Molecular zero-range potential method and its application to cyclic structures

TL;DR

This paper develops a molecular zero-range potential method based on Darboux transformations, enabling simplified modeling of cyclic molecules like benzene by replacing complex structures with single potentials, facilitating many-molecule problem analysis.

Contribution

It introduces a spectral, molecular zero-range potential approach within the conventional framework, incorporating spectral properties to model cyclic molecules with a single potential.

Findings

Successfully modeled benzene's bound states using atomic zero-range potentials and compared with Huckel method.

Demonstrated that a single zero-range potential can effectively represent an entire cyclic molecule.

Provided a method for approximating many-molecule systems with simplified potentials.

Abstract

The zero-range potentials of the radial Schrodinger equation are investigated from a point of Darboux transformations scheme. The dressing procedure is realized as a sequence of Darboux transformations in a way similar to that used to obtain the generalized zero-range potentials of Huang-Derevianko by specific choice of a family of parameters. In the present approach we stay within the framework of conventional zero-range potential method whilst the potential parameter (scattering length) is modified taken into account spectral molecular properties. This allows to introduce molecular zero-range potential once the corresponding discrete spectrum is known. The results are illustrated on example of flat cyclic molecular structures, with particular focus on a benzene molecule, which bounded states energies are first found using atomic zero-range potentials, compared with the Huckel method, and then used to introduce single zero-range potential describing the entire molecule. Reasonable scattering behavior for newly introduced potential gives a possibility to tackle many-molecule problems representing molecules as appropriate single zero-range potentials.