Abstract |
: |
Density-functional theory (DFT) is currently the ab initio method most widely used to predict electronic energy levels of new materials. However, approxima- tions intrinsic to the theory limit the accuracy of calculated energy levels to about 0.5 eV. The G0W0 approach is an alternate ab initio method that provides an enhanced precision (about 0.05 eV). However, its computational cost is currently prohibitive for systems with more than a few tens of electrons, thus limiting its use in the simulation and design of technologically relevant materials. This limitation of current G0W0 implementations can be traced to two bottle- necks : the need to invert a large matrix (the dielectric matrix) and the need to carry out summations over a large number of electronic states (conduction states). The first bottleneck is caused by the choice of the basis in which the dielectric matrix is represented : traditional G0W0 implementations use a plane wave basis, which needs to be relatively large to properly describe the matrix. This talk will explain how a Lanczos basis can be generated to substantially reduce the size of the matrix. Also, the number of conduction bands needed to reach convergence in the summations is usually an order of magnitude larger than the number of valence bands. Here, the calculation of the conduction states is avoided by refor- mulating the summations into linear equation problems (Sternheimer equations), which also substantially reduces the computation time. Finally, we will discuss how the introduction of a model dielectric operator allows further speedup in the calculation of the dielectric matrix without introducing further approximation in the method. Preliminary calculations on silane, thiophene and benzene will be presented. |