Electronic Band Structure of Helical Polyisocyanides

Restricted Hartree-Fock computations are reported for a methyl isocyanide polymer (repeating unit -C═N-CH₃), 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 L9₅, 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 L4₁ 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. Data reported include computed bond properties, atomic charge distribution, longitudinal polarizability, band structure, and the convoluted density of states. Most features of the description were found to be insensitive to the level of computational approximation. The work also illustrates the importance of exploiting line-group symmetry to extend the range of polymer structural problems that can be treated computationally.