^{1}, Chen-Wei Tsai

^{1}, Guan-De Li

^{1}and Jeng-Da Chai

^{1,2,a)}

### Abstract

We propose a long-range corrected hybrid meta-generalized-gradient approximation (GGA) functional, based on a global hybrid meta-GGA functional, M05 [Y. Zhao, N. E. Schultz, and D. G. Truhlar, J. Chem. Phys.123, 161103 (2005)10.1063/1.2126975], and empirical atom-atom dispersion corrections. Our resulting functional, ωM05-D, is shown to be accurate for a very wide range of applications, such as thermochemistry, kinetics, noncovalent interactions, equilibrium geometries, frontier orbital energies, fundamental gaps, and excitation energies. In addition, we present three new databases, IP131 (131 ionization potentials), EA115 (115 electron affinities), and FG115 (115 fundamental gaps), consisting of experimental molecular geometries and accurate reference values, which will be useful in the assessment of the accuracy of density functional approximations.

This work was supported by National Science Council of Taiwan (Grant No. NSC98-2112-M-002-023-MY3), National Taiwan University (Grant Nos. 99R70304 and 10R80914-1), and NCTS of Taiwan. We are grateful to partial support of computer resources from the groups of Dr. J.-L. Kuo (Academia Sinica) and Dr. Y.-C. Cheng (NTU).

I. INTRODUCTION

II. RATIONALES OF LC HYBRID SCHEMES

III. LC HYBRID MGGA-D FUNCTIONALS

IV. RESULTS FOR THE TRAINING SET

V. RESULTS FOR THE TEST SETS

A. Atomization energies, reaction energies, and noncovalent interactions

B. Equilibrium geometries

C. Dissociation of symmetric radical cations

D. Frontier orbital energies

E. Fundamental gaps

F. Excitation energies

VI. CONCLUSIONS

### Key Topics

- Density functional theory
- 25.0
- Laser Doppler velocimetry
- 23.0
- Excitation energies
- 12.0
- Databases
- 10.0
- Electron affinities
- 8.0

## Figures

Dissociation curve of . Zero level is set to E(H) + E(H^{+}) for each method.

Dissociation curve of . Zero level is set to E(H) + E(H^{+}) for each method.

Dissociation curve of . Zero level is set to E(He) + E(He^{+}) for each method.

Dissociation curve of . Zero level is set to E(He) + E(He^{+}) for each method.

Dissociation curve of . Zero level is set to E(Ne) + E(Ne^{+}) for each method.

Dissociation curve of . Zero level is set to E(Ne) + E(Ne^{+}) for each method.

Dissociation curve of . Zero level is set to E(Ar) + E(Ar^{+}) for each method.

Dissociation curve of . Zero level is set to E(Ar) + E(Ar^{+}) for each method.

The lowest CT excitation of C_{2}H_{4}⋅⋅⋅C_{2}F_{4} dimer along the intermolecular distance *R* (in Å). For all functionals, the excitation at 5 Å is set to zero.

The lowest CT excitation of C_{2}H_{4}⋅⋅⋅C_{2}F_{4} dimer along the intermolecular distance *R* (in Å). For all functionals, the excitation at 5 Å is set to zero.

The lowest CT excitation of C_{2}H_{4}⋅⋅⋅C_{2}F_{4} dimer along the intermolecular distance *R* (in Å).

The lowest CT excitation of C_{2}H_{4}⋅⋅⋅C_{2}F_{4} dimer along the intermolecular distance *R* (in Å).

## Tables

Optimized parameters for ωM05-D. Here, the non-linear parameter *a* is defined in Eq. (38), and others are defined in Eq. (32).

Optimized parameters for ωM05-D. Here, the non-linear parameter *a* is defined in Eq. (38), and others are defined in Eq. (32).

Comparisons between the ωM05* and ωM05s* functionals (defined in the text) for different ω values. Statistical errors are in kcal/mol.

Comparisons between the ωM05* and ωM05s* functionals (defined in the text) for different ω values. Statistical errors are in kcal/mol.

Statistical errors (in kcal/mol) of the training set. The M05-D* and M05* functionals are defined in the text. M05-2X was not particularly parametrized using this training set.

Statistical errors (in kcal/mol) of the training set. The M05-D* and M05* functionals are defined in the text. M05-2X was not particularly parametrized using this training set.

Statistical errors (in kcal/mol) of the test sets.

Statistical errors (in kcal/mol) of the test sets.

Statistical errors (in Å) of EXTS (Ref. 73) and bond lengths of 12 weakly bound complexes from the S22 set (Ref. 64). The results of *ω*B97X-D are taken from Ref. 36.

Statistical errors (in Å) of EXTS (Ref. 73) and bond lengths of 12 weakly bound complexes from the S22 set (Ref. 64). The results of *ω*B97X-D are taken from Ref. 36.

Statistical errors (in eV) for the IP131 database. Error is defined as −ε_{ N }(*N*) − . Experimental geometries and reference values are used for all molecules.

Statistical errors (in eV) for the IP131 database. Error is defined as −ε_{ N }(*N*) − . Experimental geometries and reference values are used for all molecules.

Statistical errors (in eV) for the EA115 database. Error is defined as −ε_{ N + 1}(*N* + 1) − . Experimental geometries and CCSD(T) reference values are used for all molecules.

Statistical errors (in eV) for the EA115 database. Error is defined as −ε_{ N + 1}(*N* + 1) − . Experimental geometries and CCSD(T) reference values are used for all molecules.

Statistical errors (in eV) of the minus LUMO energy of the neutral molecule for the EA115 database. Experimental geometries and CCSD(T) reference values are used for all molecules.

Statistical errors (in eV) of the minus LUMO energy of the neutral molecule for the EA115 database. Experimental geometries and CCSD(T) reference values are used for all molecules.

Statistic errors (in eV) of HOMO-LUMO gaps for the FG115 database. The energy gap of each system is evaluated by only one SCF calculation.

Statistic errors (in eV) of HOMO-LUMO gaps for the FG115 database. The energy gap of each system is evaluated by only one SCF calculation.

Statistic errors (in eV) of fundamental gaps for the FG115 database, each evaluated by the difference of HOMO energies between the neutral molecule and anion. The energy gap of each system is evaluated by two SCF calculations.

Statistic errors (in eV) of fundamental gaps for the FG115 database, each evaluated by the difference of HOMO energies between the neutral molecule and anion. The energy gap of each system is evaluated by two SCF calculations.

Statistic errors (in eV) of IP-EA values for the FG115 database. The energy gap of each system is evaluated by three SCF calculations.

Statistic errors (in eV) of IP-EA values for the FG115 database. The energy gap of each system is evaluated by three SCF calculations.

Vertical excitation energies (in eV) of several low-lying excited states of N_{2}, CO, water, formaldehyde, and ethylene using 6-311(2+,2+)G** basis set. The geometries and experimental values are taken from Ref. 90.

Vertical excitation energies (in eV) of several low-lying excited states of N_{2}, CO, water, formaldehyde, and ethylene using 6-311(2+,2+)G** basis set. The geometries and experimental values are taken from Ref. 90.

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