Lu Yangyi, Gao Jiali
Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China.
Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States.
J Phys Chem Lett. 2022 Aug 25;13(33):7762-7769. doi: 10.1021/acs.jpclett.2c02088. Epub 2022 Aug 15.
We report a rigorous formulation of density functional theory for excited states, providing a theoretical foundation for a multistate density functional theory. We prove the existence of a Hamiltonian matrix functional of the multistate matrix density () in the subspace spanned by the lowest eigenstates. Here, () is an -dimensional matrix of state densities and transition densities. Then, a variational principle of the multistate subspace energy is established, whose minimization yields both the energies and densities of the individual eigenstates. Furthermore, we prove that the -dimensional matrix density () can be sufficiently represented by nonorthogonal Slater determinants, based on which an interacting active space is introduced for practical calculations. This work establishes that the ground and excited states can be treated on an equal footing in density functional theory.
我们报告了一种用于激发态的严格密度泛函理论公式，为多态密度泛函理论提供了理论基础。我们证明了在由最低本征态所张成的子空间中，多态矩阵密度（）的哈密顿矩阵泛函的存在性。这里，（）是一个状态密度和跃迁密度的维矩阵。然后，建立了多态子空间能量的变分原理，其最小化产生了各个本征态的能量和密度。此外，我们证明了维矩阵密度（）可以由非正交斯莱特行列式充分表示，在此基础上引入了相互作用活性空间用于实际计算。这项工作表明，在密度泛函理论中，基态和激发态可以在同等基础上进行处理。
