Using Koopmans' theorem for constructing basis sets: Approaching high Rydberg excited states of lithium with a compact Gaussian basis

TL;DR

This paper introduces a method to generate diffuse basis functions using Koopmans' theorem, enabling accurate and compact Gaussian basis sets for high Rydberg states of lithium, surpassing traditional methods in accuracy.

Contribution

The study presents a novel approach to construct basis sets for Rydberg states using variational optimization of virtual orbitals, achieving high accuracy with smaller basis sets.

Findings

Successfully computed dozens of high-lying Rydberg states of lithium.

Achieved excitation energies within meV of state-of-the-art methods.

Surpassed Full-CI results on Slater basis by an order of magnitude.

Abstract

For accurate ab initio description of Rydberg excited states the study suggests generating the appropriate diffuse basis functions by a cheap variational optimization of virtual orbitals of the corresponding ion core. By following this approach, dozens of converged correlated lithium Rydberg states, namely all the states up to 24S, 25P, 14D, 16F and 16G, not yet achieved by other ab initio approaches, could be obtained at the EOM-CCSD level of theory with compact and mostly state-selective contracted Gaussian basis sets. Despite its small size and Gaussian character, the optimized basis leads to highly accurate excitation energies that differ merely in the order of meV from the reference state-of-the-art explicitly correlated Gaussian method and even surpass Full-CI results on Slater basis by an order of magnitude.