Electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment

TL;DR

This paper develops a model for valence electron binding in atoms and molecules considering electric dipole and quadrupole effects within a charge-screening environment, revealing finite bound states and the non-existence of pure quadrupole-bound anions.

Contribution

It introduces an exact solution using the Tridiagonal Representation Approach for multipole-expanded charge distributions with screening effects.

Findings

Finite number of bound states due to charge screening.

Energy jumps at the transition to the continuum.

Pure quadrupole-bound anions cannot exist in this environment.

Abstract

We make a multipole expansion of the atomic/molecular electrostatic charge distribution as seen by the valence electron up to the quadrupole term. The Tridiagonal Representation Approach (TRA) is used to obtain an exact bound state solution associated with an effective quadrupole moment and assuming that the electron-molecule interaction is screened by suborbital electrons. We show that the number of states available for binding the electron is finite forcing an energy jump in its transition to the continuum that could be detected experimentally in some favorable settings. We expect that our solution gives an alternative, viable and simple description of the binding of valence electron(s) in atoms/molecules with electric dipole and quadrupole moments. We also ascertain that our model implies that a pure quadrupole-bound anion cannot exist in such a charge-screening environment.