From Benchmarking to Periodic Fock Exchange in the Auxiliary Density Matrix Method via k-Point Sampling with Gaussian Basis Sets

Abstract

While Gaussian basis sets have been successfully used in various electronic structure codes for elucidation of structures and processes in computational chemistry, they are not nearly as popular in solid state physics. There are various reasons for this, one of them being that in comparison to the plane wave approach there is no single numerical parameter like the cutoff energy, which can be used to systematically increase the accuracy of the calculation. Furthermore do basis sets depend either on a specific method, or can only be used together with matching pseudopotentials in the case of valence basis sets. Finally, in contrast to a molecular setting are electrons in periodic systems often not localised and therefore many optimisations used with atom-centred Gaussian basis sets do not work as efficiently. The number of codes targeting the intersection of computational chemistry and solid efficiently state physics is therefore small, as is the availability of universally applicable basis set families. In this thesis we are evaluating the recently revised MOLOPT basis set with pseudopotentials and all-electron calculations in both molecular and condensed matter settings, for three different functionals in Density Functional Theory, each on a different rung on “Jacob’s Ladder”. Once again, we demonstrate the outstanding performance of the MOLOPT basis sets for molecular systems and show that Gaussian-type Orbital codes perform reasonably well for solids, and that this can also be achieved with a universal basis set family. We further investigate the required framework for running and analysing such large benchmark calculations to pave the way for fully automated benchmarking and iterative development of Gaussian basis sets and pseudopotentials. The implementation of the of the actual benchmarks with three different approaches leads to the development of Python-based parser and input generation libraries and utilities for CP2K, as well as contributions and extensions to the Automated Interactive Infrastructure and Database (AiiDA). To extend the support for periodic systems further within CP2K, we then progress to implement k-point sampling in CP2K’s Hartree-Fock Exchange, required to run calculations with Hybrid functionals. And to be able to make this usable on realistic systems, we extend the Auxiliary Density Matrix Method to k-point sampling as well. Together, this novel implementation can be used as a reference implementation and stepping stone for the development of more efficient algorithms for the Hartree-Fock approximation and Hybrid functionals in Density Functional Theory with CP2K.