^{1,2,a)}and Martin Head-Gordon

^{1,b)}

### Abstract

We extend the range of applicability of our previous long-range corrected (LC) hybrid functional, [J.-D. Chai and M. Head-Gordon, J. Chem. Phys.128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by second-order Møller–Plesset (many-body) perturbation theory. This LC “double-hybrid” density functional, denoted as , is fully optimized both at the complete basis set limit (using 2-point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive basis. On independent test calculations (as well as training set results), yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree–Fock exchange, shows significant improvement for the systems where self-interaction errors are severe, such as symmetric homonuclear radical cations.

This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC0376SF00098. J.D.C. is grateful to the Start-up Funds (Grant No. 98R0034-44 and 98R0654) from National Taiwan University and is grateful to the Computer and Information Networking Center, National Taiwan University for the partial support of high-performance computing facilities. M.H.G. is a part-owner of Q-Chem Inc.

I. INTRODUCTION

II. THE LCDH SCHEME

III. RESULTS AND DISCUSSION

A. The training set

B. The test sets

IV. CONCLUSIONS

### Key Topics

- Density functional theory
- 24.0
- Basis sets
- 12.0
- Exchange correlation functionals
- 12.0
- Correlation functions
- 6.0
- Chemical thermodynamics
- 5.0

## Figures

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Dissociation curve of curve. Zero level is set to for each method.

Same as Fig. 3, but with a focus on the unrestricted region.

Same as Fig. 3, but with a focus on the unrestricted region.

Same as Fig. 4, but with a focus on the unrestricted region.

Same as Fig. 4, but with a focus on the unrestricted region.

## Tables

Basis sets used for on the training set. denotes the extrapolation to basis set limit used for PT2 correlation.

Basis sets used for on the training set. denotes the extrapolation to basis set limit used for PT2 correlation.

Optimized parameters for the and for the . Here, the same-spin PT2 coefficient , and the opposite-spin PT2 coefficient , are defined in Eq. (1), and others are defined in Eq. (28) of Ref. 10.

Optimized parameters for the and for the . Here, the same-spin PT2 coefficient , and the opposite-spin PT2 coefficient , are defined in Eq. (1), and others are defined in Eq. (28) of Ref. 10.

Statistical errors (in kcal/mol) of the training set. The functional is defined in the text. The results for are obtained with the basis sets and extrapolation scheme described in Table I and in the text. The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Statistical errors (in kcal/mol) of the training set. The functional is defined in the text. The results for are obtained with the basis sets and extrapolation scheme described in Table I and in the text. The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Statistical errors (in kcal/mol) of the training set.

Statistical errors (in kcal/mol) of the training set.

Nonhydrogen transfer BHs (in kcal/mol) of the NHTBH38/04 set (Ref. 42). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Nonhydrogen transfer BHs (in kcal/mol) of the NHTBH38/04 set (Ref. 42). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Hydrogen transfer BHs (in kcal/mol) of the HTBH38/04 set (Refs. 41 and 42). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Hydrogen transfer BHs (in kcal/mol) of the HTBH38/04 set (Refs. 41 and 42). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Interaction energies (in kcal/mol) for the S22 set (Ref. 43). The counterpoise corrections are used to reduce the basis set superposition errors. Monomer deformation energies are not included. The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Interaction energies (in kcal/mol) for the S22 set (Ref. 43). The counterpoise corrections are used to reduce the basis set superposition errors. Monomer deformation energies are not included. The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Statistical errors (in kcal/mol) of the training set. MAE (in kcal/mol) of on the training set, using four different basis sets, are listed. denotes the extrapolation scheme with the basis sets described in Table I, while and are the corresponding basis sets for the extrapolation. LP is the basis set.

Statistical errors (in kcal/mol) of the training set. MAE (in kcal/mol) of on the training set, using four different basis sets, are listed. denotes the extrapolation scheme with the basis sets described in Table I, while and are the corresponding basis sets for the extrapolation. LP is the basis set.

Statistical errors of the additional 48 AEs (in kcal/mol) in the G3/05 set (Ref. 52). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Statistical errors of the additional 48 AEs (in kcal/mol) in the G3/05 set (Ref. 52). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Comparison of errors of different functionals for the reaction energies (in kcal/mol) of the 30 chemical reactions in the NHTBH38/04 and HTBH38/04 database (Refs. 41 and 42). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Comparison of errors of different functionals for the reaction energies (in kcal/mol) of the 30 chemical reactions in the NHTBH38/04 and HTBH38/04 database (Refs. 41 and 42). The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Binding energies (in kcal/mol) of several sets of noncovalent interactions. The first three sets are taken from Ref. 53 with monomer deformation energies taken into considerations. The last three sets are taken from Ref. 43 without considering monomer deformation energies. The counter-point corrections are applied for all the cases. The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Binding energies (in kcal/mol) of several sets of noncovalent interactions. The first three sets are taken from Ref. 53 with monomer deformation energies taken into considerations. The last three sets are taken from Ref. 43 without considering monomer deformation energies. The counter-point corrections are applied for all the cases. The results for the are taken from Ref. 11, and the results for the and are taken from Ref. 10.

Binding energies of symmetric radical cations at bond length , (in kcal/mol). The results for the and are taken from Ref. 10.

Binding energies of symmetric radical cations at bond length , (in kcal/mol). The results for the and are taken from Ref. 10.

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