Department of Chemistry , The University of Western Ontario , London , Ontario N6A 5B7 , Canada.
J Chem Theory Comput. 2018 Aug 14;14(8):4246-4253. doi: 10.1021/acs.jctc.8b00490. Epub 2018 Jul 23.
The Fermi potential, v(r), is the nonclassical part of the multiplicative effective potential appearing in the one-particle Schrödinger-type equation for the square root of the electron density. The usual way of constructing v(r) by inverting that equation produces unsatisfactory results when applied to electron densities expanded in Gaussian basis sets. We suggest a different method that is based on an explicit formula for v(r) in terms of the interacting one- and two-electron reduced density matrices of the system. This method is exact in the basis-set limit and yields accurate approximations to the basis-set-limit v(r) when applied to reduced density matrices represented in terms of finite basis sets. Illustrative applications involve atomic and molecular wave functions generated at various levels of ab initio theory. It is also shown how to construct the Pauli and exchange-correlation potentials of any system starting with only v(r).
费米势 v(r) 是非经典的部分，出现在电子密度的平方根的单粒子薛定谔型方程中的乘幂有效势中。通常通过反转该方程来构建 v(r) 的方法，当应用于在高斯基组上展开的电子密度时，会产生不理想的结果。我们建议一种不同的方法，该方法基于 v(r) 的显式公式，该公式涉及系统的相互作用的单电子和双电子约化密度矩阵。该方法在基组极限中是精确的，并且当应用于用有限基组表示的约化密度矩阵时，会得到基组极限 v(r) 的精确近似。说明性应用涉及在各种从头算理论水平上生成的原子和分子波函数。还展示了如何仅从 v(r) 开始构建任何系统的泡利和交换相关势。
