The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches.

%B Electron Correlation Methodology %S ACS Symposium Series %I American Chemical Sociegy %C Washington, DC %V 958 %@ ISBN13: 9780841238435 %G eng %0 Journal Article %J International Journal of Quantum Chemistry %D 2006 %T Automated derivation and parallel computer implementation of renormalized and active-space coupled-cluster methods %A Piotr Piecuch %A So Hirata %A K. Kowalski %A P.-D. Fan %A Theresa L. Windus %XOur recent efforts that have led to an automated derivation and computer implementation of the renormalized and active-space coupled-cluster {(CC)} methods with Tensor Contraction Engine {(TCE)} are summarized. The {TCE-generated} renormalized and active-space {CC} computer codes are parallel and applicable to closed- and open-shell references, enabling accurate calculations of potential energy surfaces along bond-breaking coordinates and excited states displaying a significant multi-reference character. The effectiveness of the new codes in describing electronic quasi-degeneracies is illustrated by the renormalized {CC} calculations of the potential energy curve of {HCl} and the active-space {CC} calculations for the low-lying excited states of the Be3 system. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

%B International Journal of Quantum Chemistry %V 106 %P 79–97 %8 08/2005 %G eng %N 1 %0 Journal Article %J Journal of Molecular Structure: THEOCHEM %D 2006 %T Intriguing Accuracies of the Exponential Wave Function Expansions Exploiting Finite Two-Body Correlation Operators in Calculations for Many-Electron Systems %A P.-D. Fan %A P. Piecuch %K xact many-electron wave functions; Generalized coupled-cluster methods; Two-body correlation operators; Nooijen's conjecture; Variational calculations; Multi-determinantal reference states; Excited states %XFollowing the ideas laid down by Nooijen and Nakatsuji, several authors have considered an intriguing possibility of representing the exact many-electron wave functions by the exponential cluster expansions involving two-body correlation operators. In particular, inspired by the symmetric form of the Horn–Weinstein exact energy formula, and exploiting the variational principle and numerical analysis, we have demonstrated that one can obtain nearly exact ground-state wave functions for a few many-electron systems using the exponential cluster expansion involving a finite two-body operator acting on the Hartree–Fock determinant [P. Piecuch et al., Phys. Rev. Lett. 90 (2003) 113001]. After summarizing these earlier findings and making some additional comments on the nature of the exponential cluster expansions involving two-body correlation operators, we examine the following issues: (i) the improvements in the accuracy and convergence toward the full configuration interaction (CI) limit offered by cluster operators containing two-body as well as one-body components, (ii) the improvements in the accuracy resulting from the use of multi-determinantal reference states, and (iii) the potential accuracy of the exponential wave function expansions involving finite one- and two-body cluster operators in excited-state calculations. All calculations are performed for an eight electron model system, which is simple enough to allow for the exact, full CI, and other electronic structure calculations, which has fewer independent parameters in the Hamiltonian than the dimension of the corresponding full CI problem, and which enables one to examine ground and excited states with a varying degree of configurational quasi-degeneracy by simple changes in the corresponding nuclear geometry.

%B Journal of Molecular Structure: THEOCHEM %V 768 %P 3-16 %8 08/31/2006 %G eng %N 1-3 %0 Journal Article %J Advances in Quantum Chemistry %D 2006 %T The Usefulness of Exponential Wave Function Expansions Employing One- and Two-Body Cluster Operators in Electronic Structure Theory: The Extended and Generalized Coupled-Cluster Methods %A P.-D. Fan %A Piotr Piecuch %XIn this paper, the applicability of exponential cluster expansions involving one- and two-body operators in high accuracy ab initio electronic structure calculations is examined. First, the extended coupled-cluster method with singles and doubles (ECCSD) is tested in the demanding studies of systems with strong quasi-degeneracies, including potential energy surfaces involving multiple bond breaking. The numerical results show that the single-reference ECCSD method is capable of providing a qualitatively correct description of quasi-degenerate electronic states and potential energy surfaces involving bond breaking, eliminating, in particular, the failures and the unphysical behavior of standard coupled-cluster methods in similar cases. It is also demonstrated that one can obtain entire potential energy surfaces with millihartree accuracies by combining the ECCSD theory with the non-iterative a posteriori corrections obtained by using the generalized variant of the method of moments of coupled-cluster equations. This is one of the first instances where the relatively simple single-reference formalism, employing only one- and two-body clusters in the design of the relevant energy expressions, provides a highly accurate description of the dynamic and significant non-dynamic correlation effects characterizing quasi-degenerate and multiply bonded systems. Second, an evidence is presented that one may be able to represent the virtually exact ground- and excited-state wave functions of many-electron systems by exponential cluster expansions employing general two-body or one- and two-body operators. Calculations for small many-electron model systems indicate the existence of finite two-body parameters that produce the numerically exact wave functions for ground and excited states. This finding may have a significant impact on future quantum calculations for many-electron systems, since normally one needs triply excited, quadruply excited, and other higher-than-doubly excited Slater determinants, in addition to all singly and doubly excited determinants, to obtain the exact or virtually exact wave functions.

%B Advances in Quantum Chemistry %V 51 %P 1-57 %8 12/2006 %G eng %0 Journal Article %J Theoretical Chemistry Accounts: Theory, Computation, and Modeling %D 2004 %T Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states %A Piotr Piecuch %A K. Kowalski %A I. S. O. Pimienta %A P.-D. Fan %A M.D. Lodriguito %A M. J. {McGuire} %A S. A. Kucharski %A T. Kuś %A M. Musial %K Coupled-cluster theory - Method of moments of coupled-cluster equations - Renormalized coupled-cluster methods - extended coupled cluster theory - Potential energy surfaces %XThe method of moments of coupled-cluster equations {(MMCC),} which provides a systematic way of improving the results of the standard coupled-cluster {(CC)} and equation-of-motion {CC} {(EOMCC)} calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The {MMCC} theory and its generalized {MMCC} {(GMMCC)} extension that enables one to use the cluster operators resulting from the standard as well as nonstandard {CC} calculations, including those obtained with the extended {CC} {(ECC)} approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction {(CI)} and {CC} or {EOMCC} energies. These relationships can be used to design the noniterative corrections to the {CC/EOMCC} energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference {CC/EOMCC} methods fail. Several {MMCC} and {GMMCC} approximations are discussed, including the renormalized and completely renormalized {CC/EOMCC} methods for closed- and open-shell states, the quadratic {MMCC} approaches, the {CI-corrected} {MMCC} methods, and the {GMMCC} approaches for multiple bond breaking based on the {ECC} cluster amplitudes.

%B Theoretical Chemistry Accounts: Theory, Computation, and Modeling %V 112 %P 349–393 %8 07/2004 %G eng