Handling Ensemble N-Representability Constraint in Explicit-by-Implicit Manner.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Reduced density matrix functional theory (RDMFT) faces convergence challenges due to improper handling of the ensemble N-representability constraint.
• Existing Lagrange methods explicitly incorporate constraints, often leading to convergence difficulties and impacting RDMFT's applicability and reproducibility.

Purpose of the Study:

• To develop a novel method for implicitly handling the ensemble N-representability constraint in RDMFT.
• To overcome the convergence issues associated with traditional Lagrange methods in RDMFT calculations.

Main Methods:

• Introduction of an explicit-by-implicit (EBI) approach, which utilizes implicit functions to manage the nonlinear relationship within the N-representability constraint.
• Transformation of the constrained optimization problem inherent in RDMFT into an unconstrained minimization problem.

Main Results:

• Demonstrated the superiority of the EBI method across various systems, initial guesses, and functionals.
• Successfully resolved the convergence issues previously encountered with Lagrange methods for the ensemble N-representability constraint.

Conclusions:

• The EBI method provides a robust solution to the convergence problems in RDMFT, paving the way for its broader application and development.
• The EBI concept offers a versatile framework applicable to diverse constrained optimization problems in physics and chemistry.