Related Experiment Video
Updated: Jun 25, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
The Finite Coulomb Lattice Sum: A Resolution of Conditional Convergence through Exact Shape and Size
Yang He1,2, Zhonghan Hu1,2
1Key Laboratory of Laser & Infrared System of Ministry of Education, Shandong University, Qingdao 266237, P. R. China.
Abstract:
This work examines conditionally convergent Coulomb lattice sums under periodic boundary conditions. The recently developed finite lattice sum cleanly decomposes the series into three distinct components: a periodic bulk term νpbc, a shape-dependent nonperiodic boundary term νb, and a finite-size correction term νcorr. This rigorous formulation explicitly parametrizes the geometry of a finite lattice by its exact shape and size and takes an effective pairwise form. We analyze it in detail and compare it with various derivations of lattice sums in the literature. Perspectives on future applications are discussed, including analytical developments for arbitrarily shaped crystals and numerical mesh-type algorithms for condensed matter simulations.
Related Concept Videos
Lattice Centering and Coordination Number
Types of Unit Cells
Imagine taking a large number of identical...
Trends in Lattice Energy: Ion Size and Charge
Coulomb's Law
Newton's third law applies to the Coulomb force — the force on...
Lattice Energies of Ionic Crystals
Structures of Solids
Unit Cells

