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The zero-range potentials of the radial Schrodinger equation are investigatedfrom a point of Darboux transformations scheme. The dressing procedure isrealized as a sequence of Darboux transformations in a way similar to that usedto obtain the generalized zero-range potentials of Huang-Derevianko by specificchoice of a family of parameters. In the present approach we stay within theframework of conventional zero-range potential method whilst the potentialparameter (scattering length) is modified taken into account spectral molecularproperties. This allows to introduce molecular zero-range potential once thecorresponding discrete spectrum is known. The results are illustrated onexample of flat cyclic molecular structures, with particular focus on a benzenemolecule, which bounded states energies are first found using atomic zero-rangepotentials, compared with the Huckel method, and then used to introduce singlezero-range potential describing the entire molecule. Reasonable scatteringbehavior for newly introduced potential gives a possibility to tacklemany-molecule problems representing molecules as appropriate single zero-rangepotentials.

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