Perturbation theory corrections to the two-particle reduced density matrix variational method

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The variational 2-particle-reduced-density-matrix (2-RDM) method optimizes ground-state energy using N-representability constraints.
• The N-electron Hamiltonian H(lambda) interpolates between the Fock Hamiltonian (lambda=0) and the fully correlated Hamiltonian (lambda=1).

Purpose of the Study:

• To improve the accuracy of the 2-RDM method for correlated atoms and molecules.
• To leverage perturbation theory's accuracy at small lambda to correct 2-RDM energies at lambda=1.

Main Methods:

• Minimizing ground-state energy with respect to the 2-RDM, subject to N-representability conditions.
• Applying a correction based on perturbation theory at small lambda to 2-RDM energies calculated at lambda=1.
• Assuming the 2-RDM method captures a consistent percentage of correlation energy across lambda in (0,1].

Main Results:

• The correction improves 2-RDM energies in the equilibrium bonding region for various molecules.
• 2-RDM energies at stretched or dissociated geometries, already accurate, showed no significant change.
• Corrected 2-RDM energies at equilibrium geometries match the accuracy of coupled-cluster singles and doubles (CCSD).

Conclusions:

• The perturbation theory correction enhances the accuracy of the variational 2-RDM method.
• The corrected 2-RDM method demonstrates superior accuracy over CCSD at nonequilibrium geometries.
• This approach offers a promising avenue for accurate calculations of molecular energies, particularly during bond stretching and dissociation.