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Non-monotonic dc Stark shifts in the rapidly ionizing orbitals of the water molecule

We extend a previously developed model for the Stark resonances of the water molecule. The method employs a partial-wave expansion of the single-particle orbitals using spherical harmonics. To find the resonance positions and decay rates, we use the exterior complex scaling approach which involves the analytic continuation of the radial variable into the complex plane and yields a non-hermitian Hamiltonian matrix. The real part of the eigenvalues provides the resonance positions (and thus the Stark shifts), while the imaginary parts $-Γ/2$ are related to the decay rates $Γ$, i.e., the full-widths at half-maximum of the Breit-Wigner resonances. We focus on the three outermost (valence) orbitals, as they are dominating the ionization process. We find that for forces directed in the three Cartesian co-ordinates, the fastest ionizing orbital always displays a non-monotonic Stark shift. For the case of fields along the molecular axis we also compare results as a function of the number of spherical harmonics included ($\ell_{\max}=3,4$). We also compare our results to the total molecular Stark shifts for the Hartree-Fock and coupled cluster methods.