A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

Abstract

A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one-or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 10 13 W/cm 2 to 5 × 10 14 W/cm 2 . We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study

“…First of all, the results presented in this paper may serve as an additional proof of applicability of the ARO Gaussian functions in the modeling of HHG, extending our previous study [120]. We have shown on the example of the helium atom that Dunning basis sets supplemented with ARO functions allow for studying the laser-driven electron dynamics in many-electron systems in the CI framework.…”

“…In our recent paper [120] we introduced a novel class of Gaussian functions we dubbed ARO functions, that proved able to approximate a wide spectrum of excited states necessary for the description of HHG in both oneand two-electron systems. Therefore, in the present calculations we use Dunning basis sets mixed with ARO functions.…”

“…In order to select an optimal basis set for the time-dependent calculations we have performed a series of test propagations of the helium atom using different augmented correlation-consistent basis sets of general type x-aug-cc-pVYZ, with x=∅,d,3,4 and Y=D,T,Q,5, supplemented with shells of ARO functions with angular momenta l from 0 (s-type functions) up to l max = 2, 3 or 4 (d-,f -and g-type functions, respectively). The ARO functions were generated according to the procedure described in [120], by fitting Gaussians to a set of Slater-type orbitals with exponent ζ = 1.7 (the effective nuclear charge of helium) and principal quantum numbers n from 2 to 90. The number of ARO fuctions added per angular momentum varied from 4 to 10.…”

Gaussian-Type Orbital Calculations for High Harmonic Generation in Vibrating Molecules: Benchmarks for H2+

“…Also several studies exist, which model the process of HHG using GTO basis sets (see, for instance, refs − ). For simpler systems such as H 2 + or the H atom, systematic studies of the performance of various (extended) GTO basis sets in comparison to B-splines or alike and grid bases to describe HHG exist. , When it comes to many-electron systems to be treated by WFT, often the time-dependent electronic Schrödinger equation is approximately solved using the time-dependent configuration interaction singles (TD-CIS) method, − again together with Gaussian basis sets. Real-space absorbers , or heuristic (energy space) ionization models − in combination with additional basis functions are often used, to avoid artifacts and noise due to the confined electron motion when applying atom-centered GTOs.…”

Single- and double-ionization processes using Gaussian-type orbitals: Benchmark on antiproton-helium collisions in the keV-energy range

“…Because GTOs are square-integrable L 2 functions they cannot describe the exact boundary conditions of continuum states. Although there have been large efforts to find optimal GTOs to approximate these states [5][6][7][8][9] or to provide corrections to the GTOs finite boundary conditions (see e.g. [10][11][12][13][14]), it is still challenging to describe molecular states above the ionization thresholds.…”