Database of Frequency Scale Factors for Electronic Model Chemistries

(Version 1.1)

 

(maintained by J. Zheng, I. M. Alecu, B. J. Lynch, Y. Zhao, and D. G. Truhlar)

Date of last update: November 21, 2010

 

Introduction

 

When vibrational frequencies are calculated by electronic structure theory, they can often be improved by scaling, and it is useful to have scale factors for doing this. Such scale factors depend on the level of electronic structure theory and the one-electron basis set, the combination of which we denote as an electronic model chemistry. Frequencies may be scaled in various ways. For example, one may scale them to try to reproduce the true vibrational harmonic frequencies (H), the observed vibrational fundamental frequencies (F), or the vibrational zero-point energy (ZPE). The aim of this database is to provide reliable scale factors that can be used in conjunction with the tabulated electronic model chemistries to accurately reproduce the aforementioned properties. References are provided to the journal articles in which the scale factors are obtained and the method employed to optimize the scale factors.

 

 

Model Chemistry

λZPE

Ref.

Method

λH

Ref.

Method

λF

Ref.

Method

 

AM1

0.981

13

14

0.992

13

14

0.953

2

2

 

B1B95/6-31+G(d,p)

0.974

6

3

0.985

13

14

0.946

13

14

 

B1B95/MG3S

0.976

6

3

0.987

13

14

0.949

13

14

 

B1LYP/MG3S

0.980

13

13

0.994

13

13

0.955

13

13

 

B3LYP/6-31(2df,2p)

0.983

9

3

0.994

13

14

0.956

13

14

 

B3LYP/6-31G(d)

0.981

2

2

0.992

13

14

0.953

13

14

 

B3LYP/MG3S

0.985

11

3

0.998

11

11

0.960

13

13

 

B3P86/6-31G(d)

0.976

2

2

0.987

13

14

0.949

13

14

 

B3PW91/6-31G(d)

0.977

2

2

0.988

13

14

0.950

13

14

 

B97-3/MG3S

0.974

11

3

0.986

11

11

0.947

13

13

 

B98/MG3S

0.984

11

3

0.995

11

11

0.956

13

13

 

BB1K/6-31+G(d,p)

0.956

6

3

0.967

13

14

0.929

13

14

 

BB1K/MG3S

0.959

6

3

0.970

13

14

0.932

13

14

 

BB95/6-31+G(d,p)

1.014

6

3

1.026

13

14

0.986

13

14

 

BB95/MG3S

1.014

6

3

1.026

13

14

0.986

13

14

 

BLYP/6-311G(df,p)

1.017

2

2

1.028

13

14

0.988

13

14

 

BLYP/6-31G(d)

1.013

2

2

1.024

13

14

0.984

13

14

 

BLYP/MG3S

1.016

11

3

1.031

11

11

0.991

13

13

 

BMC-CCSD

0.987

13

13

1.001

13

13

0.962

13

13

 

BMK/MG3S

0.973

11

3

0.984

11

11

0.945

13

13

 

BP86/6-31G(d)

1.011

2

2

1.022

13

14

0.983

13

14

 

BPW60/6-311+G(d,p)

0.936

5

3

0.947

13

14

0.910

13

14

 

BPW63/MG3S

0.925

5

3

0.936

13

14

0.899

13

14

 

G96LYP80/6-311+G(d,p)

0.914

5

3

0.924

13

14

0.888

13

14

 

G96LYP82/MG3S

0.909

5

3

0.920

13

14

0.884

13

14

 

HF/3-21G

0.921

2

2

0.931

13

14

0.895

13

14

 

HF/6-31+G(d)

0.916

2

2

0.927

13

14

0.891

13

14

 

HF/6-31+G(d,p)

0.917

6

3

0.928

13

14

0.892

13

14

 

HF/6-311G(d,p)

0.925

2

2

0.935

13

14

0.899

13

14

 

HF/6-31G(d)

0.914

1, 2

1, 2

0.924

13

14

0.888

13

14

 

HF/6-31G(d,p)

0.918

2

2

0.929

13

14

0.892

13

14

 

HF/MG3S

0.921

6, 11

3

0.932

11

11

0.895

13

13

 

HFLYP/MG3S

0.902

11

3

0.912

11

11

0.876

13

13

 

M05-2X/6-31+G(d,p)

0.963

13

13

0.974

13

13

0.936

13

13

 

M06-5X/def2-TZVPP

0.965

13

13

0.976

13

13

0.938

13

13

 

M05-2X/MG3S

0.964

11

3

0.975

11

11

0.937

13

13

 

M05/MG3S

0.979

11

3

0.989

11

11

0.951

13

13

 

M06-2X/6-31+G(d,p)

0.970

13

13

0.979

13

13

0.940

13

13

 

M06-2X/aug-cc-pVTZ

0.974

13

13

0.985

13

13

0.946

13

13

 

M06-2X/def2-TZVPP

0.972

13

13

0.983

13

13

0.945

13

13

 

M06-2X/maug-cc-pV(T+d)Z

0.973

13

13

0.984

13

13

0.945

13

13

 

M06-2X/MG3S

0.972

11

3

0.982

11

11

0.944

13

13

 

M06-HF/6-31+G(d,p)

0.957

13

13

0.969

13

13

0.931

13

13

 

M06-HF/def2-TZVPP

0.960

13

13

0.970

13

13

0.932

13

13

 

M06-HF/MG3S

0.957

11

3

0.967

11

11

0.930

13

13

 

M06-L/6-31+G(d,p)

0.980

13

13

0.992

13

13

0.953

13

13

 

M06-L/def2-TZVPP

0.978

13

13

0.995

13

13

0.956

13

13

 

