Large Scale Condensed Matter Calculations using the Gaussian and Augmented Plane Waves Method

Abstract

Density functional theory DFT Kohn-Sham [16] is the method of choice for the calculation of electronic properties of large systems. This is due to the combination of accuracy and efficiency that has been achieved for the Kohn– Sham (KS) method in DFT [19]. DFT based electronic structure calculations are nowadays routinely used by chemists and physicists to support their research. Increasingly complex systems can be treated and the inclusion of environmental effects, through implicit or explicit solvent treatments, as well as the effects of different thermodynamic parameters (temperature, pressure) through first–principles molecular dynamics, opens the door for simulations close to experimental conditions. The accuracy of the method is such that many properties of systems of interest to chemistry, physics, material science, and biology can be predicted in a parameter free way. The success of the KS method makes it also the favorite framework for new developments to improve both, accuracy and efficiency. Better accuracy in this context can be achieved along two lines. On one hand the numerical limit of a given model should be reached and on the other hand more accurate models should be developed (i.e. exchange-correlation functional in DFT). The development of new functionals is an art on its own and will not concern us here. However, it is intimately related to the efficiency problem, as only numerically accurate tests on more and more complex systems can give unambiguous information on the performance of new functionals. The goal of improved algorithms is therefore, to provide methods to accurately and efficiently solve the KS equations.