Hartree-Fock Ab Initio Treatment of Crystalline Systems

I. Different Approaches to the Study of the Electronic Properties of Periodic Systems.- I. 1 Many-electron systems: the viewpoint of theoretical chemists and physicists.- I. 2 A mosaic of options for the ab initio treatment of crystalline systems.- I. 3 Specific features of crystalline with respect to molecular Hartree-Fock computational schemes.- I. 4 Overcoming the limitations of the all-electron HF perfect-crystal model.- II. Implementation of the Hartree-Fock Equations for Periodic Systems.- II. 1 Introductory remarks.- II. 2 Basis functions and charge distributions.- II. 3 Basic equations.- II. 4 The Coulomb series and the Madelung problem.- II. 5 The exchange series.- II. 6 Interpolation and integration in reciprocal space.- II. 7 Symmetry properties.- II. 8 Choice of basis set and related problems.- II. 9 The CRYSTAL program.- III. Calculation of Observable Quantities in the HF Approximation.- III. 1 Energy and energy related quantities.- III. 2 Band structure and density of states (DOS).- III. 3 Electron charge density and related quantities.- III. 4 Electron Momentum Distribution (EMD) and related quantities.- Appendices.- A. Solid harmonics and multipolar expansion of Coulomb interactions.- B. Definition of Brillouin Zone and related quantities.- C. The McMurchie-Davidson technique for the evaluation of the molecular integrals.- C1. Hermite gaussian type functions (HGTF).- C2. The Gaussian product theorem and the expansion in HGTF.- C3. The expansion coefficients E.- a) Recursion in ?.- b) Recursion in ? and |m| =?.- c) Method of generation.- C4. Overlap and kinetic integrals.- C5. Nuclear attraction integrals.- C6. Two electron repulsion integrals.- D. Symbols and notations.- References.