Adiabatic potential energy curves of long-range Rydberg molecules: Two-electron R-matrix approach

TL;DR

This paper presents a new two-electron R-matrix computational method for calculating adiabatic potential energy curves of long-range Rydberg molecules, validated on hydrogen molecules across various internuclear distances and energy levels.

Contribution

It introduces a novel two-electron R-matrix approach for modeling long-range Rydberg molecular states, bridging quantum chemical and contact potential methods.

Findings

Accurately computed Rydberg states of hydrogen molecule for R from 20 to 400 bohrs.

Validated the method against existing quantum chemical and contact potential calculations.

Demonstrated the method's effectiveness across a wide range of quantum numbers.

Abstract

We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron \rmath approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances $R$ from 20 to 400 bohrs and energies corresponding to $n$ from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers $n$) and computations based on contact potential models (higher quantum numbers $n$).