On the self-consistent implementation of general occupied-orbital dependent exchange-correlation functionals with...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Density Functional Theory

Background:

• Occupied-orbital dependent (OOD) functionals are key in modern density functional theory (DFT).
• Implementing OOD functionals is challenging due to their implicit dependence on electron density.
• Standard methods for deriving exchange-correlation potentials are not directly applicable.

Purpose of the Study:

• To develop general, systematic, and transparent expressions for the functional derivatives with respect to orbitals (FDOs) of generalized OOD functionals.
• To provide a matrix-element version of these FDOs suitable for atomic orbital basis sets.
• To numerically test these FDOs using a complex OOD functional, the Becke's real-space model of nondynamical correlation (B05).

Main Methods:

• Derivation of general expressions for FDOs of OOD functionals.
• Formulation of a matrix-element version for atomic orbital basis sets.
• Application and numerical testing of the derived FDOs for the B05 functional.

Main Results:

• General expressions for FDOs of generalized OOD functionals are systematically derived.
• A matrix-element formulation for FDOs in atomic orbital basis sets is presented.
• Explicit FDOs for the B05 functional are derived and numerically tested for the first time.

Conclusions:

• The presented general expressions and matrix-element formulation simplify the self-consistent implementation of OOD functionals.
• The successful numerical testing on the B05 functional validates the methodology for complex cases.
• This work facilitates the broader application and development of OOD functionals in DFT.