We would like to improve our understanding of the behaviour of real solids. Why do atoms combine into molecules and solids in the way they do and what is the response of these aggregates of atoms to external fields, stress, temperature, etc. ? Answers to such questions would, for instance, be a useful guide in our, so far mostly empirical, search for new and better materials Stronger materials, materials which corrode less, better catalysts, better magnets, better semi- or superconductors, and, materials with properties unknown today. I expect that future advances in this field will be aided by insight obtained from calculations of the electronic structure.

/pdf/linear-methods-in-band-theory-2rmp4obhoy.pdf

Linear methods in band theory

Full-potential, linearized augmented plane wave programs for crystalline systems

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

The linearized-augmented-plane-wave (LAPW) method for thin films is generalized by removing the remaining shape approximation to the potential inside the atomic spheres. A new technique for solving Poisson's equation for a general charge density and potential is described and implemented in the film LAPW method. In the resulting full-potential LAPW method (FLAPW), all contributions to the potential are completely taken into account in the Hamiltonian matrix elements. The accuracy of the method---already well known for clean metal surfaces---is demonstrated for the case of a nearly free (noninteracting) ${\mathrm{O}}_{2}$ molecule which is a severe test case of the method because of its large anisotropic charge distribution. Detailed comparisons show that the accuracy of the FLAPW results for ${\mathrm{O}}_{2}$ exceeds that of existing state-of-the-art local-density linear-combination-of-atomic-orbitals (LCAO)-type calculations, and that taking the full potential LAPW results as a reference, the LCAO basis can be improved by adding off-site functions. Thus the full-potential LAPW is a unified method which is ideally suited to test not only molecular adsorption on surfaces, but also the components of the same system separately, i.e., the extreme limits of the molecule and the clean surface.

Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O 2 molecule

The WIEN2k program is based on the augmented plane wave plus local orbitals (APW+lo) method to solve the Kohn-Sham equations of density functional theory. The APW+lo method, which considers all electrons (core and valence) self-consistently in a full-potential treatment, is implemented very efficiently in WIEN2k, since various types of parallelization are available and many optimized numerical libraries can be used. Many properties can be calculated, ranging from the basic ones, such as the electronic band structure or the optimized atomic structure, to more specialized ones such as the nuclear magnetic resonance shielding tensor or the electric polarization. After a brief presentation of the APW+lo method, we review the usage, capabilities, and features of WIEN2k (version 19) in detail. The various options, properties, and available approximations for the exchange-correlation functional, as well as the external libraries or programs that can be used with WIEN2k, are mentioned. References to relevant applications and some examples are also given.

/pdf/wien2k-an-apw-lo-program-for-calculating-the-properties-of-3o6g3g0hz7.pdf

WIEN2k: An APW+lo program for calculating the properties of solids

By a suitable combination inside the muffin-tin sphere of a radial solution to the Schrodinger equation and its energy derivative, the dependence of the APW matrix elements on the energy E used to construct the basis functions can be greatly reduced. This has a number of advantages. The authors present an application of the method, previously suggested by Marcus (1967) and analysed by Andersen to the Chodorow copper potential and examine its precision and its convergence properties. It was found the method converges about equally well or somewhat more slowly than the standard APW method in number of basis functions. The eigenvalue error of the method is proportional to (E-E0)4. The error of the wavefunction is proportional to (E-Eo)2. The d states limit the range of mod E-E0 mod <0.1 Ryd for acceptable wavefunctions. The limit for non-d states is larger than 1 Ryd.

http://iopscience.iop.org/article/10.1088/0305-4608/5/11/016/pdf

Use of energy derivative of the radial solution in an augmented plane wave method: application to copper

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Use of energy derivative of the radial solution in an augmented plane wave method: application to copper