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This book presents a computational scheme for calculating the electronic properties of crystalline systems at an ab-ini tio Hartree-Fock level of approximation. The first chapter is devoted to discussing in general terms the limits and capabilities of this approximation in solid state studies, and to examining the various options that are open for its implementation. The second chapter illustrates in detail the algorithms adopted in one specific computer program, CRYSTAL, to be submitted to QCPE. Special care is given to illustrating the role and in:fluence of computational parameters, because a delicate compromise must always be reached between accuracy and costs. The third chapter describes a number of applications, in order to clarify the possible use of this kind of programs in solid state physics and chemistry. Appendices A, B, and C contain various standard expressions, formulae, and definitions that may be useful for reference purposes; appendix D is intended to facilitate the interpretations of symbols, conventions, and acronyms that occur in the book. Thanks are due to all those who have contributed to the implementation and test of the CRYSTAL program, especially to V.R. Saunders and M. Causal, and to F. Ricca, E. Ferrero, R. Or lando, E. Ermondi, G. Angonoa, P. Dellarole, G. Baracco.



Chapter I. Different Approaches to the Study of the Electronic Properties of Periodic Systems

It is the purpose of this book to present and discuss an ab initio Hartree-Fock (HF) scheme for the calculation of the electronic structure of crystalline systems. The techniques adopted are in a sense midway between those currently used in molecular quantum chemistry and those traditionally employed in solid state physics.
C. Pisani, R. Dovesi, C. Roetti

Chapter II. Implementation of the Hartree-Fock Equations for Periodic Systems

This chapter describes in detail a specific HF-CS approach for the calculation of the electronic structure of crystalline systems. Among the several options that can be adopted at each computational stage, the one that is presented is currently implemented in the program CRYSTAL (see section I.3a). CRYSTAL is still in rather rapid evolution, so some of the techniques here described will probably be improved in the near future. In any event, we shall indicate those topics where progress is expected to occur first.
C. Pisani, R. Dovesi, C. Roetti

Chapter III. 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).
C. Pisani, R. Dovesi, C. Roetti


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