M06-L/MG3S

0.980

11

3

0.996

11

11

0.958

13

13

 

M06/6-31+G(d,p)

0.982

13

13

0.989

13

13

0.950

13

13

 

M06/def2-TZVPP

0.981

13

13

0.992

13

13

0.953

13

13

 

M06/MG3S

0.983

11

3

0.994

11

11

0.955

13

13

 

M08-HX/6-31+G(d,p)

0.974

13

13

0.983

13

13

0.944

13

13

 

M08-HX/cc-pVTZ+

0.976

13

13

0.987

13

14

0.949

13

14

 

M08-HX/MG3S

0.975

13

13

0.984

13

13

0.946

13

13

 

M08-SO/6-31+G(d,p)

0.982

12

3

0.989

13

13

0.951

13

13

 

M08-SO/cc-pVTZ+

0.985

12

3

0.995

13

13

0.956

13

13

 

M08-SO/MG3SXP

0.986

12

3

0.996

13

13

0.957

13

13

 

M08-SO/MG3S

0.985

12

3

0.995

13

13

0.956

13

13

 

MC-QCISD/3

0.994

7

3

1.005

13

14

0.966

13

14

 

MC3BB

0.968

7

3

0.979

13

14

0.940

13

14

 

MC3MPW

0.967

7

3

0.978

13

14

0.940

13

14

 

MP2(FC)/6-31+G(d,p)

0.970

7

3

0.981

13

14

0.943

13

14

 

MP2(FC)/6-311G(d,p)

0.975

2

2

0.986

13

14

0.948

13

14

 

MP2(FC)/6-31G(d)

0.967

2

2

0.978

13

14

0.940

13

14

 

MP2(FC)/6-31G(d,p)

0.961

2

2

0.972

13

14

0.934

13

14

 

MP2(FC)/cc-pVDZ

0.979

3

3

0.990

13

14

0.952

13

14

 

MP2(FULL)/6-31G(d)

0.965

1

1

0.976

13

14

0.938

13

14

 

MPW1B95/6-31+G(d,p)

0.972

8

3

0.983

13

14

0.945

13

14

 

MPW1B95/MG3

0.972

10

3

0.983

13

14

0.945

13

14

 

MPW1B95/MG3S

0.975

8

3

0.986

13

14

0.947

13

14

 

MPW1K/6-31+G(d,p)

0.952

4

3

0.962

13

14

0.925

13

14

 

MPW1K/MG3

0.955

4

3

0.966

13

14

0.928

13

14

 

MPW1K/MG3S

0.958

6

3

0.969

13

14

0.931

13

14

 

MPW3LYP/6-31+G(d,p)

0.983

8

3

0.994

13

14

0.955

13

14

 

MPW3LYP/MG3S

0.985

8

3

0.996

13

14

0.957

13

14

 

MPW74/6-311+G(d,p)

0.915

5

3

0.925

13

14

0.889

13

14

 

MPW76/MG3S

0.912

5

3

0.922

13

14

0.886

13

14

 

MPWB1K/6-31+G(d,p)

0.954

8

3

0.965

13

14

0.927

13

14

 

MPWB1K/MG3S

0.957

8

3

0.968

13

14

0.930

13

14

 

PBE/MG3S

1.012

11

3

1.025

11

11

0.985

13

13

 

PBE1KCIS/MG3

0.983

10

3

0.995

13

14

0.956

13

14

 

PBE1KCIS/MG3S

0.983

10

3

0.995

13

14

0.956

13

14

 

PBE0/MG3S

0.978

11

3

0.989

11

11

0.950

13

13

 

PM3

1.004

13

14

1.016

13

14

0.976

2

2

 

PM6

1.014

13

14

1.026

13

14

0.986

15

2

 

PW6B95/6-31+G(d,p)

0.972

10

3

0.983

13

14

0.945

13

14

 

QCISD(FC)/6-31G(d)

0.978

2

2

0.989

13

14

0.950

13

14

 

TPSSh/MG3S

0.986

11

3

1.002

11

11

0.963

13

13

 

VSXC/MG3S

0.989

11

3

1.001

11

11

0.962

13

13

 

X1B95/6-31+G(d,p)

0.971

8

3

0.982

13

14

0.944

13

14

 

X1B95/MG3S

0.973

8

3

0.985

13

14

0.946

13

14

 

XB1K/6-31+G(d,p)

0.955

8

3

0.966

13

14

0.928

13

14

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

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, M¿ller-Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors" A. P. Scott and L. Radom, J. Phys. Chem. 100, 16502-16513 (1996).

3. "Optimized Parameters for Scaling Correlation Energy" P. L. Fast, J. Corchado, M. L. S‡nchez, 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 KineticsÓ 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. ÒKinetics of Hydrogen-Transfer Isomerization of Butoxyl RadicalsÓ J. Zheng and D. G. Truhlar, Phys. Chem. Chem. Phys. 12, 7782-7793 (2010).

13. I. M. Alecu, unpublished (2010). These scale factors were optimized using the ZPVE15/06 database. Note that these scale factors were subsequently re-optimized using the updated ZPE15/10 database in version 2 of this database.

14. The universal scale factor ratios of 0.972 and 1.012 for the ratios of the F scale factor to the ZPE scale factor and the H scale factor to the ZPE scale factor, respectively, were employed in obtaining the appropriate scale factor. Note that the values for the universal scale factor ratios were subsequently re-optimized in version 2 of this database.

15. Z. A. Fekete, E. A. Hoffmann, T Kortvelyesi, and B. Penke, Mol. Phys. 105, 2597-2605 (2007).