Database of Frequency Scale Factors for Electronic Model Chemistries
(Version 3 Beta 2)
(maintained by Junwei Lucas Bao, J. Zheng, I. M. Alecu, B. J. Lynch, Y. Zhao, and D. G. Truhlar)

(For thermochemistry and kinetics, use ZPE scale factor; and for comparing with experimental IR spectra, use F scale factor. )

Model Chemistry

Scale Factor

Zero Point Energy (ZPE)

Harmonic Frequencies (H)

Fundamentals (F)

Value

Reference

Method

Value

Reference

Method

Value

Reference

Method

AM1

0.948

1

R

0.961

1

R

0.923

1

R

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

0.971

1

C

0.985

1

R

0.946

1

R

B1B95/MG3S

0.973

1

C

0.987

1

R

0.948

1

R

B1LYP/MG3S

0.978

1

D

0.994

1

D

0.955

1

D

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

0.981

1

C

0.995

1

R

0.955

1

R

B3LYP/6-31G(d)

0.977

1

R

0.991

1

R

0.952

1

R

B3LYP/aug-cc-pVTZ

0.985

3

R

0.999

3

R

0.959

3

R

B3LYP/def2-TZVP

0.985

3

R

0.999

3

R

0.959

3

R

B3LYP/ma-TZVP

0.986

1

R

1.000

1

R

0.960

1

R

B3LYP/MG3S

0.983

1

D

0.998

1

D

0.960

1

D

B3P86/6-31G(d)

0.971

1

R

0.985

1

R

0.946

1

R

B3PW91/6-31G(d)

0.972

1

R

0.986

1

R

0.947

1

R

B97-3/ma-TZVP

0.975

1

R

0.989

1

R

0.950

1

R

B97-3/MG3S

0.972

1

D

0.986

1

D

0.947

1

D

B98/def2-TZVP

0.984

1

R

0.998

1

R

0.958

1

R

B98/ma-TZVP

0.985

1

R

0.999

1

R

0.959

1

R

B98/MG3S

0.982

1

D

0.995

1

D

0.956

1

D

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

0.954

1

C

0.967

1

R

0.929

1

R

BB1K/MG3S

0.957

1

C

0.970

1

R

0.932

1

R

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

1.011

1

C

1.025

1

R

0.985

1

R

BB95/MG3S

1.012

1

C

1.026

1

R

0.986

1

R

BLYP/6-311G(df,p)

1.013

1

R

1.027

1

R

0.987

1

R

BLYP/6-31G(d)

1.009

1

R

1.023

1

R

0.983

1

R

BLYP/MG3S

1.013

1

D

1.031

1

D

0.991

1

D

BMC-CCSD

0.985

1

D

1.001

1

D

0.962

1

D

BMK/ma-TZVP

0.972

1

R

0.986

1

R

0.947

1

R

BMK/MG3S

0.971

1

D

0.984

1

D

0.945

1

D

BP86/6-31G(d)

1.007

1

R

1.021

1

R

0.981

1

R

BP86/ma-TZVP

1.014

1

R

1.028

1

R

0.988

1

R

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

0.934

2

C

0.910

2

R

0.947

2

R

BPW63/MG3S

0.923

2

C

0.899

2

R

0.936

2

R

CAM-B3LYP/ma-TZVP

0.976

1

R

0.990

1

R

0.951

1

R

CCSD(T)/jul-cc-pVTZ

0.984

1

R

0.998

1

R

0.958

1

R

CCSD(T)/aug-cc-pVTZ

0.987

1

R

1.001

1

R

0.961

1

R

CCSD(T)-F12/jul-cc-pVTZ

0.981

1

R

0.995

1

R

0.955

1

R

CCSD(T)-F12a/cc-pVTZ-F12

0.984

1

R

0.998

1

R

0.958

1

R

CCSD/jul-cc-pVTZ

0.973

1

R

0.987

1

R

0.948

1

R

CCSD-F12/jul-cc-pVTZ

0.971

1

R

0.985

1

R

0.946

1

R

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

0.911

2

C

0.887

2

R

0.924

2

R

G96LYP82/MG3S

0.907

2

C

0.883

2

R

0.920

2

R

GAM/def2-TZVP

0.980

7

D

0.994

7

D

0.955

7

D

GAM/ma-TZVP

0.981

7

D

0.995

7

D

0.956

7

D

HF/3-21G

0.919

1

R

0.932

1

R

0.895

1

R

HF/6-31+G(d)

0.911

1

R

0.924

1

R

0.887

1

R

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

0.915

1

C

0.928

1

R

0.891

1

R

HF/6-311G(d,p)

0.920

1

R

0.933

1

R

0.896

1

R

HF/6-311G(df,p)

