A Computational Environment for Multiscale Modelling

Abstract

We implement two different ab initio electronic structure methods: Hartree-Fock (HF), and quantum variational Monte Carlo (VMC). Gaussian type orbitals are used for the HF method, while the VMC framework allows more general orbital bases (including the possibility of using the optmized HF orbitals). A thorough introduction to the underlying theory of both methods is presented, and the codes are tested on selected first row atoms and simple molecules. Ground state energies are found to be in good agreement with the litterature. Secondly, a general function approximation scheme is implemented using artificial neural networks (ANN). The ANN implementation is based on the TensorFlow library developed by the Google Brain team. It is thoroughly tested on single and multivariable functions and subsequently shown to be able to approximate potential energy surfaces (PES) using data from the aforementioned ab initio calculations. The ANN may then be used as a force field in molecular dynamics (MD) simulations--in place of ordinary parametrized effective MD potentials--thereby successfully bridging the quantum mechanical and the microscopic regimes. Whereas traditional MD potentials require hand crafting and tuning of a parametrized functional form, the present work implements a multiscale modelling approach in which essentially no human intervention is needed. Such "parameter-free" multiscale modelling is preferable for obvious reasons: the results should be fundamentally independent of the human experimenter's ability to guess an appropriate functional form. Lastly: Showcasing the full usage of the computational framework developed, we present a simple--proof of concept--MD simulation using an ANN trained to approximate a PES.