Orbital Optimization and Neural-Network-Assisted Configuration Interaction Calculations of Rydberg States

Abstract

Rydberg excited states of molecules pose a challenge for electronic structure calculations because of their highly diffuse electron distribution. Even large and elaborate atomic basis sets tend to underrepresent the long-range tail, overly confining the Rydberg state. An approach is presented here where the molecular orbitals are variationally optimized for the excited state using a plane wave basis set in a Hartree-Fock calculation, followed by a configuration interaction calculation. The use of excited state optimized orbitals greatly enhances the convergence of the many-body calculation, as illustrated by a full configuration interaction calculation of the $2s$ Rydberg state of H${}_2$. A neural-network-based selective configuration interaction approach is then applied to calculations of $3s$ and $3p$ states of H${}_2$O and NH${}_3$. The obtained values of excitation energy are in close agreement with experimental measurements as well as previous many-body calculations where sufficiently diffuse atomic basis sets were used. Calculations using atomic basis sets lacking extra diffuse functions, such as aug-cc-pVTZ, give significantly higher estimates due to confinement of the Rydberg states.

13 pages, 7 figures (main), 4 pages, 8 figures (SI)