Deriving approximate functionals with asymptotics
Deriving approximate functionals with asymptotics
复制标题
用渐近函数推导近似泛函
DOI：
10.1039/d0fd00057d
复制
发表时间：
2020
影响因子：
3.4
通讯作者：
Burke, Kieron
中科院分区：
文献类型：
--
作者：
Burke, Kieron
现代密度泛函近似在许多电子结构计算中以较低的计算成本达到中等精度。给出了密度泛函理论的梯度展开与一维WKB展开的一些背景，以及渐近展开的现代方法。一个分析能量和渐近行为的数学框架将DFT梯度展开的修正和的超渐近性结合起来。给出了一维无轨道DFT模型问题的简单实例。在某些情况下，误差可以小到10−32，哈特里认为，如果这些新成分可以应用，它们可能会产生比目前使用的近似函数精确得多的近似函数。欧拉-麦克劳林公式的一个变体推广了以前的结果。
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB expansion in one dimension, and modern approaches to asymptotic expansions. A mathematical framework for analyzing asymptotic behavior for the sums of energies unites both corrections to the gradient expansion of DFT and hyperasymptotics of sums. Simple examples are given for the model problem of orbital-free DFT in one dimension. In some cases, errors can be made as small as 10−32 Hartree suggesting that, if these new ingredients can be applied, they might produce approximate functionals that are much more accurate than those in current use. A variation of the Euler–Maclaurin formula generalizes previous results.