Calculation of Observable Quantities in the HF Approximation

For a long time we have known about the merits of the LCAO-MO approximation in the calculation and interpretation of the electronic properties of molecules and the various ways of overcoming the limitations implicit therein (Schaefer 1977, Hehre et al 1986). The same is not true in the case of crystalline systems since the experience gained in the field of molecular studies is not immediately transferable to crystals. First of all, there are some observables (x-ray structure factors, directional Compton profiles, band structure of quasiparticle energy levels) which are characteristic and specially important for periodic systems: the question arises of how to calculate them, and to what extent they are affected by the approximation implicit in the HF approach. Secondly, effects related to basis set noncompleteness are often quite different in molecules and in condensed matter (see section II.8). Thirdly, numerical approximations (series truncation, point by point integration in direct and reciprocal space), as adopted in the study of infinite systems, affect calculated data to a much larger extent than in the case of molecules. Finally, the techniques for improving upon HF results are far from established in the case of crystalline systems (see section I. 4c).