ON THE ELECTROSTATIC POTENTIAL IN LINEAR PERIODIC POLYMERS

The evaluation of the electrostatic potential arising from a line latt ice with an electroneutral basis is formulated as an integral over an ''effective'' potential function. A procedure for the calculation of t he ''effective'' potential function based on the Euler-MacLaurin summa tion formula is presented, and compared with Fourier representation an d Taylor series expansion methods. A recursive scheme for the evaluati on of the derivatives (of arbitrary order) of the ''effective'' potent ial based on the Euler-MacLaurin representation is given. Finally, int egrals involving products of Gaussian type functions and the ''effecti ve'' potential are evaluated. Such integrals are required in studies o f the electronic structure of linear periodic polymers if Gaussian bas is sets are used.