Database of Frequency Scaling Factors for Electronic Structure Methods

(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 Transition State Geometries and Barrier Heights?" B. J. Lynch and D. G. Truhlar, J. Phys. Chem. A  105, 2936-2941 (2001).

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.