Enhancing the Flexibility of First Principles Simulations of Materials via Wavelets

We illustrate how the properties of a Daubechies wavelet basis set can be exploited to build an effective computational method that enables one to perform electronic structure calculations of systems containing up to many thousands of atoms. This is achieved by implementing a ladder of approaches of different scaling behaviours and decreasing computational complexity. We will explain that such an approach is suitable both for extended systems and for systems with molecular character. We define quantitative indicators that provide guidelines to the end-user about the pertinence of the employed methodology, thereby guaranteeing limited impact on the precision of the result. We provide a quantitative illustration of these concepts to defective systems with an extended character, by presenting the differences in computational walltime and in precision among the various methodological steps of the ladders.