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

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.