## Abstract

Linear-response time-dependent density-functional theory (TDDFT)[1] is nowadays one of the most widely used method to compute molecular excitation energies thanks to its good cost versus accuracy ratio. The key object in TDDFT is the Hartree-exchange-correlation kernel which must describe the effects of the electron-electron interaction on the excitation energies of the system. Unfortunately the form of this kernel is unknown and the design of approximations remains a major challenge. Within the usual adiabatic semi-local approximations, although it reproduces correctly valence excitations, TDDFT is not able to describe properly Rydberg, charge-transfer or multiple excitations. Range separation of the electron-electron interaction [2] allows one to mix rigorously density-functional methods at short range and wave-function or Green’s function methods at long range. When applied to the exchange kernel, the inclusion of the long-range Hartree-Fock exchange kernel already corrects most of TDDFT deficiencies [3] as in particular the correct asymptotic behavior of the potential at long range is recovered. However multiple excitations are still missed by such a kernel as they need a frequency-dependent kernel in order to be captured which is prevented by the adiabatic approximation. In this talk, I will present several developments in range-separated time-dependent and time-independent density-functional theory to improve the treatment of such excitations. The effects of range separation are first assessed on the excitation energies of a partially-interacting system in an analytic and numerical study in order to provide guidelines for future developments of range-separated methods for excitation energy calculations [4]. It is then applied on the exchange and correlation TDDFT kernels in a single-determinant approximation in which the long-range part of the correlation kernel vanishes [5]. A long-range frequency-dependent second-order correlation kernel is then derived from the Bethe-Salpeter equation and added perturbatively to the range-separated TDDFT kernel in order to take into account the effects of double excitations.

## Presentation slides

Winterschool 2016 - presentation slides Elisa Rebolini1.5 MB

## Recorded presentation

## References

[1] M. Casida. “Time-Depent Density-functional response theory for molecules”. In: *Recent Adv. Density Funct. Methods, Part I.* Ed. by D. P. Chong. Singapore: World Scientific, 1995, p. 155.

[2] A. Savin. “On degeneracy, near-degeneracy and density functional theory”. In: *Recent Dev. Appl. Mod. Density Funct. Theory.* Ed. by J.M. Seminario. Amsterdam: Elsevier, 1996, p. 327.

[3] Y. Tawada, T. Tsuneda, S. Yanagisawa, et al. 2004. *J. Chem. Phys.* 120. P. 8425.

[4] E. Rebolini, J. Toulouse, A. M. Teale, et al. 2014. *J. Chem. Phys.* 141. P. 044123.

[5] E. Rebolini, A. Savin, and J. Toulouse. 2013.* Mol. Phys.* 111. Pp. 1219–1234.