热力学极限和广义梯度近似中自由电子气体的狄拉克交换能的下阶修正

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Thiago Carvalho Corso, Gero Friesecke
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引用次数: 0

摘要

我们推导出在热力学极限下,自由电子气体在零边界条件盒中的狄拉克交换能的次阶修正。修正量与盒子的表面积相当,来自三个不同的贡献:(i) 实际空间边界层,(ii) 边界条件引起的费米动量和体积密度的微小移动,以及 (iii) 长程静电有限尺寸修正。此外,我们还证明了局部密度近似除了能准确捕捉体量项之外,还能产生正确阶次的修正,但修正的大小并不正确。只要梯度增强因子满足一个简单的显式积分约束,广义梯度近似(GGA)修正就能准确捕捉表面项。对于目前的 GGA,如 B88 和 Perdew,Burke 和 Ernzerhof,我们发现新的约束条件无法满足,表面修正的大小被高估了约百分之十。因此,新约束条件可能对未来交换函数的设计有意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations
We derive the next order correction to the Dirac exchange energy for the free electron gas in a box with zero boundary conditions in the thermodynamic limit. The correction is of the order of the surface area of the box, and comes from three different contributions: (i) a real-space boundary layer, (ii) a boundary-condition-induced small shift of Fermi momentum and bulk density, and (iii) a long-range electrostatic finite-size correction. Moreover we show that the local density approximation, in addition to capturing the bulk term exactly, also produces a correction of the correct order but not the correct size. Generalized gradient approximation (GGA) corrections are found to be capable of capturing the surface term exactly, provided the gradient enhancement factor satisfies a simple explicit integral constraint. For current GGAs such as B88 and Perdew, Burke and Ernzerhof we find that the new constraint is not satisfied and the size of the surface correction is overestimated by about ten percent. The new constraint might thus be of interest for the design of future exchange functionals.
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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