To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn–Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle–particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

中文翻译：

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具有基态和激发态广义辅助系统的多参考密度泛函理论

为了描述静态相关性，我们开发了密度泛函理论（DFT）的新方法，该方法使用了与物理系统具有不同对称性（例如粒子数或自旋）的广义辅助系统。物理系统的总能量由两部分组成：辅助系统的能量，由选定的密度泛函近似（DFA）确定，以及来自近似线性响应理论的激励能量，该理论将对称性恢复为能量。因此，严格地导致对物理系统的多决定性描述。物理系统的电子密度与辅助系统的电子密度不同，它是由总能量相对于外部电势的函数导数唯一确定的。因此，我们的能量函数是物理系统密度的隐式函数，但是辅助系统密度的显式函数。我们表明，可以通过对显式变量（广义Kohn-Sham非相互作用密度矩阵）进行自洽优化来获得描述物理系统的基态和激发态的总能量最小值和稳态。我们已经开发了用于自洽优化的广义优化有效势方法。在辅助系统选项和相关的线性响应理论中，选择了颗粒-颗粒随机相位近似（pp-RPA）和自旋翻转时间相关密度泛函理论（SF-TDDFT）的重新制定版本。