Hartree-Fock AB Initio Treatment of Crystalline Systems

ISBN-13: 9783540193173 / Angielski / Miękka / 1988 / 193 str.

Cesare Pisani; Roberto Dovesi; Carla Roetti

Opis

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

Spis treści

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.- a) Introduction.- b) Hamiltonians.- c) Basis sets.- d) Solution techniques.- e) An example: beryllium.- I. 3 Specific features of crystalline with respect to molecular Hartree-Fock computational schemes.- a) HF schemes in solid state physics.- b) Basis set selection.- c) The treatment of Coulomb interactions.- d) The treatment of exchange interactions.- e) Sampling and integration in reciprocal space.- f) Exploitation of local symmetry.- I. 4 Overcoming the limitations of the all-electron HF perfect-crystal model.- a) Introduction.- b) Pseudopotentials.- c) Correlation corrections.- d) Local defects in crystals.- II. Implementation of the Hartree-Fock Equations for Periodic Systems.- II. 1 Introductory remarks.- II. 2 Basis functions and charge distributions.- a) Atomic orbitals, Bloch functions, and representation of operators.- b) Compact expressions for charge distributions.- II. 3 Basic equations.- II. 4 The Coulomb series and the Madelung problem.- a) General considerations.- b) Rearrangement of the Coulomb series: partition of the h space in a “bielectronic” and a “monoelectronic” zone.- c) Further partition of the bielectronic zone: the bipolar expansion.- d) Further partition of the monoelectronic zone: the two center expansion.- e) Remarks and comments on the “partition and multipolar expansion scheme”.- f) On the evaluation of the integrals.- g) Evaluation of field and multipole integrals.- h) Integrals involving infinite summations.- i) Numerical examples on the Coulomb series.- II. 5 The exchange series.- a) Introduction.- b) Long range behavior of the bond order matrix and influence on total energy and wavefunction.- c) Truncation criteria of the exchange series.- II. 6 Interpolation and integration in reciprocal space.- a) Theory.- b) Examples of application.- II. 7 Symmetry properties.- a) Local symmetry operators.- b) Transformation properties of the AOs.- c) Symmetry properties of the Bloch functions and of the COs.- d) Transformation properties of direct space integrals and matrices.- e) The irreducible set.- f) Sums of two electron integrals.- g) Multipole and field integrals.- h) Symmetry and SCF procedure. Fock matrix and energy expression.- II. 8 Choice of basis set and related problems.- II. 9 The CRYSTAL program.- a) General scheme of the program.- b) Further considerations about the computational parameters.- c) SCF convergence.- d) Limits of applicability.- III. Calculation of Observable Quantities in the HF Approximation.- III. 1 Energy and energy related quantities.- a) General considerations.- b) Polyacetylene, as a test of accuracy of computational techniques.- c) Basis set and numerical accuracy effects: different crystalline phases of MgO.- d) The slab model in the study of surfaces and their adsorption properties: MgO (001) and (011) and Be (0001) crystal faces.- e) Formation energy of crystals: MgO, diamond, graphite and lithium.- III. 2 Band structure and density of states (DOS).- a) One-electron HF levels and single particle excitation spectrum of crystals.- b) Projected DOSs and Mulliken populations.- c) Chemical information from band structure and DOSs: 3D and 2D systems.- III. 3 Electron charge density and related quantities.- a) Computational techniques and general considerations.- b) Total and difference electron charge density maps: beryllium, ?-alumina.- c) Comparison of calculated and experimental x-ray structure factors: beryl1ium.- III. 4 Electron Momentum Distribution (EMD) and related quantities.- a) Computational techniques: Momentum density, Compton profiles (CP) and Autocorrelation function (AF).- b) Momentum distribution properties: lithium and MgO.- c) Mulliken analysis of the AF: the case of MgO.- 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.