论文标题
元本地密度功能：雅各布梯子上的新梯级
Meta-local density functionals: a new rung on Jacob's ladder
论文作者
论文摘要
同质电子气（HEG）是构建大多数密度功能理论的交换相关功能的关键要素。通常，HEG的能量是其自旋密度$ n $的函数的参数化，从而导致对不均匀系统的局部密度近似（LDA）。但是，可以使用HEG的电子密度和动能密度之间的连接来概括LDA，通过以局部旋转密度的加权几何平均值以及具有不均匀系统的局部动能密度的局部动能密度进行评估，并具有混合率$ x $ $ x $。这导致了一个新的功能家族，我们将其称为元位本位密度近似（元LDAS），这对于仅从HEG的性质中得出的HEG仍然是精确的，并且形成了雅各布密度函数的新梯级。不幸的是，该梯子的第一个功能，即Ernzerhof和Scuseria的本地$τ$近似（LTA），不幸的是，对应于$ x = 1 $，不足以稳定，无法用于自一致的现场计算中，因为它会在这项工作中表现出不同的潜力。但是，$ x $值较小的LDA和LTA密度的几何平均，不仅会导致所得功能的数值稳定性，而且在原子计算中比LDA，LTA或TLDA函数（$ x = 1/4 $ eich and eich and eich and grangren and eich and grangren）产生了原子计算中更准确的交换能量。我们选择$ x = 0.50 $，因为它为氩原子提供了最佳的总能量总计计算。雾化能基准确认，选择$ x = 0.50 $与分子中的相关功能相结合，可以提高能量，几乎消除了LDA的众所周知的过度结合，并将其误差减少了三分之二。
The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density $n$, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a weighted geometric average of the local spin density and the spin density of a HEG that has the local kinetic energy density of the inhomogeneous system, with a mixing ratio $x$. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG, and which form a new rung of Jacob's ladder of density functionals. The first functional of this ladder, the local $τ$ approximation (LTA) of Ernzerhof and Scuseria that corresponds to $x=1$ is unfortunately not stable enough to be used in self-consistent field calculations, because it leads to divergent potentials as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of $x$ not only leads to numerical stability of the resulting functional, but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional ($x=1/4$) of Eich and Hellgren. We choose $x=0.50$ as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice $x=0.50$ also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.
