Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science , Hamburg 22761 , Germany.
Center for Computational Quantum Physics (CCQ) , Flatiron Institute , New York , New York 10010 , United States.
J Chem Theory Comput. 2018 Aug 14;14(8):4072-4087. doi: 10.1021/acs.jctc.8b00292. Epub 2018 Jul 19.
We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that, by including more observables explicitly in a density-functional approach, already simple approximation strategies lead to very accurate results. Here, we promote the kinetic-energy density to a fundamental variable alongside the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. On the basis of this mapping, we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, which force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn-Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and comparing the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange (for the effective potential) and a uniform (for the effective hopping) approximation for the keKS and the exact-exchange approximation for the KS system, respectively.
我们提出了一种格点上的动能密度泛函理论和相应的动能 Kohn-Sham（keKS）方案，并表明通过在密度泛函方法中更显式地包含更多可观测量，即使是简单的近似策略也能得到非常精确的结果。在这里，我们将动能提升为一个基本变量，与密度并列，并针对特定情况（分析和数值）表明，在外部的局域位势和局域跳跃与内部的密度和动能密度之间存在一一对应关系。基于这种映射，我们建立了两个未知的有效场，平均场交换关联势和平均场交换关联跳跃，它们迫使 keKS 系统生成与完全相互作用系统相同的动能密度和密度。我们通过基于密度和动能密度运动方程的分解表明，我们可以构建简单的轨道相关泛函，其性能优于标准密度泛函理论的相应精确交换 Kohn-Sham（KS）近似。我们通过考虑精确的 KS 和 keKS 系统，并比较未知的相关贡献，以及通过比较基于平均场交换（用于有效势）和均匀（用于有效跳跃）近似的 keKS 和用于 KS 系统的精确交换近似的自洽计算来实现这一点。
