Abstract

Modern electronic structure theory usually employs atom-centered basis functions in order to evaluate the required integrals and to find approximations to the electronic wave function. Whilst from a chemist’s point of view this intuitively makes sense, one should also keep in mind that this gives rise to an implicit bias regarding the positions of the electrons.

An alternative approach is to use finite elements as basis functions instead. Finite elements are piecewise polynomial functions, which are used to discretise partial differential equations on a grid. Such a grid can be adaptively refined according to the a posteriori error, which allows an automatic on-the-fly optimisation of the discretisation to fit the electronic structure of a molecule best.

This talk will discuss how the aforementioned properties are exploited in our and previous work in order to solve the Hartree-Fock equations. In particular the computational scaling due to the local nature fo the finite elements will be analysed and the difficulties which might arise when employing finite elements in the context of electronic structure theory will be detailed.