# Linear-response range-separated density-functional theory for atomic photoexcitation and photoionization spectra

## TL;DR

This paper evaluates the effectiveness of range-separated hybrid density-functional theory, especially the TDRSH scheme, in accurately predicting atomic photoexcitation and photoionization spectra, highlighting its advantages over traditional methods.

## Contribution

It demonstrates that the linear-response TDRSH scheme provides more accurate spectra for atomic systems than standard methods, emphasizing the potential of range-separated DFT for optical property calculations.

## Key findings

- TDRSH yields more accurate spectra than linear-response HF.
- Using local long-range exchange supports Rydberg states.
- Range-separated DFT effectively models continuum states.

## Abstract

We investigate the performance of the range-separated hybrid (RSH) scheme, which combines long-range Hartree-Fock (HF) and a short-range density-functional approximation (DFA), for calculating photoexcitation/photoionization spectra of the H and He atoms, using a B-spline basis set in order to correctly describe the continuum part of the spectra. The study of these simple systems allows us to quantify the influence on the spectra of the errors coming from the short-range exchange-correlation DFA and from the missing long-range correlation in the RSH scheme. We study the differences between using the long-range HF exchange (nonlocal) potential and the long-range exact exchange (local) potential. Contrary to the former, the latter supports a series of Rydberg states and gives reasonable photoexcitation/photoionization spectra, even without applying linear-response theory. The most accurate spectra are obtained with the linear-response time-dependent range-separated hybrid (TDRSH) scheme. In particular, for the He atom at the optimal value of the range-separation parameter, TDRSH gives slightly more accurate photoexcitation and photoioniza-tion spectra than standard linear-response time-dependent HF. More generally, the present work shows the potential of range-separated density-functional theory for calculating linear and nonlinear optical properties involving continuum states.