原子动能密度的大$Z$标度的可视化
Visualizing the large-$Z$ scaling of the kinetic energy density of atoms
摘要：
将中性原子标度到大的$Z$，结合周期性和逐渐趋于均匀性，是密度泛函理论的基本探索，它推动了对动力学和交换相关能的理解的最新进展。虽然研究的重点通常是能量的缩放，但也可以从能量密度中获得见解。我们可视化的标度的正定动能密度（KED）在闭壳层原子，在比较不变的数量的基础上的梯度和拉普拉斯的密度。我们注意到一个惊人的适合的KED的核心内的任何原子的梯度扩展使用的梯度和拉普拉斯算子，出现作为一个渐近极限周围的KED振荡。的梯度膨胀是定性不同的从第一原理的缓慢变化的电子气和相关的非零泡利贡献的KED附近的核。我们提出并探索轨道自由元GGA模型的动能来描述这些功能，取得了一定的成功，但量子振荡的影响，在原子的内壳层，使一个完整的参数化困难。我们讨论了改进的无轨道描述的分子性质的影响。
英文摘要：
The scaling of neutral atoms to large $Z$, combining periodicity with a gradual trend to homogeneity, is a fundamental probe of density functional theory, one that has driven recent advances in understanding both the kinetic and exchange-correlation energies. Although research focus is normally upon the scaling of energies, insights can also be gained from energy densities. We visualize the scaling of the positive-definite kinetic energy density (KED) in closed-shell atoms, in comparison to invariant quantities based upon the gradient and Laplacian of the density. We notice a striking fit of the KED within the core of any atom to a gradient expansion using both the gradient and the Laplacian, appearing as an asymptotic limit around which the KED oscillates. The gradient expansion is qualitatively different from that derived from first principles for a slowly-varying electron gas and is correlated with a nonzero Pauli contribution to the KED near the nucleus. We propose and explore orbital-free meta-GGA models for the kinetic energy to describe these features, with some success, but the effects of quantum oscillations in the inner shells of atoms makes a complete parametrization difficult. We discuss implications for improved orbital-free description of molecular properties.
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