Challenges with range-separated exchange-correlation functionals in time-dependent density functional theory calculations

Abstract

The conventional approximate exchange-correlation functionals and kernels can lead to a large error in time-dependent density functional theory (TDDFT) calculations in certain cases, such as in the descriptions of charge-transfer excited states, Rydberg states, and double excitations, which can be remedied to some degree with the recently developed range-separated exchange-correlation functionals. How do these range-separated functionals perform in the TDDFT calculations? In this work, we explored the S₀(A′) → T₁(A′) and S₀(A′) → S₁(A′) transition energies of C₂H₄ and other molecules by TDDFT methods and ▵SCF calculations in density functional theory (DFT), with several regular and range-separated exchange-correlation functionals. We have found the following: (1) for the S₀ → S₁ transition, both range- and non-range-separated exchange-correlation functionals work well and consistently in the TDDFT calculations; (2) for the S₀ → T₁ transition, the used range-separated exchange-correlation functionals work on average worse than the non-separated ones in the TDDFT calculations; in the ▵SCF DFT calculations, however, both kinds of functionals achieve a similar performance. Because of the common approximations used in DFT and TDDFT, our present computational results suggest that the adiabatic approximation error in the range-separated exchange-correlation functionals is much larger than that in the non-range-separated ones for the S₀ → T₁ transition, and the adiabatic approximation error for the S₀ → T₁ transition – a spin-flip process – is larger than that for the S₀ → S₁ transition. These findings will be useful for designing better exchange-correlation functionals and kernels that will work well not only for excited singlet states, but also for excited triplet states. Furthermore, this study will provide insights into the drawbacks of the present approximate exchange-correlation functionals and kernels used in TDDFT calculations.

Keywords:

• exchange-correlation functional
• time-dependent density functional theory
• electronic structure theory
• excited states

Acknowledgements

This work has been supported by the National Science Foundation (CHE-09-11119) and the National Institute of Health (5R01-GM-061870-09).

Notes

Note

Supplementary material can be viewed online.