AI 中文总结
该研究提出适用于任意晶体几何的马德隆常数计算的闭式解析边界项，开发了三斜晶格马德隆常数的稳健直和方法，通过布拉维晶格计算验证了方法有效性。
AI 中文摘要
直和法计算马德隆常数因晶格和的条件收敛而变得复杂，这会产生与形状相关的边界项。本研究首次提出适用于任意晶体几何的该边界项的闭式解析表达式。对于一般三斜晶格，该边界项精确映射到一组均匀带电平行四边形产生的静电势。此外，我们证明特征尺寸为p的晶体的有限尺寸修正项残差按(2p+1)⁻²衰减。基于这些结果，我们开发了一种稳健的直和方法，用于精确计算任意三斜晶格的马德隆常数，并通过对代表性布拉维晶格的显式计算验证了其有效性。
英文摘要
The direct-sum evaluation of Madelung constants is complicated by the conditional convergence of lattice sums, which gives rise to a shape-dependent boundary term. In this work, we present, for the first time, a closed-form analytic expression for this boundary term that is valid for arbitrary crystal geometries. For general triclinic lattices, this boundary term maps exactly onto the electrostatic potential generated by a set of uniformly charged parallelograms. In addition, we demonstrate that the residual finite-size correction for a crystal of characteristic size $p$ decays as $(2p+1)^{-2}$. Building on these results, we develop a robust direct-sum method for the accurate computation of Madelung constants in arbitrary triclinic lattices and validate its effectiveness through explicit calculations on representative Bravais lattices.
Comments11 pages, 4 tables, 3 figures
Journal refJournal of Chemical Theory and Computation, 2026
