A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

http://ronald-wagner.de/diss/html/lit/share/surfsci411(98)186.pdf

The surface energy of metals

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

Advances in the accuracy and efficiency of first-principles electronic structure calculations have allowed detailed studies of the energetics of materials under high pressures. At the same time, improvements in the resolution of powder x-ray diffraction experiments and more sophisticated methods of data analysis have revealed the existence of many new and unexpected high-pressure phases. The most complete set of theoretical and experimental data obtained to date is for the group-IVA elements and the group-IIIA--VA and IIB--VIA compounds. Here the authors review the currently known structures and high-pressure behavior of these materials and the theoretical work that has been done on them. The capabilities of modern first-principles methods are illustrated by a full comparison with the experimental data.

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High-pressure phases of group-IV, III–V, and II–VI compounds

Plots of the tight-binding (TB) orbitals recently derived by exact transformation of the conventional set of linear muffin-tin orbitals (LMTO's) are presented for crystalline silicon. The TB-LMTO's are found to be extremely compact. As a simple application we show how non-spherically-averaged charge densities may be obtained from standard LMTO calculations. For silicon this charge density is found to be in excellent agreement with the one obtained from a linear augmented plane-wave full-potential calculation. This is true even when the LMTO calculation employs the atomic-sphere approximation for the one-electron potential. A self-contained account of the TB-MTO formalism is presented and a simple way of including the quadratic energy dependence of the MTO's is derived.

Illustration of the linear-muffin-tin-orbital tight-binding representation: Compact orbitals and charge density in Si

Theoretical investigations of the bonding properties of 34 elemental and compound semiconductors are reported. From self-consistent band-structure calculations (within the local-density approximation) valence charge densities are calculated. The densities are obtained by transforming muffin-tin orbitals to a localized basis. Using another representation, an orthogonal basis, we construct ${\mathrm{sp}}^{3}$ hybrids and project out the bond and antibond characters, i.e., we derive first-principles values for ${\mathrm{sp}}^{3}$ bond orders. These, together with the first-principles tight-binding parameters, are used to study chemical trends. Relations to Phillips ionicity (${f}_{i}$) scale are established and it is demonstrated, for example, that the critical ionicity value ${f}_{i}$=0.786 found empirically separating the fourfold- from the sixfold-coordinated crystal structures also follows from total-energy calculations.

Bonding and ionicity in semiconductors.

From linear muffin-tin-orbital calculations using suitable basis sets we derive, from first principles, $s{p}^{3}$ bonding characteristics for group-IV elements. Particular attention is paid to lead, for which the importance of relativistic effects in determining the most stable structure is examined. The mass-velocity shift of the $\mathrm{Pb} 6s$ state is so large that the $s\ensuremath{-}p$ hybridization in a hypothetical diamond structure is too weak to allow the formation of sufficiently strong $s{p}^{3}$ bonding. Omission of relativistic effects would make the diamond structure of Pb more stable than the observed (fcc).

First-principles theory of tetrahedral bonding and crystal structure of lead.

Bond-centered Wannier functions are constructed for the valence bands of silicon by a direct superposition of the Bloch functions whose phases are chosen on physical grounds. The Bloch functions are calculated using the linear muffin-tin orbitals method within the local density approximation. The resulting four Wannier functions per unit cell are equivalent to one another. Each is localized on a bond-center, has the Γ1 symmetry of the D3d group, and falls off exponentially.



Bindungszentrierte Wannierfunktionen fur die Valenzbander von Silizium werden durch direkte Uberlagerung der Blochfunktionen konstruiert. Die Phasen der Blochfunktionen werden aufgrund physikalischer Uberlegungen gewahlt. Die Blochfunktionen werden unter Verwendung der Linear-Muffin-Tin-Orbital (LMTO)-Methode innerhalb der lokalen Approximation der Dichtefunktionaltheorie berechnet. Die resultierenden vier Wannierfunktionen pro Einheitszelle sind aquivalent. Jede ist an einem Bindungszentrum lokalisiert, hat die Γ1-Symmetrie der D3d-Gruppe und fallt exponentiell ab.

Z. Pawlowska

Papers

Illustration of the linear-muffin-tin-orbital tight-binding representation: Compact orbitals and charge density in Si

Bonding and ionicity in semiconductors.

First-principles theory of tetrahedral bonding and crystal structure of lead.

Construction of Bond‐Centered Wannier Functions for Silicon Valence Bands

Systematics of wetting and layering phenomena in smectic materials.