Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particle...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Accurate computation of ground-state energies and reduced density matrices (RDMs) is crucial for understanding molecular systems.
• Existing methods often face challenges with N-representability conditions, limiting accuracy.

Purpose of the Study:

• To implement and assess three-particle N-representability conditions (three-positivity) within the variational doubly occupied configuration interaction (DOCI) framework.
• To compute ground-state energies and 2-RDMs for various molecules and models using these enhanced constraints.

Main Methods:

• Variational computation of ground-state energies and 2-RDMs within the DOCI space.
• Enforcement of three-positivity conditions on the 2-RDM using semidefinite programming.
• Comparison with exact DOCI and approximated variational 2-RDM methods.

Main Results:

• Accurate ground-state energies and 2-RDMs were obtained for N2, CO, CN-, and NO+ molecules.
• The three-positivity conditions improved accuracy compared to two-positivity approximations.
• The method demonstrated computational efficiency.

Conclusions:

• The three-particle variational constraints within the DOCI framework are effective for accurate RDM calculations.
• This approach offers a computationally viable path for studying complex quantum systems.
• The findings highlight the importance of N-representability conditions in quantum chemistry.