(168c) Obtaining the Contribution of Individual Atoms to the Energy and Stress Tensor From the Ewald and P3M Lattice Sum Methods

In molecular simulations, Coulombic interactions are frequently treated using a lattice sum because the interactions decay very slowly and simple truncation can lead to artifacts. Traditional lattice sum methods such as Ewald and particle-particle particle-mesh (P3M) give total (volume-averaged) energy and virial stress, as well as particle forces, but unfortunately the contribution of individual atoms to the energy and stress tensor are not typically computed. Per-atom energy and stress contributions are useful in the calculation of transport properties such as thermal conductivity using the Green-Kubo method, as well as predicting local properties of inhomogeneous systems such as local surface tension. Per-atom properties also allow one to predict chemical potential using the recently developed chemical potential perturbation (CPP) method [1].  In this presentation, methods for obtaining per-atom energy and stress contributions are shown for both the Ewald and P3M lattice sum methods. The proposed methods are implemented in the LAMMPS Ewald and P3M codes and are tested by calculating the thermal conductivity of several different water models. We demonstrate that a complete accounting of electrostatic contributions to the heat flux vector can resolve previously reported conflicting values of thermal conductivity for equilibrium and non-equilibrium simulations. Chemical potential results using the CPP method are also given for extended simple point-charge water (SPC/E), and these results show a high level of agreement with an SPC/E equation of state [2].

References:

[1]  S. G. Moore and D. R. Wheeler, J. Chem. Phys. 134, 114514 (2011)

[2]  S. G. Moore and D. R. Wheeler, J. Chem. Phys. 136, 164503 (2012)