Approximate Functionals for Multistate Density Functional Theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density functional theory (DFT) traditionally focuses on ground states.
• Excited states in quantum chemistry present significant computational challenges.
• Accurate modeling of electronic interactions is vital for understanding chemical and physical processes.

Purpose of the Study:

• To develop a novel, rigorous density functional theory (DFT) for excited electronic states.
• To establish a universal functional of the matrix density for kinetic and electron-repulsion operators.
• To propose the first approximation for multistate universal functionals.

Main Methods:

• Formulating a projection of kinetic and electron-repulsion operators onto the subspace of lowest electronic states.
• Adapting the Thomas-Fermi-Dirac-von Weizsäcker model and homogeneous electron gas correlation energy into matrix functionals.
• Ensuring matrix functionals transform correctly under basis set transformations and recover ground-state functionals for single states.

Main Results:

• The developed multistate universal functional is independent of the number of electronic states and is analytic.
• The approximation accurately reproduces matrix elements of the electron-repulsion operator for LiF, including off-diagonal elements representing inter-state interactions.
• The kinetic energy functional shows the largest error, indicating a need for improved constraints.

Conclusions:

• The study presents a significant advancement in DFT for excited states by introducing matrix functionals.
• The proposed approximation shows promise for accurately calculating electronic interactions, even off-diagonal Hamiltonian elements.
• Further development is required, particularly for the kinetic energy functional, to improve accuracy beyond the local density approximation.