A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States.

Dávid Mester,Mihály Kállay

doi:10.1021/acs.jctc.0c01135

Abstract

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm–Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Highlights

Electronic excitations are cardinal phenomena in many areas of chemistry, physics, and biology
A robust two-parameter RS-DH Tamm−Dancoff approximation (TDA)-time-dependent density functional theory (TDDFT) approach has been proposed for excited-state calculations, which is based on the Coulombattenuating method (CAM)-like decomposition of the Coulomb potential utilizing the ansatz introduced by Toulouse et al.[71] for the ground-state XC energy
The detailed working equations were presented for the perturbative LR/SR second-order corrections for singlet excitations using the numerically stable robust fitting formulas[87] supposing a closed-shell system

Summary

INTRODUCTION

Electronic excitations are cardinal phenomena in many areas of chemistry, physics, and biology. In most cases, a more approximate form of the RS XC energy is employed where solely the exchange contributions are rangeseparated.[77−80] The connection between the fraction of the exact exchange in the RS XC energy and the optimal rangeseparation parameter for the nonempirical functionals was presented by Adamo et al.[78] Later, it was demonstrated that these parameters are in line with the results obtained by relying on the so-called optimally tuned procedure.[79] The only excited-state RS-DH approach proposed[81] and carefully benchmarked[82,83] recently by Goerigk and co-workers originated from this scheme. We present a flexible implementation of the new approach, and we demonstrate its advantages through numerous benchmark calculations

THEORY

RESULTS

CONCLUSIONS

■ ACKNOWLEDGMENTS

■ REFERENCES