Wavelets for electronic structure calculations

Abstract

In 2005, the EU FP6-STREP-NEST BigDFT project funded a consortium of four laboratories, with the aim of developing a novel approach for Density Functional Theory (DFT) calculations based on Daubechies wavelets. Rather than simply building a DFT code from scratch, the objective of this three-years project was to test the potential benefit of a new formalism in the context of electronic structure calculations. Daubechies wavelets exhibit a set of properties which make them ideal for a precise and optimised DFT approach. In particular, their systematicity allows to provide a reliable basis set for high-precision results, whereas their locality (both in real and reciprocal space) is highly desired for improve the efficiency and the flexibility of the treatment. In this contribution we will provide a bird's-eye view on the computational methods in DFT, and we then focus on DFT approaches and on the way they are implemented in the BigDFT code, to explain how we can take benefit from the peculiarities of such basis set in the context of electronic structure calculations. In the recent years, the development of efficient and reliable methods for studying matter at atomistic level has become an asset for important advancements in the context of material science. Both modern technological evolution and the need for new conception of materials and nanoscaled devices require a deep understanding of the properties of systems of many atoms from a fundamental viewpoint. To this aim, the support of computer simulation can be of great importance. Indeed, via computer simulation scientists try to model systems with many degrees of freedom by giving a set of rules of general validity (under some assumptions). Once these rules come from first-principles laws, these simulation have the ambition to model system properties from a fundamental viewpoint. With such a tool, the properties of existing materials can be studied in deep, and new materials and molecules can be conceived, with potentially enormous scientific and technological impact. In this context, the advent of modern supercomputers represents an important resource in view of advancements in this field. In other terms, the physical properties which can be analysed via such methods are tightly connected to the computational power which can be exploited for calculation. A high-performance computing electronic structure program will make the analysis of more complex systems and environments possible, thus opening a path towards new discoveries. It is thus important to provide reliable solutions to benefit from the enhancements of computational power in order to use these tools in more challenging systems.