Pair 2-electron reduced density matrix theory using localized orbitals.

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Full configuration interaction (FCI) provides accurate correlation energies but scales exponentially with system size.
• Variational two-electron reduced-density-matrix (2-RDM) methods offer a more scalable approach but can be computationally intensive.
• Pair FCI methods restricted to a pairing space are size-extensive but computationally demanding.

Purpose of the Study:

• To develop an efficient and approximately size-extensive pair 2-RDM method.
• To investigate the impact of localized molecular orbitals on the accuracy and computational cost of the pair 2-RDM method.
• To assess the applicability of the localized-orbital pair 2-RDM method to strongly correlated systems.

Main Methods:

• Restricting the variational 2-RDM method to a pairing space.
• Employing localized molecular orbitals to define the pairing space, avoiding iterative optimization.
• Applying the localized-orbital pair 2-RDM method to model systems like hydrogen chains, acenes, and cadmium telluride polymers.

Main Results:

• The localized-orbital pair 2-RDM method achieves mean-field-like computational scaling (O(r^3)).
• This approach yields accurate lower bounds to pair FCI energies and is approximately size-extensive.
• Canonical Hartree-Fock orbitals proved inaccurate and non-size-extensive for this method.
• The method recovers significant correlation energy for hydrogen chains compared to iterative optimization.

Conclusions:

• Localized molecular orbitals provide an efficient and accurate way to implement the pair 2-RDM method.
• The localized-orbital pair 2-RDM method offers a computationally feasible route to study strongly correlated phenomena.
• This method has broad applications in chemistry and physics for systems exhibiting multi-reference correlation.