Ewald summation for ferroelectric perovskites with charges and dipoles

Abstract

Ewald summation is an important technique used to deal with long-range Coulomb interaction. While it is widely used in simulations of molecules and solid state materials, many important results are dispersed in literature and their implementations are often buried deep in large software packages. Since reliable and systematic calculation of Coulomb interaction is critical for the investigation of perovskites, here we start from the fundamentals of Ewald summation and derive clear expressions for long-range charge-charge, dipole-dipole, and charge-dipole interactions, which can be readily used for numerical computations. We also provide the interaction matrix for efficient Monte Carlo simulations involving charges and dipoles, implementing them in a Python software package. A new type of interaction matrix, which accounts for the electrostatic energy change when ions are displaced, is also derived and implemented. These results are the foundations for the investigation of ferroelectric perovskites.

Python program: https://gitlab.com/dwang5/PyEwald Documentation: https://dwang5.github.io/PyEwaldDoc/

References in corpus (6)

• First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3
• Finite-Temperature Properties of Ba(Zr,Ti)O${}_3$ Relaxors From First Principles
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• Dipole Ordering of Water Molecules in Cordierite: Monte Carlo Simulations
• Understanding the morphotropic phase boundary of perovskite solid solutions as a frustrated state
• Bose one-component plasma in 2D: a Monte Carlo study
• Anticlinic order of long-range repulsive rod-like magnetic particles in 2D