Theoretical description of the ionization processes with a discrete basis set representation of the electronic continuum

Abstract

In this work we present a new method of approximating the continuum wavefunctions with a discrete basis set. This method aims to be at least compatible with other well known methods of the electronic structure theory to describe processes in the electronic continuum. As an example of the application we present the results of the calculations of the photoionization cross sections for the hydrogen atom and hydrogen molecule and for the helium atom. We also obtained the photoelectron angular distribution for the hydrogen molecule. The agreement of our results with the experimental data is very good in the energy range from the ionization threshold up to photon energies of about 60 eV.

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

“…46,48,125 Some more elaborate approaches, such as the B-spline basis sets or combinations of Gaussians and grid-based methods, have also been employed with moderate success in describing both ionization rates and HHG. [126][127][128][129][130][131] Fiori and Miraglia 132 and later Szczygieł et al 133 explored the approximation of the continuum wave functions of the hydrogen atom with plane wave functions multiplied by the Gaussian-type orbitals (GTOPWs or London orbitals), which can mimic the oscillatory behavior of continuum orbitals. Such basis sets were able to very accurately reproduce the measured ionization spectra of the hydrogen and helium atoms as well as molecular-frame photoelectron angular distributions for the hydrogen molecule 132,133 but failed to exceed beyond the perturbative regime.…”

“…[126][127][128][129][130][131] Fiori and Miraglia 132 and later Szczygieł et al 133 explored the approximation of the continuum wave functions of the hydrogen atom with plane wave functions multiplied by the Gaussian-type orbitals (GTOPWs or London orbitals), which can mimic the oscillatory behavior of continuum orbitals. Such basis sets were able to very accurately reproduce the measured ionization spectra of the hydrogen and helium atoms as well as molecular-frame photoelectron angular distributions for the hydrogen molecule 132,133 but failed to exceed beyond the perturbative regime. Rowan et al showed that only their counterparts with time-dependent parameters are able to reasonably describe the wavefunction propagation in laser fields.…”

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

“…It is quite obvious that the construction of a Gaussian basis that correctly mimics the oscillatory behavior of the continuum orbitals is far from trivial. Fiori and Miraglia [135] and later Szczygieł et al [136] introduced a new approach for approximating the continuum wave functions of the hydrogen atom with a square integrable basis set to describe the ionization processes. This basis set consists of plane wave functions multiplied by the Gaussian type orbitals (GTOPWs or London orbitals), which mimic the oscillatory behavior of the continuum orbital.…”

“…This basis set consists of plane wave functions multiplied by the Gaussian type orbitals (GTOPWs or London orbitals), which mimic the oscillatory behavior of the continuum orbital. It turned out that with this basis set one could very accurately reproduce the measured ionization spectra of the hydrogen and helium atoms as well as molecular-frame photoelectron angular distributions for the hydrogen molecule [135,136]. However, this approach failed to exceed beyond the perturbative regime.…”