论文标题
得出渐近学的近似功能
Deriving approximate functionals with asymptotics
论文作者
论文摘要
现代密度功能近似在许多电子结构计算中以低计算成本达到中等精度。给出了一些背景，将密度功能理论的梯度扩展与WKB扩展在一个维度上以及渐近扩展的现代方法。用于分析能量之和分析渐近行为的数学框架将同时校正与DFT的梯度扩展和总和的渐近膨胀。给出了一个简单的示例，以在一个维度中为无轨道DFT的模型问题提供。在某些情况下，错误可以使错误至10 $^{ - 32} $ HARTREE建议，如果可以应用这些新成分，它们可能会产生近似功能，这些功能比当前使用的功能要准确得多。 Euler-Maclaurin公式的变化概括了先前的结果。
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.
