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

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 to represent the radial part of the wave function. The angular parts of the wave function are represented by spherical harmonics. The problem of Stark resonances is treated with the exterior complex scaling method which incorporates a wave-function 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 1b1, 3a1, and the bonding orbital 1b2. Furthermore, comparison is made with total molecular decay rates and dc shifts obtained recently within the Hartree-Fock and coupled-cluster approaches.

Automated summary

A partial-wave method is proposed to deal with small molecules dominated by a central atom. The method extends the earlier single-center methods and expands the model potential for the water molecule over a basis of spherical harmonics. The radial part of the wave function is represented by local polynomial functions generated through a finite-element method, while the angular parts are represented by spherical harmonics. The problem of Stark resonances is treated with the exterior complex scaling method, and the resulting non-Hermitian matrix eigenvalue problem provides resonance positions and widths. The study presents the dc Stark shifts and exponential decay rates for specific valence orbitals and compares them with results obtained from other approaches.