The Staggered Mesh Method: Accurate Exact Exchange Toward the Thermodynamic Limit for Solids,Journal of Chemical Theory and Computation

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The Staggered Mesh Method: Accurate Exact Exchange Toward the Thermodynamic Limit for Solids
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2024-08-30 , DOI: 10.1021/acs.jctc.4c00771
Stephen Jon Quiton ₁ , Hamlin Wu ₁ , Xin Xing ₂ , Lin Lin _{2,

3} , Martin Head-Gordon _{1,

4}

Affiliation

In periodic systems, the Hartree–Fock (HF) exchange energy exhibits the slowest convergence of all HF energy components as the system size approaches the thermodynamic limit. We demonstrate that the recently proposed staggered mesh method for Fock exchange energy [Xing, Li, and Lin, Math. Comp., 2024], which is specifically designed to sidestep certain singularities in exchange energy evaluation, can expedite the finite-size convergence rate for the exact exchange energy across a range of insulators and semiconductors when compared to the regular and truncated Coulomb methods. This remains true even for two computationally cheaper versions of this new method, which we call non-SCF and split-SCF staggered mesh. Additionally, a sequence of numerical tests on simple solids showcases the staggered mesh method’s ability to improve convergence toward the thermodynamic limit for band gaps, bulk moduli, equilibrium lattice dimensions, energies, and phonon force constants.

中文翻译：

交错网格法：向固体热力学极限精确交换

在周期系统中，当系统尺寸接近热力学极限时，Hartree-Fock (HF) 交换能量表现出所有 HF 能量分量中最慢的收敛速度。我们证明了最近提出的用于 Fock 交换能量的交错网格方法 [Xing，Li 和 Lin，Math. Comp., 2024] 专门设计用于回避交换能量评估中的某些奇点，与常规库仑方法和截断库仑方法相比，可以加快一系列绝缘体和半导体上精确交换能量的有限尺寸收敛速度。即使对于这种新方法的两个计算成本较低的版本（我们称之为非 SCF 和分割 SCF 交错网格）来说，情况仍然如此。此外，对简单固体的一系列数值测试展示了交错网格方法能够提高带隙、体积模量、平衡晶格尺寸、能量和声子力常数的热力学极限收敛性。

更新日期：2024-08-30

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