0.920

1

R

0.933

1

R

0.896

1

R

HF/6-31G(d)

0.909

1

R

0.922

1

R

0.885

1

R

HF/6-31G(d,p)

0.913

1

R

0.926

1

R

0.889

1

R

HF/MG3S

0.919

1

D

0.932

1

D

0.895

1

D

HFLYP/MG3S

0.899

1

D

0.912

1

D

0.876

1

D

HSEh1PBE/ma-TZVP

0.979

1

R

0.993

1

R

0.954

1

R

M05/aug-cc-pVTZ

0.978

1

R

0.992

1

R

0.953

1

R

M05/def2-TZVP

0.978

3

R

0.991

3

R

0.952

3

R

M05/ma-TZVP

0.979

1

R

0.993

1

R

0.954

1

R

M05/maug-cc-pVTZ

0.978

1

R

0.992

1

R

0.953

1

R

M05/MG3S

0.977

1

D

0.989

1

D

0.951

1

D

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

0.961

1

D

0.974

1

D

0.936

1

D

M05-2X/aug-cc-pVTZ

0.964

1

R

0.977

1

R

0.939

1

R

M05-2X/def2-TZVPP

0.962

1

D

0.976

1

D

0.938

1

D

M05-2X/ma-TZVP

0.965

1

R

0.979

1

R

0.940

1

R

M05-2X/maug-cc-pVTZ

0.964

1

R

0.977

1

R

0.939

1

R

M05-2X/MG3S

0.962

1

D

0.975

1

D

0.937

1

D

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

0.980

1

D

0.989

1

D

0.950

1

D

M06/aug-cc-pVTZ

0.984

1

R

0.998

1

R

0.958

1

R

M06/def2-TZVP

0.982

3

R

0.996

3

R

0.956

3

R

M06/def2-TZVPP

0.979

1

D

0.992

1

D

0.953

1

D

M06/ma-TZVP

0.982

1

R

0.996

1

R

0.956

1

R

M06/maug-cc-pVTZ

0.982

1

R

0.996

1

R

0.956

1

R

M06/MG3S

0.981

1

D

0.994

1

D

0.955

1

D

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

0.967

1

D

0.979

1

D

0.940

1

D

M06-2X/6-311+G(d,p)

0.970

5

D

0.983

5

R

0.944

5

R

M06-2X/6-311++G(d,p)

