Variational calculation of second-order reduced density matrices by strong N-representability conditions and an...

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• The reduced density matrix (RDM) method offers a variational approach for electronic structure calculations.
• Accurate calculation of ground state energies and properties is crucial in quantum chemistry and condensed matter physics.
• Existing methods like CCSD(T) have limitations, particularly for high spin states and anionic systems.

Purpose of the Study:

• To apply the RDM method to calculate ground state energies and dipole moments for various atomic and molecular systems.
• To investigate the impact of N-representability conditions (P, Q, G, T1, T2, T2(')) on calculation accuracy.
• To enhance the accuracy of RDM calculations through improved semidefinite programming (SDP) solvers.

Main Methods:

• Variational calculation using the second-order reduced density matrix (2-RDM).
• Incorporation of N-representability conditions, including the stronger T1 and T2(') conditions.
• Implementation of equality constraints and multiple precision arithmetic within the SDP solver.

Main Results:

• The RDM method achieved correlation energy calculations from 100% to 101%, comparable or superior to CCSD(T).
• Handling equality constraints improved accuracy by 0.1–0.6 mhartree.
• Replacing the T2 condition with T2(') yielded improvements of 0.1–0.5 mhartree.

Conclusions:

• The RDM method, augmented with advanced N-representability conditions and SDP solver techniques, provides highly accurate electronic structure data.
• The newly developed multiple precision arithmetic SDP solver delivers exceptional energy precision (≥16 significant digits) for systems like the Hubbard model and Be atom.
• This approach offers a robust and accurate alternative for quantum mechanical calculations, especially in challenging regimes like high correlation.