Applications of Multiwavelets to Energies and Properties

Abstract

The goal of quantum chemistry is to provide fast and accurate algorithms for the computation of molecular energies and properties. Over the years, a large number of methods have become available, and today computational chemists have a very rich toolbox of protocols that can be used to gain insight to chemistry. Gaussian type orbital (GTO) basis sets are at the core of most modern algorithms, and they have served the community well since they were first introduced. However, during the last 20 years, Multiwavelets (MWs) have emerged as a promising alternative to traditional GTO basis sets. Multiwavelets are built up from polynomial functions, and systematically approach completeness due to their robust mathematical foundation in multiresolution analysis.The in-house MW code MRChem has reached a level of maturity where it can be used to study chemical systems of 1000s of electrons. It provides functionality for the calculation of SCF energies, as well as electric and magnetic properties via density functional pertubation theory. This thesis presents the application of MWs in benchmark studies of static electric dipole polarizabilities (Paper I) and transition metal-ligand interaction energies (Paper II). Here we provide highly precise numerical results practically at the complete basis set limit, and with this reference we are able to quantify basis set incompleteness errors (BSIEs) in large GTO basis sets without ambiguity. The thesis also presents a prototype implementation of scalar relativistic effects via the zeroth order regular approximation into MRChem (Paper III, in preparation), and a preliminary quantification of BSIEs in several all-electron GTO basis sets for elements in the fifth row of the periodic table.