Partial-wave approach to the Stark resonance problem of the water molecule

TL;DR

This paper introduces a partial-wave approach with finite element methods and exterior complex scaling to analyze Stark resonances in water molecules, providing detailed resonance data and comparisons with other quantum chemistry methods.

Contribution

It extends single-center methods to small molecules like water using a basis of spherical harmonics and finite element techniques for accurate Stark resonance calculations.

Findings

Calculated Stark shifts and decay rates for water valence orbitals.

Compared results with Hartree-Fock and coupled-cluster methods.

Provided detailed resonance data for specific molecular orbitals.

Abstract

A partial-wave method is developed to deal with small molecules dominated by a central atom as an extension of earlier single-center methods. In particular, a model potential for the water molecule is expanded over a basis of spherical harmonics. A finite element method is employed to generate local polynomial functions in subintervals over a finite range for the radial variable. The angular parts of the system are represented by spherical harmonics. The problem of Stark resonances is treated with the exterior complex scaling method which incorporates a wavefunction discontinuity at the scaling radius. The resultant non-hermitian matrix eigenvalue problem yields resonance positions and widths (decay rates). We present these DC Stark shifts and exponential decay rates for the valence orbitals $1b_1$, $3a_1$, and the bonding orbital $1b_2$. Furthermore, comparison is made with total molecular decay rates and DC shifts obtained recently within the Hartree-Fock and coupled-cluster approaches.