An Efficient Implementation of the ESM-RISM Method for Simulating Electrode/Electrolyte Interfaces

We present an efficient implementation of an effective screening medium method combined with a reference interaction site model (ESM-RISM). The ESM-RISM theory is a straightforward extension of the three-dimensional RISM (3D-RISM) theory, which solves the Laue-represented RISM equation to describe atomistic-scale phenomena at the electrified electrode/electrolyte interface. However, the original ESM-RISM approach employed an approximate solution susceptibility, which leads to deviations of the ESM-RISM results from the 3D-RISM level and requires higher computational costs than 3D-RISM. In this study, we analytically addressed these limitations and applied the present implementation to a water molecule in bulk solution and a Pt(111)/HCl aqueous solution interface. The results for a hydrated water molecule show that the current implementation cures the different approximation levels between ESM-RISM and 3D-RISM. In addition, the analytical reformulation enables us to reduce the computational complexity of evaluating the Laue-represented RISM equation from O(N4/3) to O(NlogN). Subsequently, we re-examined the computational flow of ESM-RISM and found that the present scheme reasonably reduces the wall time required to reach convergence in the overall ESM-RISM calculation. The results of the application to the Pt(111)/HCl aqueous solution interface demonstrated that the current implementation enabled us to capture the properties of the electrified interface.