We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-generalized gradient approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory. Both types of functionals can thus be subsumed as special cases of a novel functional form that is naturally placed on the third rung of Jacob’s ladder. Moreover, the kinetic energy tensor is related to the exchange hole curvature, is gauge invariant, and has very clearcut N-representability conditions. The latter conditions enable the definition of an effective number of non-negligible orbitals. Whereas quantities such as the electron localization function can discriminate effective one-orbital regions from other regions, the present kinetic energy tensor can discriminate between one-, two-, three-, and four-or-more orbital regions.

中文翻译：

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在密度泛函理论中统一动能密度和涡度的局部张量

我们提出了一个动能张量，它统一了通常用于亚广义梯度逼近函数的标量动能密度和顺磁电流密度函数理论中出现的涡旋密度。因此，这两种类型的功能都可以归类为新功能形式的特殊情况，这种特殊形式自然而然地放在了雅各布梯子的第三梯级上。此外，动能张量与交换孔的曲率有关，规格不变，并且具有非常清晰的N-代表性条件。后面的条件可以定义有效数量的不可忽略的轨道。尽管诸如电子定位功能之类的量可以将有效的一个轨道区域与其他区域区分开，但是本动能张量可以在一个，两个，三个和四个或更多个轨道区域之间进行区分。