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

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 H2. A neural-network-based selective configuration interaction approach is then applied to calculations of 3s and 3p states of H2O and NH3. 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.