Study of the Electronic Structure of Molecules. XIV. Point Charge Perturbation on Periodic Systems

Abstract

We have simulated the perturbation involved by a solvent (or by other periodic perturbants) on a polymer (polyethylene) and we have analyzed (1) the effect of the perturbation on the energy bands of the polymer and (2) the internal charge transfer occurring on the polymer as a response to the external perturbation. The band structure is computed in the tight binding approximation using a self-consistent field model originally proposed by Ladik and subsequently improved and programmed by Andre. The model is an ab initio model, aimed at Hartree–Fock solutions for the band structure of periodic systems. All the many center integrals of coulomb and exchange type are accurately computed (the computation is an all-electron computation, and with no approximation for the atomic potential of the atoms in the unit cell). We have found that by surrounding the polymer with positive or negative point charges, the entire band system raises or lowers its entire energy spectrum. The band structure (and the energy gap) was left relatively stationary when the polymers were surrounded by alternate layers of point charges with different signs. The raising (or the lowering) of the band structure upon perturbation suggests that positive (or negative) charges on a polymeric medium can alter the band structure of the medium in the vicinity of the point charge, and that these perturbed sites can act as traps (or as sources) of electrons. We have in addition found that whereas the internal charge transfer for the polymer is not greatly altered by external perturbation of point charges of the same sign, it is highly altered by placing positive charges on one side of the polymer, and negative charges on the opposite side of the polymer (Stark effect simulation). The band energy shifts due to the external charge perturbation are sufficiently large to suggest that ESCA type experiments could be used to determine the structure of solvent molecules surrounding the polymers. The presentation of this work demonstrates that band structure computations of polymers are feasible and we expect that this type of computation will become a familiar aspect in quantum chemical work as computations on small molecules are today. As known, ab initio computations on the band structure of polymers are nearly unknown in today's scientific literature.