Development and implementation of reduced density matrix functionals for relativistic quantum chemistry.

Computational chemistry (CC) methods supply approximate solutions to the Schrödinger equation (SE) and make it possible to compute a wide range of chemical properties.

A problem is, however, that the work horse method in CC, Kohn-Sham Density Functional Theory, cannot always describe the process of chemical bonds breaking or formation accurately (the errors produced in H2 dissociation are a simple example). Wave function-based methods are more reliable but their computational cost is prohibitive for large systems.

Recent advances in reduced density matrix functional theory (RDMFT) have demonstrated the potential of this methodology to treat such non-dynamic electron correlation effects (near degeneracies occurring in bond dissociation) at reasonable computational cost.In this project I aim to explore RDMFT in an area in which a proper treatment of non-dynamic electron correlation effects is essential: the chemistry of heavy elements.

For compounds of such elements, near-degeneracies of electronic energies is the rule rather than the exception, and RDFMT emerges as an excellent alternative in relativistic CC to wave function based and DFT methods .

An important complication is the importance of relativistic effects requiring the use of the Dirac equation (DE) instead of the SE.

In this project, I will work on transferring RDMFT to this domain by taking the following steps: a) set up the required theoretical background, b) analyze the performance of the currently available RDMFT approximations (for two-component Hamiltonians), c) develop a RDMFT approximation for the DE (four-component Hamiltonian), and d) make this methodology available to the scientific community by implementing it in the DIRAC code.

I expect that RDMFT will predict energies accurately for the DE, and it can become a powerful method to predict properties of novel materials formed by heavy elements.