Semilocal density functional obeying a strongly tightened bound for exchange
Semilocal density functional obeying a strongly tightened bound for exchange
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DOI：
10.1073/pnas.1423145112
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发表时间：
2015-01
期刊：
影响因子：
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通讯作者：
Jianwei Sun;J. Perdew;A. Ruzsinszky
中科院分区：
文献类型：
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作者：
Jianwei Sun;J. Perdew;A. Ruzsinszky
在计算机上有效地计算原子、分子和固体的性质需要交换相关能的密度泛函的半局部近似值，从而成为三维空间上的单个积分。最近，交换能的一个严格的下界被建立在近似“非常简单的元广义梯度近似”或MGGA-MVS中，它对生成热、能垒、分子的弱相互作用和固体的晶格常数有精确的结果。除了标准的两种成分（局部电子密度及其梯度）之外，如果不使用第三种成分（局部动能密度），这是不可能的。这第三种成分即使在急剧收紧的边界下也能保证精确的能量。密度泛函理论（DFT）是物理、材料科学、化学等领域应用最广泛的电子结构理论之一。只有交换相关能是未知的，在实际中需要进行近似。精确的约束提供了关于这个函数的有用信息。局部自旋密度近似（LSDA）是第一个基于约束的密度泛函。任意密度的交换相关能的Lieb-Oxford下界是另一个约束，它在广义梯度近似和元梯度近似的发展中起着重要作用。最近，对单电子密度和双电子密度证明了交换能的强和最佳收紧下界，并推测了所有密度的交换能下界。在本文中，我们提出了一个现实的“非常简单的meta-GGA”（MGGA-MVS）交换，它尊重这个最优边界，而以前的超越lsda近似不满足这个最优边界。这种约束可能会使预测的热化学性质变差，但实际上它们比Perdew-Burke-Ernzerhof GGA的热化学性质有所改善，后者具有几乎相同的相关性部分。然而，MVS交换与其他gga和元gga的交换有根本的不同。它的交换增强因子对轨道动能密度有很强的依赖性，这使得即使在急剧收紧的边界下也能得到精确的能量。当这种非经验MVS meta-GGA以25%的精确交换进行杂化时，得到的全局杂化可以很好地预测原子化能、反应势垒和分子的弱相互作用。
Significance Efficient calculation of the properties of atoms, molecules, and solids on the computer requires a semilocal approximation to the density functional for the exchange-correlation energy, which becomes thereby a single integral over three-dimensional space. A recent, strongly tightened lower bound on the exchange energy has been built into the approximation “meta-generalized gradient approximations made very simple,” or MGGA-MVS, with accurate results for heats of formation, energy barriers, and weak interactions of molecules, and for lattice constants of solids. This would not have been possible without the use of a third ingredient (the local kinetic energy density) in addition to the standard two (the local electron density and its gradient). This third ingredient permits accurate energies even with the drastically tightened bound. Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.