Quantum drude oscillators for accurate many-body intermolecular forces

Abstract

One of the important early applications of Quantum Mechanics was to explain the Van-der-Waal’s 1/R6 potential that is observed experimentally between two neutral species, such as noble gas atoms, in terms of correlated uncertainty between interacting dipoles, an effect that does not occur in the classical limit [London-Eisenschitz,1930]. When many-body correlations and higher-multipole interactions are taken into account they yield additional many-body and higher-multipole dispersion terms. Dispersion energies are closely related to electrostatic interactions and polarisation [Hirschfelder-Curtiss-Bird,1954]. Hydrogen bonding, the dominant force in water, is an example of an electrostatic effect, which is also strongly modified by polarisation effects. The behaviour of ions is also strongly influenced by polarisation. Where hydrogen bonding is disrupted, dispersion tends to act as a more constant cohesive force. It is the only attractive force that exists between hydrophobes, for example. Thus all three are important for understanding the detailed behaviour of water, and effects that happen in water, such as the solvation of ions, hydrophobic de-wetting, and thus biological nano-structures. Current molecular simulation methods rarely go beyond pair-wise potentials, and so lose the rich detail of many-body polarisation and dispersion that would permit a force field to be transferable between different environments. Empirical force-fields fitted in the gas phase, which is dominated by two-body interactions, generally do not perform well in the condensed (many-body) phases. The leading omitted dispersion term is the Axilrod-Teller-Muto 3-body potential, which does not feature in standard biophysical force-fields. Polarization is also usually ommitted, but it is sometimes included in next-generation force-fields following seminal work by Cochran [1971]. In practice, many-body forces are approximated using two-body potentials fitted to reflect bulk behaviour, but these are not transferable because they do not reproduce detailed behaviour well, resulting in spurious results near inhomogeneities, such as solvated hydrophobes and ions, surfaces and interfaces. The Quantum Drude Oscillator model (QDO) unifies many-body, multipole polarisation and dispersion, intrinsically treating them on an equal footing, potentially leading to simpler, more accurate, and more transferable force fields when it is applied in molecular simulations. The Drude Oscillator is simply a model atom wherein a single pseudoelectron is bound harmonically to a single pseudonucleus, that interacts via damped coulomb interactions [Drude,1900]. Path Integral [Feynman-Hibbs,1965] Molecular Dynamics (PIMD) can, in principle, provide an exact treatment for moving molecules at finite temperature on the Born- Oppenheimer surface due to their pseudo-electrons. PIMD can be applied to large systems, as it scales like N log(N), with multiplicative prefactor P that can be effectively parallelized away on modern supercomputers. There are other ways to treat dispersion, but all are computationally intensive and cannot be applied to large systems. These include, for example, Density Functional Theory provides an existence proof that a functional exists to include dispersion, but we dont know the functional. We outline the existing methods, and then present new density matrices to improve the discretisation of the path integral. Diffusion Monte Carlo (DMC), first proposed by Fermi, allows the fast computation of high-accuracy energies for static nuclear configurations, making it a useful method for model development, such as fitting repulsion potentials, but there is no straightforward way to generate forces. We derived new methods and trial wavefunctions for DMC, allowing the computation of energies for much larger systems to high accuracy. A Quantum Drude model of Xenon, fit in the gas-phase, was simulated in the condensed-phase using both DMC and PIMD. The new DMC methods allowed for calculation of the bulk modulus and lattice constant of FCC-solid Xenon. Both were in excellent agreement with experiment even though this model was fitted in the gasphase, demonstrating the power of Quantum Drudes to build transferable models by capturing many-body effects. We also used the Xenon model to test the new PIMD methods. Finally, we present the outline of a new QDO model of water, including QDO parameters fitted to the polarisabilities and dispersion coefficients of water.