# Pressure Profile Calculation with Mesh Ewald Methods

## TL;DR

This paper introduces an efficient mesh Ewald method for calculating local pressure profiles in charged systems, maintaining N log N scaling, and applies it to water/vapor interfaces to compare pressure distributions.

## Contribution

It presents a novel mesh Ewald approach for pressure profile calculation that is faster and more scalable than previous methods.

## Key findings

- The new method retains N log N scaling for large systems.
- Pressure profiles across water/vapor interfaces are accurately computed.
- Stress distributions from different methods are consistent within 0.05 nm.

## Abstract

The importance of calculating pressure profiles across liquid interfaces is increasingly gaining recognition, and efficient methods for the calculation of long-range contributions are fundamental in addressing systems with a large number of charges. Here, we show how to compute the local pressure contribution for mesh-based Ewald methods, retaining the typical N log N scaling as a function of the lattice nodes N. This is a considerable improvement on existing methods, which include approximating the electrostatic contribution using a large cut-off and the, much slower, Ewald calculation. As an application, we calculate the contribution to the pressure profile across the water/vapour interface, coming from different molecular layers, both including and removing the effect of thermal capillary waves. We compare the total pressure profile with the one obtained using the cutoff approximation for the calculation of the stresses, showing that the stress distribution obtained by the Harasima and Irving-Kirkwood are quite similar and shifted with respect to each other at most 0.05~nm.