Gaussian basis sets for highly excited and resonance states of helium

Abstract

A consistent method for optimizing Gaussian primitives for Rydberg and multiply excited helium states is designed. A novel series for the "exponentially tempered Gaussians" is introduced, which is markedly more efficient than the commonly used series of even tempered Gaussians. The optimization is made computationally feasible due to an approximate calculation of excited states using the effective one-electron Hamiltonian that is defined as Fockian from which the redundant Coulomb and exchange terms are dropped. Finally, ExTG5G and ExTG7F Gaussian basis sets are proposed. They enable calculations of the helium spectrum all the way from the ground state up to the (5, 4)(5) (1)S(e) and (6, 5)(7) (1)S(e) doubly excited resonances, respectively, mostly in the spectroscopic accuracy of 1 cm(-1).

Excitation of helium Rydberg states and doubly excited resonances in strong extreme ultraviolet fields: Full-dimensional quantum dynamics using exponentially tempered Gaussian basis sets

“…The solution of the complex scaled Hamiltonian is based on the Full Configuration Interaction (FCI) expansion constructed from the exponentially tempered Gaussian basis sets, ExTG5G and ExTG7F. 38 The ExTG5G and ExTG7F basis sets excel in their stability with respect to complex scaling of the Hamiltonian in the radial coordinate due to an ample sampling of the radial subspace. The basis sets are tailored for an accurate calculation of highly excited states up to n = 5 or 7 with the error of 1 cm −1 .…”

“…38 as a generalization of the well known even tempered Gaussians. The new series is better suited for Coulomb-like problems including highly excited states.…”

“…38 It should be stressed that the standard quantum chemistry basis sets (such as the Dunning-Huzinaga or Lund Atomic Natural Orbital basis sets 39 ) are inadequate for the purpose of simulations of the electronic phenomena in strong laser fields for two reasons. First, they do not include basis functions which are broad enough, and second, they are optimized only up to chemical accuracy.…”

“…The latter problem is reflected in rotations of bound states to the complex plane when using complex scaling (see Table IX in Ref. 38). These artifacts would derail dynamical simulation after a few attoseconds, which clearly shows in the course of the present paper.…”

“…In our previous work, Ref. 38, we have suggested preferable expo-nentially tempered Gaussian (ExTG) basis sets with a higher density of Gaussians improving the stability with respect to complex rotation, and additional diffuse functions describing more Rydberg states. Two Gaussian basis sets, ExTG5G and ExTG7F, are now available for the helium atom.…”