Multistate Density Functional Theory: Theory, Methods, and Applications

A quantum theory of density functionals and its applications is presented. By introducing a matrix density $D\left(r\right)$ of rank $N$ as the fundamental variable, a one-to-one correspondence has been established between $D\left(r\right)$ and the Hamiltonian matrix representing $N$ electronic states—that is, a matrix density functional $H\left(D\right)$. Moreover, no more than $N^2$ Slater determinants are sufficient to represent $D\left(r\right)$ exactly, giving rise to the concept of minimal active space (MAS). The use of a MAS naturally leads to the definition of correlation matrix functional $E^c\left(D\right)$, the multi-state extension of the exchange-correlation functional in Kohn–Sham DFT. Variational minimization of the multistate energy, which is defined as the trace of the Hamiltonian matrix functional, yields the exact energies and densities of the lowest $N$ eigenstates. A nonorthogonal state interaction (NOSI) algorithm has been developed to optimize the orbitals associated with $D\left(r\right)$ and to approximate the correlation matrix functional. The MSDFT-NOSI method is demonstrated across a range of applications, particularly in cases where KS-DFT and linear-response time-dependent DFT fail, with its accuracy validated through comparison with high-level multiconfigurational wave function theory.

This article is categorized under: