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Parametrisation of electronic energies via reduced density matrices using machine learning techniques

The electronic energy of a system is expressible via a relatively simple contraction of the electronic hamiltonian with the 1- and 2-particle reduced density matrices of the ground state electronic wavefunction. These density matrices can be calculated to high accuracy using quantum chemical methods such as the FCIQMC technique, for individual configurations of nuclei. In this project we will investigate if these density matrices are amenable to interpolation using machine learning techniques, so that accurate energies (and other properties) can be computed at geometries not contained in the training data-set via the density matrices. Such a methodology would provide a radically new method to parameterise potential energy surfaces in chemically difficult situations involving bond breaking and open-shell systems.