Lu Yangyi, Gao Jiali
Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China.
College of Chemical Biology and Biotechnology, Beijing University Shenzhen Graduate School, Shenzhen 518055, China.
J Chem Phys. 2025 Mar 14;162(10). doi: 10.1063/5.0249583.
On the basis of recent advancements in the Hamiltonian matrix density functional for multiple electronic eigenstates, this study delves into the mathematical foundation of the multistate density functional theory (MSDFT). We extend a number of physical concepts at the core of Kohn-Sham DFT, such as density representability, to the matrix density functional. In this work, we establish the existence of the universal matrix functional for many states as a proper generalization of the Lieb universal functional for the ground state. Consequently, the variation principle of MSDFT can be rigorously defined within an appropriate domain of matrix densities, thereby providing a solid framework for DFT of both the ground state and excited states. We further show that the analytical structure of the Hamiltonian matrix functional is considerably constrained by the subspace symmetry and invariance properties, requiring and ensuring that all elements of the Hamiltonian matrix functional are variationally optimized in a coherent manner until the Hamiltonian matrix within the subspace spanned by the lowest eigenstates is obtained. This work solidifies the theoretical foundation to treat multiple electronic states using density functional theory.
基于哈密顿矩阵密度泛函在多个电子本征态方面的最新进展，本研究深入探讨了多态密度泛函理论（MSDFT）的数学基础。我们将一些作为科恩 - 沈密度泛函理论（Kohn - Sham DFT）核心的物理概念，如密度可表示性，扩展到矩阵密度泛函。在这项工作中，我们确立了多态通用矩阵泛函的存在性，它是基态的李布通用泛函的恰当推广。因此，MSDFT的变分原理可以在矩阵密度的适当域内严格定义，从而为基态和激发态的密度泛函理论提供了一个坚实的框架。我们进一步表明，哈密顿矩阵泛函的解析结构受到子空间对称性和不变性性质的显著约束，这要求并确保哈密顿矩阵泛函的所有元素以连贯的方式进行变分优化，直到获得由最低本征态所跨越的子空间内的哈密顿矩阵。这项工作巩固了使用密度泛函理论处理多个电子态的理论基础。
