Band-structure methods

Abstract

The theoretical determination of the unoccupied electronic states is an important tool for understanding the results of experimental techniques such as X-ray absorption, inverse photoemission and bremsstrahlung isochromat spectroscopy. The availability of reliable calculations always serves as a starting point to interpret the measured spectra in the one-electron picture. In periodic crystals the electronic states have historically been named band structures, and their calculation is the aim of band-structure methods. A large variety of methods have been invented and an enormous amount of literature exists on the calculation of occupied and low-lying unoccupied states. There is much less work on higher lying unoccupied states and particular problems arising from the higher energy range are seldom discussed. In this chapter I describe several modern band-structure methods and discuss their applicability to calculate the unoccupied electronic states within an energy range of about 10 Rydbergs above the occupied states. To simplify my presentation, I consider only lattices with one atom per unit cell and I omit the discussion of spin-polarisation and relativistic effects and of group theory to exploit symmetry. The multiple-scattering method will be emphasized because it leads to the smallest matrices in the computations and it can be developed into the linear muffin-tin orbital (LMTO) method, the fastest band-structure technique. The multiple-scattering method is in principle exact and easily extended to nonperiodic systems, such as crystals locally perturbed by impurities or excitations, clusters of atoms, surfaces and disordered alloys.