Variational optimization of the two-electron reduced-density matrix under pure-state N-representability conditions

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Direct variational optimization of ground-state two-electron reduced-density matrices (2-RDMs) often relies on ensemble N-representability conditions.
• Ensemble 2-RDMs may not represent pure states, leading to inaccuracies in excited-state properties.
• Previous methods using ensemble densities in extended random phase approximation (ERPA) yield poor excitation energy estimates.

Purpose of the Study:

• To develop an approach for direct variational optimization of ground-state 2-RDMs that satisfy pure-state N-representability.
• To investigate the impact of generalized Pauli constraints on the accuracy of excitation energy calculations.
• To improve the reliability of electronic structure calculations for atomic and molecular systems.

Main Methods:

• Direct variational optimization of the ground-state 2-RDM.
• Incorporation of generalized Pauli constraints to enforce pure-state N-representability.
• Application within the extended random phase approximation (ERPA) framework.

Main Results:

• The proposed method successfully optimizes 2-RDMs under pure-state N-representability conditions using generalized Pauli constraints.
• 2-RDMs satisfying both ensemble conditions and generalized Pauli constraints yield significantly more reliable excitation energy estimates.
• The improved accuracy was demonstrated even for simple atomic systems where previous ensemble-based methods failed.

Conclusions:

• Direct variational optimization of 2-RDMs with generalized Pauli constraints is a viable strategy for accurate electronic structure calculations.
• Enforcing pure-state N-representability is crucial for obtaining reliable excitation energies within the ERPA.
• This work provides a more robust theoretical framework for predicting excited-state properties in quantum chemistry.