A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled cluster (CC) theory is a powerful method for electronic structure calculations.
• Perturbation series are used to approximate higher-level CC models, such as CC with single, double, and triple excitations (CCSDT).
• Comparing different perturbation expansions is crucial for developing more efficient and accurate computational methods.

Purpose of the Study:

• To introduce and analyze the E-CCSD(T-n) perturbation series.
• To compare the E-CCSD(T-n) series with the recently developed CCSD(T-n) series.
• To investigate the convergence properties and underlying reasons for differences between these perturbation series.

Main Methods:

• Development of the E-CCSD(T-n) perturbation series, satisfying CCSD amplitude equations at the expansion point.
• Comparison with the CCSD(T-n) series, which satisfies both CCSD amplitude and multiplier equations.
• Analysis of computational scaling and term-wise size extensivity.
• Tracing convergence differences to the information utilized at the expansion point.

Main Results:

• Both E-CCSD(T-n) and CCSD(T-n) series exhibit similar computational scaling and formal convergence towards the CCSDT energy.
• The CCSD(T-n) series demonstrates more rapid convergence compared to the E-CCSD(T-n) series.
• The faster convergence of CCSD(T-n) is attributed to the utilization of both amplitude and multiplier information at the expansion point.

Conclusions:

• The CCSD(T-n) perturbation series offers a more efficient route to CCSDT energies than the E-CCSD(T-n) series.
• The bivariational Lagrangian formulation provides a basis for faster converging perturbation series when parent parameters depend on the perturbation operator.
• These findings generalize to other perturbation expansions between parent and target CC models.