0.970

5

D

0.983

5

R

0.944

5

R

M06-2X/aug-cc-pVTZ

0.971

1

D

0.985

1

D

0.946

1

D

M06-2X/def2-TZVP

0.971

7

D

0.984

7

D

0.946

7

D

M06-2X/def2-QZVP

0.970

7

D

0.983

7

D

0.945

7

D

M06-2X/def2-TZVPP

0.970

1

D

0.983

1

D

0.945

1

D

M06-2X/ma-TZVP

0.972

1

R

0.986

1

R

0.947

1

R

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

0.971

1

D

0.984

1

D

0.945

1

D

M06-2X/MG3S

0.970

1

D

0.982

1

D

0.944

1

D

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

0.954

1

D

0.969

1

D

0.931

1

D

M06-HF/aug-cc-pVTZ

0.961

1

R

0.974

1

R

0.936

1

R

M06-HF/def2-TZVPP

0.958

1

D

0.970

1

D

0.932

1

D

M06-HF/ma-TZVP

0.957

1

R

0.970

1

R

0.932

1

R

M06-HF/maug-cc-pVTZ

0.959

1

R

0.972

1

R

0.934

1

R

M06-HF/MG3S

0.955

1

D

0.967

1

D

0.930

1

D

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

0.978

1

D

0.992

1

D

0.953

1

D

M06-L/aug-cc-pVTZ

0.980

1

R

0.994

1

R

0.955

1

R

M06-L(DKH2)/aug-cc-pwcVTZ-DK

0.985

1

D

0.999

1

R

0.959

1

R

M06-L/def2-TZVP

0.976

3

R

0.990

3

R

0.951

3

R

M06-L/def2-TZVPP

0.976

1

D

0.995

1

D

0.956

1

D

M06-L/ma-TZVP

0.977

1

R

0.991

1

R

0.952

1

R

M06-L/maug-cc-pVTZ

0.977

1

R

0.991

1

R

0.952

1

R

M06-L/MG3S

0.978

1

D

0.996

1

D

0.958

1

D

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

0.972

1

D

0.983

1

D

0.944

1

D

M08-HX/aug-cc-pVTZ

0.975

1

R

0.989

1

R

0.950

1

R

M08-HX/cc-pVTZ+

0.974

1

D

0.985

1

D

0.946

1

D

M08-HX/def2-TZVPP

0.973

1

D

0.984

1

D

0.945

1

D

M08-HX/jun-cc-pVTZ

0.974

6

D

0.986

6

D

0.947

6

D

M08-HX/ma-TZVP

0.976

1

R

0.990

1

R

0.951

1

R

M08-HX/maug-cc-pVTZ

0.976

1

R

0.990

1

R

0.951

1

R

M08-HX/MG3S

0.973

1

D

0.984

1

D

0.946

1

D

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

0.979

1

D

0.989

1

D

0.951

1

D

M08-SO/aug-cc-pVTZ

0.985

1

R

0.999

1

R

0.959

1

R

M08-SO/cc-pVTZ+

0.982

1

D

0.995

1

D

0.956

1

D

M08-SO/def2-TZVPP

0.980

1

D

0.993

1

D

0.954

1

D

M08-SO/ma-TZVP

0.984

1

R

0.998

1

R

0.958

1

R

M08-SO/maug-cc-pVTZ

0.983

1

R

0.997

1

R

0.957

1

R

M08-SO/MG3

0.984

4

D

0.998

4

R

0.959

4

R

M08-SO/MG3S

0.983

1

D

0.995

1

D

0.956

1

D

M08-SO/MG3SXP

0.984

1

D

0.996

1

D

0.957

1

D

MN12-L/MG3S

0.968

6

D

0.981

6

D

0.943

6

D

MN12-SX/6-311++G(d,p)

0.976

6

D

0.986

6

D

0.947

6

D

MN15-L/MG3S

0.977

1

D

0.991

1

R

0.952

1

R

MN15-L/maug-cc-pVTZ

0.979

1

D

0.993

1

R

0.954

1

R

MC3BB

0.965

1

C

0.979

1

R

0.940

1

R

MC3MPW

0.964

1

C

0.977

1

R

0.939

1

R

MC-QCISD/3

0.992

1

C

1.006

1

R

0.966

1

R

MOHLYP/ma-TZVP

1.027

1

R

1.041

1

R

1.000

1

R

MOHLYP/MG3S

1.022

1

R

1.036

1

R

0.995

1

R

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

0.968

1

C

0.982

1

R

0.943

1

R

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

0.970

1

R

0.984

1

R

0.945

1

R

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

0.964

1

R

0.977

1

R

0.939

1

R

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

0.958

1

R

0.971

1

R

0.933

1

R

MP2(FC)/cc-pVDZ

0.977

1

C

0.991

1

R

0.952

1

R

MP2(FC)/cc-pVTZ

0.975

1

D

0.992

1

D

0.953

1

D

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

0.963

1

R

0.976

1

R

0.938

1

R

MP4(SDQ)/jul-cc-pVTZ

0.973

1

R

0.987

1

R

0.948

1

R

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

0.970

1

C

0.984

1

R

0.945

1

R

MPW1B95/MG3

0.970

1

C

0.984

1

R

0.945

1

R

MPW1B95/MG3S

0.972

1

C

0.986

1

R

0.947

1

R

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

0.949

1

C

0.962

1

R

0.924

1

R

MPW1K/ma-TZVP

0.956

1

R

0.969

1

R

0.931

1

R

MPW1K/MG3

0.953

1

C

0.966

1

R

0.928

1

R

MPW1K/MG3S

0.956

1

C

0.969

1

R

0.931

1

R

MPW1K/MIDI!

0.953

1

R

0.966

1

R

0.928

1

R

MPW1K/MIDIY

0.947

1

R

0.960

1

R

0.922

1

R

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

0.980

1

C

0.994

1

R

0.955

1

R

MPW3LYP/6-311+G(2d,p)

0.986

1

R

1.000

1

R

0.960

1

R

MPW3LYP/6-31G(d)

