Ewald summation and physically equivalent methods such as particle-mesh Ewald, kubic-harmonic expansions, or Lekner sums are commonly used to calculate long-range electrostatic interactions in computer simulations of polar and charged substances. The calculation of pressures in such systems is investigated. We find that the virial and thermodynamic pressures differ because of the explicit volume dependence of the effective, resummed Ewald potential. The thermodynamic pressure, obtained from the volume derivative of the Helmholtz free energy, can be expressed easily for both ionic and rigid molecular systems. For a system of rigid molecules, the electrostatic energy and the forces at the atom positions are required, both of which are readily available in molecular dynamics codes. We then calculate the virial and thermodynamic pressures for the extended simple point charge (SPC/E) water model at standard conditions. We find that the thermodynamic pressure exhibits considerably less system size dependence than the virial pressure. From an analysis of the cross correlation between the virial and thermodynamic pressure, we conclude that the thermodynamic pressure should be used to drive volume fluctuations in constant-pressure simulations.
Fast Ewald Summation with Prolates for Charged Systems in the NPT Ensemble
Center for Computational Mathematics, Flatiron Institute（西蒙斯基金会平顿研究所计算数学中心）；School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）
Fast and Scalable GPU-Accelerated Quantum Chemistry for Periodic Systems with Gaussian Orbitals: Implementation and Hybrid Density Functional Theory Calculations
Long-range electrostatics for machine learning interatomic potentials is easier than we thought
Department of Chemistry, UC Berkeley, California 94720, United States（加州大学伯克利分校化学系）；Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, 94720, United States（伯克利国家实验室化学科学部）；Bakar Institute of Digital Materials for the Planet, UC Berkeley, California 94720, United States（为地球数字化材料研究所）；The Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria（奥地利科学与技术研究所）
