The Fourier Space Restricted Hartree-Fock Method for the Electronic Structure Calculation of One-Dimensionally Periodic Systems

Computational studies of the electronic structures of periodic systems at the level of Hartree-Fock or density functional theory require the evaluation to appropriate accuracy of the lattice sums that appear in these formalisms. This chapter describes and illustrates a method for treating systems that are periodic in one of the three dimensions (i.e., stereoregular polymers), showing how a combination of Fourier-transform techniques and an Ewald-type partitioning enables these sums to be divided between physical (direct) space and reciprocal (Fourier) space in a way that enhances their convergence rate. It is also shown how the spatial (line-group) symmetry (including rotational and screw axes, reflection, and glide planes) can be exploited to improve the efficiency of computation, extending to this domain the technique of Dupuis and King for building a complete Fock matrix from a minimal set of its matrix elements. Other issues of computational efficiency are also reviewed. The methods, implemented in our computer program ft-1d, are illustrated for a problem of significant size: A carbon single-wall (7, 0) nanotube with 56 spatial symmetry operations and bases of up to 420 atomic orbitals per unit cell.