Using Derivative Information from Molecular Simulations to Enhance Predictions of Structural Properties across State Conditions

Accurately determining shifts in structural properties is crucial for predicting phase and self-assembly behavior in molecular fluids. In the case of water, for example, such transitions provide a basis for defining regions of anomalous thermodynamic and dynamic properties. Thermodynamic extrapolation has previously been shown to provide information about arbitrary structural observables at temperatures (or relative chemical potentials in open-system mixtures) different from those at which simulations were performed. This relies on the use of derivative information that is readily available from molecular simulations, though infrequently utilized. We present a detailed analysis of the uncertainty associated with derivatives of structural properties with respect to temperature and density for both an analytically solvable ideal gas model, as well as rigid water. We present formulae for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water’s structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We demonstrate conditions under which extrapolation methods are applicable, clearly explaining performance through connections to re-weighting techniques associated with free energy calculations. Through such considerations, we propose a recursive algorithm implementing polynomial interpolation to efficiently predict variation in structural properties with state conditions, as well as a simple visual self-consistency check to facilitate its use.