Electronic Band Structure of Helical Polyisocyanides.

Restricted Hartree-Fock computations are reported for a methyl isocyanide polymer (repeating unit -C═N-CH), whose most stable conformation is expected to be a helical chain. The computations used a standard contracted Gaussian orbital set at the computational levels STO-3G, 3-21G, 6-31G, and 6-31G**, and studies were made for two line-group configurations motivated by earlier work and by studies of space-filling molecular models: (1) A structure of line-group symmetry L9, containing a 9-fold screw axis with atoms displaced in the axial direction by 5/9 times the lattice constant, and (2) a structure of symmetry L4 that had been proposed, containing a 4-fold screw axis with translation by 1/4 of the lattice constant. Full use of the line-group symmetry was employed to cause most of the computational complexity to depend only on the size of the asymmetric repeating unit.

Ewald-type formulas for Gaussian-basis Bloch states in one-dimensionally periodic systems.

Expressions for integrals involving general Gaussian (s, p, d, [ellipsis (horizontal)]) basis Bloch functions are presented. Applying the Poisson transformation and the Ewald-type partitioning scheme, all lattice sums appearing in these expressions lead to fast convergence in both direct and Fourier spaces. Numerical results produced for selected test cases show that a limited number of terms in the lattice sums are necessary to get convergence in the two spaces.