Relativistic two- and four-component density functional theory with periodic boundary conditions

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Relativistic effects are important for compounds containing heavy elements. The relativistic effects affect the electron density of a molecule in two ways: 1) Through scalar relativistic effects due to the high velocity of core electrons and 2) through sp in-orbit effects arising from the spin- and orbital-magnetic moments of the electrons. As such, the chemistry of heavy-element compounds can be strongly affected by relativistic effects. Many compounds containing heavy elements exists in the solid phase. Solid-state systems are conventionally treated with plane waves, where relativistic effects only can be included through effective core potential. Since relativistic effects affect core electrons, such a treatment can only be approximate, and a rigorous treatment of relativistic effects requires that the core electron are treated explicitly and that the spin-orbit interactions are accounted for. Whereas recent years have seen an impressive development of two- and four-component wave functions for molecu les in the gas phase, no such developments have been reported for the solid state, despite the importance of an accurate treatment of relativistic effects in these systems. The present project aims at rectifying this hiatus by developing a relativistic t wo- and four-component code for calculating energies and molecular properties under periodic boundary conditions (PBC). Building on the recent development of PBC codes based on linear-scaling technology using Gaussian basis functions, we will combine this with recent developments in our group of a two-electron integral program that enforces restricted kinetic and magnetic balance at the integral level. In this manner, a computationally efficient approach can be designed making relativistic calculations us ing Gaussian orbitals under PBC computationally feasible and efficient. The code will be extended to also calculate different molecular properties for which relativistic effects can be expected to be important