A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle–hole (ph) and particle–particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.

中文翻译：

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轨道函数的广义优化有效势和随机相近似的自洽计算

在当前的工作中，开发了一种新的自洽程序，用于计算与轨道相关的密度泛函近似（DFA）的总能量，即广义优化有效势（GOEP）。GOEP是一种非局部的Hermitian势能，它可以提供一组被占用的和虚拟的轨道，并使总能量最小化。GOEP优化导致的最小值与轨道优化的最小值相同。GOEP方法有望作为一种有效的优化轨道依赖函数的方法，正如对粒子-孔（ph）和粒子-粒子（pp）的相关函数的随机相位近似（RPA）的自洽计算所证明的那样）频道。结果表明，在自洽计算中，描述弱相互作用的范德华系统的准确性显着提高。特别是，可以通过GOEP优化自洽地捕获非自洽RPA计算中重要的单激励贡献，从而导致轨道重新归一化，而无需在能量函数中使用单激励。