Multistate Density Functional Theory: Theory, Methods, and Applications

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Standard density functional theory (DFT) faces limitations in accurately describing complex electronic structures and excited states.
• Existing methods often struggle with systems requiring a multi-state treatment, necessitating more robust theoretical frameworks.

Purpose of the Study:

• To develop a quantum mechanical theory of density functionals applicable to multi-state systems.
• To establish a framework for calculating exact energies and densities of multiple electronic eigenstates.
• To introduce a novel computational method overcoming limitations of conventional DFT and time-dependent DFT.

Main Methods:

• Introduced matrix density $D(r)$ of rank $N$ as the fundamental variable, establishing a correspondence with the Hamiltonian matrix.
• Defined a matrix density functional $\mathcal{H}[D]$ and correlation matrix functional $\mathcal{E}^c[D]$ within the minimal active space (MAS) concept.
• Developed a nonorthogonal state interaction (NOSI) algorithm for orbital optimization and correlation functional approximation, leading to the MSDFT-NOSI method.

Main Results:

• Achieved a one-to-one mapping between matrix density and the Hamiltonian matrix for $N$ electronic states.
• Demonstrated that no more than $N^2$ Slater determinants are needed for exact matrix density representation.
• The MSDFT-NOSI method accurately calculates energies and densities for multiple eigenstates, validated against high-level wave function theory.

Conclusions:

• The developed quantum theory and MSDFT-NOSI method provide an accurate and efficient approach for multi-state electronic structure calculations.
• This method successfully addresses challenging systems where Kohn-Sham DFT and linear-response time-dependent DFT fail.
• The findings pave the way for more reliable computational studies in quantum chemistry and materials science.