Calculations of 1D Periodic Systems at the Hartree-Fock Level and Beyond

Joseph Delhalle, Joseph G. Fripiat, and Frank E. Harris

Laboratoire Interdisciplinaire de Spectroscopie
Electronique and

Laboratoire de Chimie Théorique Appliquée,
Facultés Universitaires

Notre-Dame de la Paix, Namur, Belgium

and

Department of Physics, University of Utah and

Quantum Theory Project, University of Utah

(submitted to Int. J. Quantum Chem.)

A major challenge in electronic structure calculations of extended systems is to compute to appropriate accuracy the lattice sums arising in the various ab initio formalsims. Unsatisfactory convergence of all or some of these contributions can lead to such imbalance in the matrix elements that total energy, hence most stable structure, and other more sensitive properties such as force constants cannot be computed. The purpose of this paper is to point out the intrinsic virtues of the Fourier transform method for handling accurately the lattice sums arising in Hartree-Fock and many-body approaches such as MP2. The infinite chain of Be atoms, is used to illustrate some of the points addressed in the present contribution. Even in this simple system it is seen that direct-space methods do not permit the exchange energy sum to be converged sufficiently to permit computations near the equilibrium lattice spacing. However, the Fourier transform method enables identification of the equilibrium configuration in a stable and accurate fashion.