Bridging a calculation gap extracts exact molecular bridge functions

To investigate the statistical physics of liquids, researchers must typically run time-consuming numerical simulations to derive a pair distribution function (PDF), which is related to the probability of finding two atoms a given distance from each other. This technique suffers from the limitations of simulation data that are only available at short distances.

The alternative, integral equation-based approach often involves solving the Ornstein-Zernike equation based on some closure relation, an approximation for a set of integrals known as the bridge function. However, the integral equation approach can provide powerful results only if the bridge function assumed is sufficiently accurate. In liquid water, the bridge function has remained unknown, and previous approximation attempts have fallen short.

In The Journal of Chemical Physics, Luc Belloni, from CEA in France, extracted the exact bridge function of the extended simple point-charge model of liquid water at room temperature. He first performed Monte Carlo simulations, using boxes containing 512 molecules to accumulate PDF data. The angular dependence of the strongly anisotropic correlations was described in terms of projections onto generalized spherical harmonics to simplify the analysis. He then combined these simulation data available at short distances with the hypernetted chain closure, which assumes that the bridge function is zero for all distances and is therefore valid for long distances. To derive the direct correlation function and bridge function projections, he then solved and inverted the resulting hybrid closure to the molecular equation.

According to Belloni, the general formalism and numerical procedure from this study can be applied to many different related systems, such as other liquids, solutions and electrolytes. With colleagues, he has applied the knowledge of the exact direct correlation function to calculate the free energy of various solutes in water.

Source: “Exact molecular direct, cavity, and bridge functions in water system,” by Luc Belloni, Journal of Chemical Physics (2017). The article can be accessed at https://doi.org/10.1063/1.5001684 .