Quantum Drude Oscillators for Accurate Many-body Intermolecular Forces

One of the important early applications of quantum mechanics was to explain the 1/R^6 potential observed experimentally between two rare gas atoms, often known as the London potential, which is due to electronic dispersion, an effect which arises from correlations in the quantum-uncertainty of the charge distribution. Thus is a purely quantum effect with no analogue in the classical limit. The dominant term 1/R^6 is due to dipole-dipole interactions, but at closer ranges there are terms involving higher multipole moments, as well as correlations between 3 or more atoms, e.g. the Axelrod-Teller-Muto potential due to triple-dipole interactions. Although these interactions are weaker than those due to permanent (or averaged) charge distributions, and covalent or metal bonding, they are too big to ignore in many condensed matter systems. Because this detail is missing, potentials fitted to bulk behaviour do not reproduce correct behaviour in the gas-phase, or at interfaces (even for strongly polar water), or in the gas-phase. Understanding the self-assembly of the biological nanostructures, requires detailed knowledge of hydrophobic attractions (due to electronic dispersion), as well as the behaviour of water against surfaces and other objects that disrupt the hydrogen bonding network. Due to its many-body character, electronic dispersion is awkward to implement, as the terms become exponentially complicated and expensive to compute: methods exist for Density Functional Theory to treat it, but they do not scale at well for large systems (N^6). The Quantum Drude Oscillator is a simple model of a polarisable charge distribution. Together with Path Integral Molecular Dynamics (PIMD), it can be used to treat both many-body polarisation and dispersion in a unified way. Because it uses more fundamental physics, it can be expected to produce more general models. This in turn aids model-building, as models fit in the gas phase can be expected to reproduce much more of the bulk behaviour. We have an example of this in our model of Xenon, where dispersion dominates, and will outline a planned model of water. The computational cost of PIMD to treat QDO's scales like P classical simulations in parallel, at Nlog(N), where P is the length in 'beads' of the discretised path. This means that PIMD can be used to simulate systems as arbitrarily large as those for classical MD, provided that P can be kept reasonably small, and that is the main challenge of our work.