Developing the random phase approximation into a practical post-Kohn-Sham correlation model
Developing the random phase approximation into a practical post-Kohn-Sham correlation model
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DOI：
10.1063/1.2977789
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发表时间：
2008-09-21
影响因子：
4.4
通讯作者：
Furche, Filipp
中科院分区：
文献类型：
--
作者：
Furche, Filipp
密度泛函相关能的随机相位近似（RPA）系统地改进了现有半局部泛函的许多局限性，但在过去被认为计算量太大而无法广泛应用。在这里，开发了一个物理上吸引人的RPA相关模型的重新表述，大大降低了其计算复杂性。密度泛函RPA相关能等于在全阶和一阶耦合下计算的所有RPA电子激发能之差的一半。因此，RPA相关能可以被认为是电子零点振动能的差，其中每个特征模对应于一个电子激发。这个惊人的简单结果与电子相关的等离子体理论密切相关。讨论了流行的相关波函数方法与电子对相关模型的区别。RPA相关能进一步转化为Kohn-Sham轨道的显式泛函。这个函数唯一重要的组成部分是响应算子的符号函数。提出了一种基于牛顿-舒尔茨迭代的求解该符号函数的稳定迭代算法。积分直接实现规模为系统大小的五次方，类似于二阶Moller-Plesset计算。有了这些改进，RPA可能成为长期寻求的鲁棒和高效的零阶后kohn - sham相关模型。(c) 2008年美国物理研究所。[doi: 10.1063/ 1.2977789]
The random phase approximation (RPA) to the density functional correlation energy systematically improves upon many limitations of present semilocal functionals, but was considered too computationally expensive for widespread use in the past. Here a physically appealing reformulation of the RPA correlation model is developed that substantially reduces its computational complexity. The density functional RPA correlation energy is shown to equal one-half times the difference of all RPA electronic excitation energies computed at full and first order coupling. Thus, the RPA correlation energy may be considered as a difference of electronic zero point vibrational energies, where each eigenmode corresponds to an electronic excitation. This surprisingly simple result is intimately related to plasma theories of electron correlation. Differences to electron pair correlation models underlying popular correlated wave function methods are discussed. The RPA correlation energy is further transformed into an explicit functional of the Kohn-Sham orbitals. The only nontrivial ingredient to this functional is the sign function of the response operator. A stable iterative algorithm to evaluate this sign function based on the Newton-Schulz iteration is presented. Integral direct implementations scale as the fifth power of the system size, similar to second order Moller-Plesset calculations. With these improvements, RPA may become the long-sought robust and efficient zero order post-Kohn-Sham correlation model. (c) 2008 American Institute of Physics. [DOI: 10.1063/ 1.2977789]