Gaussian continuum basis functions for calculating high-harmonic generation spectra

TL;DR

This paper investigates the use of specialized Gaussian basis functions, originally designed for continuum states, to compute high-harmonic generation spectra in hydrogen atoms, showing promising results for molecular applications.

Contribution

It introduces and assesses Kaufmann et al.'s continuum Gaussian functions for high-harmonic spectra calculations, demonstrating their effectiveness compared to grid methods.

Findings

Improved description of continuum states with Kaufmann basis functions.

Good agreement with grid calculations at specific laser wavelengths.

Enhanced basis sets significantly improve spectral accuracy.

Abstract

We explore the computation of high-harmonic generation spectra by means of Gaussian basis sets in approaches propagating the time-dependent Schr{\"o}dinger equation. We investigate the efficiency of Gaussian functions specifically designed for the description of the continuum proposed by Kaufmann et al. [J. Phys. B 22, 2223 (1989)]. We assess the range of applicability of this approach by studying the hydrogen atom, i.e. the simplest atom for which "exact" calculations on a grid can be performed. We notably study the effect of increasing the basis set cardinal number, the number of diffuse basis functions, and the number of Gaussian pseudo-continuum basis functions for various laser parameters. Our results show that the latter significantly improve the description of the low-lying continuum states, and provide a satisfactory agreement with grid calculationsfor laser wavelengths $\lambda$0 = 800 and 1064 nm. The Kaufmann continuum functions therefore appear as a promising way of constructing Gaussian basis sets for studying molecular electron dynamics in strong laser fields using time-dependent quantum-chemistry approaches.