Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

Area of Science:

• Quantum Many-Body Theory
• Computational Chemistry
• Nuclear Physics

Background:

• Accurate calculations in quantum many-body theories require including three-body interactions.
• Existing methods often face computational limitations when incorporating these terms.

Purpose of the Study:

• To develop and evaluate novel approaches for including connected three-body terms in unitary many-body theories.
• To improve the accuracy and efficiency of computational methods for quantum systems.

Main Methods:

• Development of approximate linearized DSRG truncated to one-, two-, and three-body operators (LDSRG(3)) models.
• Introduction of iterative LDSRG(3)-n and -n' methods based on perturbative analysis.
• Proposal of perturbative triples corrections using qDSRG(2) with recursive semi-quadratic commutators.

Main Results:

• The LDSRG(3)-2 scheme achieves similar computational cost to CCSDT but with superior accuracy for correlation energies.
• The qDSRG(2)+(T) approach demonstrates accuracy comparable to CCSD(T) for atomic and molecular energetics.
• Evaluated energetics for twenty-eight closed-shell atoms and small molecules.

Conclusions:

• The developed LDSRG(3) variants offer efficient and accurate ways to include three-body effects.
• The qDSRG(2)+(T) method provides a highly accurate and computationally feasible alternative for electronic structure calculations.