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

Tridiagonal representation approach in quantum mechanics

“…Some of these new solutions lead to interesting applications in atomic, molecular and nuclear physics. As examples, we mention the anion problem where an electron becomes bound to a neutral molecule with an electric dipole moment [16,17], the binding of a charged particle to an electric quadrupole in two dimensions [18], energy density bands engineering [19], electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment [20], etc. In applied mathematics, the TRA was also used to obtain series solutions of new types of ordinary differential equations of the second order with three and four singular points [21][22][23].…”

Non-relativistic and relativistic equations for the Kratzer potential plus a dipole in 2D systems

“…When we study non central potentials, the difficulty already appears in Schrödinger equation, where the separation of variables is only possible when the potential is of the type V (r)+V (θ) r −2 + V (ϕ) r −2 sin −2 (θ) [1,2,3,4], and among them there is only few ones that can be studied analytically [5,4]. The study of this kind of potential began with the works of Makarov [6] and Hartmann [7] in molecular systems and now they are in focus in various fields, especially in quantum chemistry and nuclear physics.…”