0.976

1

R

0.990

1

R

0.951

1

R

MPW3LYP/ma-TZVP

0.986

1

R

1.000

1

R

0.960

1

R

MPW3LYP/MG3S

0.982

1

C

0.996

1

R

0.956

1

R

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

0.912

2

C

0.888

2

R

0.925

2

R

MPW76/MG3S

0.909

2

C

0.885

2

R

0.922

2

R

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

0.951

1

C

0.964

1

R

0.926

1

R

MPWB1K/MG3S

0.954

1

C

0.967

1

R

0.929

1

R

MPWLYP1M/ma-TZVP

1.009

1

R

1.023

1

R

0.983

1

R

OreLYP/ma-TZVP

1.010

7

D

1.024

7

D

0.984

7

D

OreLYP/def2-TZVP

1.008

7

D

1.023

7

D

0.982

7

D

PBE/def2-TZVP

1.011

3

R

1.026

3

R

0.985

3

R

PBE/MG3S

1.010

1

D

1.025

1

D

0.985

1

D

PBE/ma-TZVP

1.014

1

D

1.028

1

D

0.987

1

D

PBE0/MG3S

0.975

1

D

0.989

1

D

0.950

1

D

PBE1KCIS/MG3

0.981

1

C

0.995

1

R

0.955

1

R

PBE1KCIS/MG3S

0.981

1

C

0.995

1

R

0.955

1

R

PM3

0.940

1

R

0.953

1

R

0.916

1

R

PM6

1.078

1

R

1.093

1

R

1.050

1

R

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

0.970

1

C

0.984

1

R

0.945

1

R

PW6B95/6-311G(d,p)

0.971

1

D

0.985

1

D

0.946

1

D

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

0.973

1

R

0.987

1

R

0.948

1

R

revTPSS/def2-TZVP

0.998

7

D

1.012

7

D

0.972

7

D

revTPSS/ma-TZVP

0.999

7

D

1.013

7

D

0.973

7

D

SOGGA/ma-TZVP

1.017

1

R

1.031

1

R

0.991

1

R

τHCTHhyb/ma-TZVP

0.989

1

R

1.003

1

R

0.963

1

R

TPSS1KCIS/def2-TZVP

0.982

1

R

0.996

1

R

0.956

1

R

TPSS1KCIS/ma-TZVP

0.983

1

R

0.997

1

R

0.957

1

R

TPSSh/MG3S

0.984

1

D

1.002

1

D

0.963

1

D

VSXC/MG3S

0.986

1

D

1.001

1

D

0.962

1

D

ωB97/def2-TZVP

0.969

1

R

0.983

1

R

0.944

1

R

ωB97/ma-TZVP

0.970

1

R

0.984

1

R

0.945

1

R

ωB97X/def2-TZVP

0.970

1

R

0.984

1

R

0.945

1

R

ωB97X/ma-TZVP

0.971

1

R

0.985

1

R

0.946

1

R

ωB97X-D/def2-TZVP

0.975

1

R

0.989

1

R

0.950

1

R

ωB97X-D/ma-TZVP

0.975

1

R

0.989

1

R

0.950

1

R

ωB97X-D/maug-cc-pVTZ

0.974

1

R

0.988

1

R

0.949

1

R

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

0.968

1

C

0.982

1

R

0.943

1

R

X1B95/MG3S

0.971

1

C

0.985

1

R

0.946

1

R

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

0.952

1

C

0.965

1

R

0.927

1

R

XB1K/MG3S

0.955

1

C

0.968

1

R

0.930

1

R

References
1.  "Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries," I. M. Alecu, J. Zheng, Y. Zhao, and D. G. Truhlar, J. Chem. Theory Comput. 6, 2872-2887 (2010). DOI URL Electronic Reprint URL Supporting information
2.  Scale factor for ZPE from Y. Zhao and D. G. Truhlar, unpublished (2003), modified by systematic correction of -0.0025 by I. M. Alecu (2010). Scale factors for H and F obtained using the Reduced Scale Factor Optimization Model by I. M. Alecu (2010). The last two digits in the level of theory represent the percentage to which the Hartree-Fock exchange was adjusted.
3.  I. M. Alecu, unpublished (2011).
4.  "A Product Branching Ratio Controlled by Vibrational Adiabaticity and Variational Effects: Kinetics of the H + trans-N2H2 Reactions," J. Zheng, R. J. Rocha, M. Pelegrini, L. F. A. Ferrčo, E. F. V. Carvalho, O. Roberto-Neto, F. B. C. Machado, and D. G. Truhlar, Journal of Chemical Physics 136, 184310/1-10 (2012).
5. J. Zheng and D. G. Truhlar, unpublished (2014).
6. J. Bao and D. G. Truhlar, unpublished (2014).
7. H. Yu, J. Zheng, and D. G. Truhlar, unpublished (2015)

 
Methods

D: The scale factor was directly obtained from the ZPVE15/10 or F38/10 databases given in Ref. 1. Note that one can easily determine the scale factor with equation 12 in Ref. 1.

C: The scale factor was obtained by applying a small systematic correction of -0.0025 to preexisting scale factor. The references for the preexisting (uncorrected) scale factors are given in Supporting Information of Ref. 1 and in Version 1 of this database

R: The scale factor was obtained via the Reduced Scale Factor Optimization Model described in Ref. 1. Briefly, this entails using the ZPE6 database for determining ZPE scale factors, and/or using the universal scale factor ratios of aF/ZPE = 0.974 and aH/ZPE = 1.014 to obtain the respective values for the scale factors for fundamental and harmonic frequencies.

 

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