Electron structure of a dipole-bound anion confined in a spherical box

We propose a model describing the interaction of an electron confined in a spherical box with a polar molecule in the center of the box, including an inner repulsive potential. As a preparation to its investigation, we calculate the average radius of a dipole-bound nonconfined electron, for which a closed form expression is found. The angular dependence of the wave function is also discussed, with implications for the choice of basis functions for ab initio calculations. The Schrödinger equation in the spherical box is then solved. The negative energy eigenstates of the system and the dependence of the ground-state energy on the radius of the confining sphere are obtained. Interestingly, a very simple expression is found for the total number of negative energy levels for a given dipole strength and confining sphere radius.