Fundamental Variable and Density Representation in Multistate DFT for Excited States

Area of Science:

• Quantum Chemistry
• Computational Physics
• Density Functional Theory

Background:

• Theophilou's subspace theory links total energy to subspace density but not individual eigenstate energies.
• Existing subspace density functional theory methods do not directly yield individual eigenstate energies.
• Recent work proved the projected Hamiltonian is a matrix functional of the multistate matrix density.

Purpose of the Study:

• To demonstrate that the matrix density is the fundamental variable for exact individual eigenstate energies and densities.
• To introduce novel representations of the matrix density using nonorthogonal and orthogonal orbitals.
• To present an explicit formulation of the Hamiltonian matrix functional.

Main Methods:

• Representing the matrix density using nonorthogonal and orthogonal orbitals.
• Constructing a multistate active space of auxiliary states to represent the matrix density.
• Developing an explicit formulation of the Hamiltonian matrix functional.
• Implementing multistate self-consistent-field optimization (MS-SDSCF) with orthonormal orbitals.

Main Results:

• The matrix density $$(r) is identified as the essential variable for exact individual eigenstate properties.
• Two representations of the matrix density are introduced, enabling its exact representation.
• An explicit formulation of the Hamiltonian matrix functional $$ is derived.
• Multistate self-consistent-field optimization (MS-SDSCF) is shown to be feasible.

Conclusions:

• The matrix density formalism provides a direct route to exact individual eigenstate energies and densities.
• This approach extends the capabilities of subspace theory for accurate quantum mechanical calculations.
• The developed methods offer a powerful tool for investigating complex electronic structures.