Method for making 2-electron response reduced density matrices approximately N-representable

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Direct computation of the 2-electron reduced density matrix (2-RDM) is often impractical in quantum chemistry methods.
• 2-RDMs derived from response theory lack N-representability, failing to correspond to a physical N-electron wave function.

Purpose of the Study:

• To present a novel algorithm for rendering non-N-representable 2-RDMs approximately N-representable.
• To develop a specific optimization procedure for seniority-zero 2-RDMs.

Main Methods:

• An algorithm is introduced to enforce N-representability by ensuring symmetry, normalization, and fulfillment of P-, Q-, and G-conditions.
• A constrained optimization approach minimizes the difference between the response 2-RDM and a target N-representable 2-RDM using the Frobenius norm.

Main Results:

• The developed algorithm successfully makes non-N-representable 2-RDMs approximately N-representable.
• The optimization procedure ensures the corrected 2-RDM satisfies normalization and positive semidefiniteness of the 2-RDM, Q-matrix, and G-matrix.

Conclusions:

• The method is effective for correcting 2-RDMs that are close to being N-representable.
• This approach provides a way to obtain physically meaningful 2-RDMs from response theory calculations.