Ab initio calculation of the 66 low lying electronic states of HeH$^+$: adiabatic and diabatic representations

TL;DR

This paper provides a comprehensive ab initio analysis of the low-lying electronic states of HeH$^+$, including adiabatic and diabatic representations, potential energy curves, and non-adiabatic couplings, advancing molecular quantum chemistry understanding.

Contribution

It introduces a detailed ab initio calculation of 66 electronic states of HeH$^+$ with new diabatization procedures and extensive comparison with previous studies.

Findings

Calculated potential energy curves for 66 states.

Defined diabatic representation using radial couplings.

Analyzed asymptotic behavior of states and couplings.

Abstract

We present an ab initio study of the HeH$^+$ molecule. Using the quantum chemistry package MOLPRO and a large adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 $^1 \Sigma^+$, 19 $^3\Sigma^+$, 12 $^1\Pi$, 9 $^3\Pi$, 4 $^1\Delta$ and 2 $^3\Delta$ electronic states of the ion in CASSCF and CI approaches. The results are compared with previous works. The radial and rotational non-adiabatic coupling matrix elements as well as the dipole moments are also calculated. The asymptotic behaviour of the potential energy curves and of the various couplings between the states is also studied. Using the radial couplings, the diabatic representation is defined and we present an example of our diabatization procedure on the $^1\Sigma^+$ states.