3 |
|
BMK/MG3S |
0.9734 |
ZPE |
11 |
3 |
|
PBEh/MG3S |
0.9779 |
ZPE |
11 |
3 |
|
M05/MG3S |
0.9789 |
ZPE |
11 |
3 |
|
M05-2X/MG3S |
0.9642 |
ZPE |
11 |
3 |
|
M06-2X/MG3S |
0.9721 |
ZPE |
11 |
3 |
|
M06/MG3S |
0.9830 |
ZPE |
11 |
3 |
|
HF/MG3S |
0.9209 |
ZPE |
11 |
3 |
|
M06-HF/MG3S |
0.9570 |
ZPE |
11 |
3 |
|
HFLYP/MG3S |
0.9016 |
ZPE |
11 |
3 |
|
VSXC/MG3S |
1.0014 |
Harmonic |
11 |
11 |
|
PBE/MG3S |
1.0248 |
Harmonic |
11 |
11 |
|
B98/MG3S |
0.9954 |
Harmonic |
11 |
11 |
|
TPSSh/MG3S |
1.0016 |
Harmonic |
11 |
11 |
|
BLYP/MG3S |
1.0307 |
Harmonic |
11 |
11 |
|
B3LYP/MG3S |
0.9983 |
Harmonic |
11 |
11 |
|
B97-3/MG3S |
0.9856 |
Harmonic |
11 |
11 |
|
M06-L/MG3S |
0.9964 |
Harmonic |
11 |
11 |
|
BMK/MG3S |
0.9835 |
Harmonic |
11 |
11 |
|
PBEh/MG3S |
0.9887 |
Harmonic |
11 |
11 |
|
M05/MG3S |
0.9894 |
Harmonic |
11 |
11 |
|
M05-2X/MG3S |
0.9748 |
Harmonic |
11 |
11 |
|
M06-2X/MG3S |
0.9824 |
Harmonic |
11 |
11 |
|
M06/MG3S |
0.9939 |
Harmonic |
11 |
11 |
|
HF/MG3S |
0.9323 |
Harmonic |
11 |
11 |
|
M06-HF/MG3S |
0.9672 |
Harmonic |
11 |
11 |
|
HFLYP/MG3S |
0.9119 |
Harmonic |
11 |
11 |
|
M08-HX/cc-pVTZ+ |
0.9832 |
ZPE |
12 |
3 |
1. J. A. Pople, A. P. Scott, M. W. Wong, and L. Radom, Israel J. Chem. 33, 345-350 (1993).
2. "Harmonic Vibrational Frequencies: An Evaluation of
Hartree-Fock, Møller-Plesset, Quadratic Configuration Interaction, Density
Functional Theory, and Semiempirical Scale
Factors" A. P. Scott and L. Radom, Journal of
Physical Chemistry 100, 16502-16513 (1996).
3. "Optimized Parameters for Scaling Correlation
Energy" P. L. Fast, J. Corchado, M. L. Sánchez, D. G. Truhlar, J. Phys. Chem. A 103, 3139-3143 (1999).
4. "How Well Can Density Functional Methods Predict
5. Y. Zhao and D. G. Truhlar,
unpublished (2003).
6. "Development and Assessment of a New Hybrid Density
Functional Model for Thermochemical Kinetics" Y. Zhao, B. J. Lynch, and D.
G. Truhlar, Y. Zhao, B. J. Lynch and D. G. Truhlar, J. Phys. Chem. A 108, 2715-2719 (2004).
7. "Doubly Hybrid DFT: New Multi-Coefficient Correlation and Density Functional Methods for Thermochemistry and Thermochemical Kinetics” Y. Zhao, B. J. Lynch, and D. G. Truhlar. J. Phys. Chem. A 108, 4786-4791 (2004).
8. "Hybrid Meta Density Functional Theory Methods for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions: The MPW1B95 and MPWB1K Models and Comparative Assessments for Hydrogen Bonding and van der Waals Interactions" Y. Zhao and D. G. Truhlar, J. Phys. Chem. A 108, 6908-6918 (2004).
9. "Databases for Transition Element
Bonding: Metal–Metal Bond Energies and Bond Lengths and Their Use to Test
Hybrid, Hybrid Meta, and Meta Density Functionals and Generalized Gradient
Approximations" N. E. Schultz, Y. Zhao, and D. G. Truhlar, J. Phys. Chem. A 109, 4388-4403, (2005).
10. "The Reaction of Hydrogen Atom with Hydrogen Peroxide" B. A. Ellingson, D. P. Theis, O. Tishchenko, J. Zheng, and D. G. Truhlar, J. Phys. Chem. A 111, 13554-13566, (2007).
11. "The M06 Suite of Density Functionals for Main Group Thermochemistry, Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06 Functionals and Twelve Other Functionals," Y. Zhao and D. G. Truhlar, Theor. Chem. Acc. 120, 215-241 (2008) at http://dx.doi.org/10.1007/s00214-007-0310-x (Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue)
12. "Direct Dynamics Study of Hydrogen-Transfer Isomerization of 1-Pentyl and 1-Hexyl Radicals", J. Zheng and D. G. Truhlar, J. Phys. Chem., to be submitted.