Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
J Chem Phys. 2012 Feb 14;136(6):064116. doi: 10.1063/1.3684261.
The common way to obtain energies from Kohn-Sham exchange potentials is by using the Levy-Perdew virial relation. For potentials that are not functional derivatives (i.e., nearly all model exchange potentials in existence), this approach leads to energy expressions that lack translational and rotational invariance. We propose a method for constructing potential-based energy functionals that are free from these artifacts. It relies on the same line-integration technique that gives rise to the Levy-Perdew relation, but uses density scaling instead of coordinate scaling. The method is applicable to any exchange or correlation potential that depends on the density explicitly, and correctly recovers the parent energy functional from a functional derivative. To illustrate our approach we develop a properly invariant generalized gradient approximation for exchange starting from the model potential of van Leeuwen and Baerends.
从 Kohn-Sham 交换势中获取能量的常用方法是使用 Levy-Perdew 维里关系。对于不是泛函导数的势（即，几乎所有现有的模型交换势），这种方法导致缺乏平移和旋转不变性的能量表达式。我们提出了一种构造无这些伪影的基于势的能量泛函的方法。它依赖于产生 Levy-Perdew 关系的相同线积分技术，但使用密度缩放而不是坐标缩放。该方法适用于任何显式依赖于密度的交换或相关势，并且可以从泛函导数正确恢复母体能量泛函。为了说明我们的方法，我们从 van Leeuwen 和 Baerends 的模型势出发，开发了一个适用于交换的正确不变广义梯度近似。
