Lehtola Susi, Marques Miguel A L
Department of Chemistry, University of Helsinki, P.O. Box 55 (A.I. Virtasen aukio 1), FI-00014 University of Helsinki, Finland.
Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle, Saale, Germany.
J Chem Theory Comput. 2021 Feb 9;17(2):943-948. doi: 10.1021/acs.jctc.0c01147. Epub 2021 Jan 27.
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 , 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 geometric average () = ()() of the local spin density () and the spin density () of a HEG that has the local kinetic energy density τ() of the inhomogeneous system. 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 [ 2001, 577, 1]. The first functional of this ladder, the local τ approximation (LTA) of Ernzerhof and Scuseria [ 1999, 111, 911] that corresponds to = 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 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 ( = 1/4) of Eich and Hellgren [ 2014, 141, 224107]. We choose = 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 = 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.
均匀电子气（HEG）是构建密度泛函理论中大多数交换关联泛函的关键要素。通常，HEG的能量被参数化为其自旋密度的函数，从而产生了非均匀系统的局域密度近似（LDA）。然而，HEG的电子密度与动能密度之间的联系可用于推广LDA，方法是在具有非均匀系统局域动能密度τ( )的HEG的局域自旋密度( )和自旋密度( )的几何平均值( ) = ( )( )上进行评估。这导致了一类新的泛函，我们称之为元局域密度近似（meta-LDAs），它们对于HEG仍然是精确的，仅从HEG的性质导出，并且构成了密度泛函的雅各布阶梯的新一级[2001, 577, 1]。不幸的是，该阶梯的第一个泛函，即Ernzerhof和Scuseria [1999, 111, 911]的局域τ近似（LTA），对应于 = 1，由于会导致发散的势，其稳定性不足以用于自洽场计算，正如我们在这项工作中所展示的。然而，对LDA和LTA密度进行较小值的几何平均，不仅会导致所得泛函的数值稳定性，而且在原子计算中产生的交换能比LDA、LTA或Eich和Hellgren [2014, 141, 224107]的tLDA泛函（ = 1/4）更准确。我们选择 = 0.50，因为它在氩原子的仅自洽交换计算中给出了最佳总能量。原子化能基准证实， = 0.50的选择在与分子中的相关泛函结合时也能产生更好的能量学结果，几乎消除了LDA众所周知的过度束缚，并将其误差降低了三分之二。
