# Stark resonance parameters for the $3a_{1}$ orbital of the water molecule

## TL;DR

This paper calculates the Stark resonance parameters for the $3a_{1}$ orbital of water molecules using a single-center approach and exterior complex scaling, providing insights into ionization under external electric fields.

## Contribution

It introduces a method to compute Stark resonance parameters for water's $3a_{1}$ orbital without multi-center integrals, using a single-center potential and complex scaling.

## Key findings

- Resonance positions and widths are obtained for different field directions.
- The method accounts for molecular geometry in the field-free case.
- The approach simplifies calculations by avoiding multi-center integrals.

## Abstract

The Stark resonance parameters for the $3a_{1}$ molecular orbital of H$_{2}$O are computed by solving a system of partial differential equations in spherical polar coordinates. The starting point of the calculation is the quantum potential derived for this orbital from a single-center expanded Hartree-Fock orbital. The resonance positions and widths are obtained after applying an exterior complex scaling technique to describe the ionization regime for external fields applied along the two distinct $\hat{z}$ directions associated with the symmetry axis. The procedure thus avoids the computation of multi-center integrals, yet takes into account the geometric shape of a simplified molecular orbital in the field-free case.