# Ab initio lifetime correction to scattering states for time-dependent electronic-structure calculations with incomplete basis sets

## TL;DR

This paper introduces an ab initio method to accurately determine the lifetimes of scattering states in time-dependent electronic-structure calculations, addressing basis set limitations without empirical parameters.

## Contribution

It presents a rigorous, basis-set-adapted lifetime correction method derived from complex-energy solutions of the Schrödinger equation, improving scattering state modeling.

## Key findings

- Accurately extracts lifetimes from wave function decay
- Validates method on H and He atoms for high-harmonic spectra
- Provides basis-set-specific lifetime corrections without empirical parameters

## Abstract

We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schr{\"o}dinger equation. It gives lifetimes adapted to any given basis set without using any empirical parameters. The method can be considered as an ab initio version of the heuristic lifetime model of Klinkusch et al. [J. Chem. Phys. 131, 114304 (2009)]. The method is validated on the H and He atoms using Gaussian-type basis sets for calculation of high-harmonic-generation spectra.