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	λ^ZPE	Ref.	Method	λ^H	Ref.	Method	λ^F	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, Møller-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. 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. “Kinetics of Hydrogen-Transfer Isomerization of Butoxyl Radicals” 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).