# Creating a Coarse-Grain Interaction Potential from All-Atom Simulation Data

## Description

The aim of the task was to use radial distribution functions (RDF) derived from classical molecular dynamics simulations to generate a coarse-grain interaction potential and compare it to an all-atom potential. Coarse grained models offer efficient ways to simulate systems whose properties lie at the mesoscale, which therefore cannot be represented by full atomistic models or continuum theory. The potential is applied to the molecular dynamics simulations of the coarse grained representation of molecules so as to see how successful the potential is in capturing the underlying physics. The species which have been taken into account were the ethanol (ETH) and trifluoroethanol (TFE) species.

## Files

## Steps to reproduce

we will be using one method that is commonly used for fitting the intermolecular interactions between molecules, determining the potential of mean force, A(r), from the radial distribution function, g(r). These two quantities are related by the following simple expression: A(r) = -kBT ln (g(r)) + C where kB is the Boltzmann constant, T is the system temperature, and C is a constant as a result of integration. The potential derived in the first instance will not reproduce the physics of the reference system so there is an iterative process through which to improve the description of the reference system. This iterative Boltzmann inversion method is summarized by the following equation for a single state: Vi+1(r) = Vi(r) – αkBT ln(gi(r)/gt(r)) where Vi(r) is the interaction potential after step i, α is a scaling factor to prevent large fluctuations in the updated potential, kB the Boltzmann constant, T the temperature, gi(r) the trial RDF, gt(r) the target RDF. This method will typically yield a potential that matches the target RDF well; however, the derived potentials tend to be state dependent and non-unique. The resulting potentials derived via this method may not capture the underlying potential, and therefore may lead to significant artifacts when considering other state points not included in the original optimization. Multi-state iterative Boltzmann inversion methods have been developed in order to overcome this limitation. In these methods, a single potential is updated to match structural data over N number of states by using the following: Vi+1(r) = Vi(r) – (1/N) Σ {αs(r)kBTs ln(gsi(r)/gst(r))} where the sum is taken over all states, and the “s” script denotes the property at state s. The scaling factor αs(r) is now a weighting factor for state s, allowing more or less emphasis to be put on this state in the potential update. The parameter αs(r) is set to be a linear function of r such that the potential smoothly approaches zero at the cutoff.