title: A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.
abstract: We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.
authors.affiliation: Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
authors.forename: Kasper
authors.initials: K
authors.lastname: Kristensen
authors.affiliation: Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
authors.forename: Janus J
authors.initials: JJ
authors.lastname: Eriksen
authors.affiliation: The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA.
authors.forename: Devin A
authors.initials: DA
authors.lastname: Matthews
authors.affiliation: Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
authors.forename: Jeppe
authors.initials: J
authors.lastname: Olsen
authors.affiliation: Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.
authors.forename: Poul
authors.initials: P
authors.lastname: Jørgensen