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 European Physics Journal A %D 2006 %T Ab Initio Coupled-Cluster Calculations for Nuclei Using Methods of Quantum Chemistry %A Piotr Piecuch %A M. Wloch %A D. J. Dean %A J. R Gour %A M. {Hjorth-Jensen} %A T. Papenbrock %A K. Kowalski %XWe report preliminary large scale ab initio calculations of ground and excited states of 16O using quantum chemistry inspired coupled cluster methods and realistic two-body interactions. By using the renormalized Hamiltonians obtained with a no-core G-matrix approach, we obtain the virtually converged results at the level of two-body interactions. Due to the polynomial scaling with the system size that characterizes coupled cluster methods, we can probe large model spaces with up to seven major oscillator shells, for which standard non-truncated shell-model calculations are not possible.

%B European Physics Journal A %V 25 %P 485-488 %8 09/2005 %G eng %N 1 %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 The Journal of Physical Chemistry A %D 2006 %T Experimental and Theoretical UV Characterizations of Acetyloacetone and its Isomers %A Piotr Piecuch %A S. Coussan %A Y. Ferro %A A. Trivella %A P. Roubin %A R. Wieczorek %A C. Manca %A K. Kowalski %A M. Wloch %A S. Kucharski %A M. Musial %XCryogenic matrix isolation experiments have allowed the measurement of the UV absorption spectra of the high-energy non-chelated isomers of acetylacetone, these isomers being produced by UV irradiation of the stable chelated form. Their identification has been done by coupling selective UV-induced isomerization, infrared spectroscopy, and harmonic vibrational frequency calculations using density functional theory. The relative energies of the chelated and non-chelated forms of acetylacetone in the S0 state have been obtained using density functional theory and coupled-cluster methods. For each isomer of acetylacetone, we have calculated the UV transition energies and dipole oscillator strengths using the excited-state coupled-cluster methods, including EOMCCSD (equation-of-motion coupled-cluster method with singles and doubles) and CR-EOMCCSD(T) (the completely renormalized EOMCC approach with singles, doubles, and non-iterative triples). For dipole-allowed transition energies, there is a very good agreement between experiment and theory. In particular, the CR-EOMCCSD(T) approach explains the blue shift in the electronic spectrum due to the formation of the non-chelated species after the UV irradiation of the chelated form of acetylacetone. Both experiment and CR-EOMCCSD(T) theory identify two among the seven non-chelated forms to be characterized by red-shifted UV transitions relative to the remaining five non-chelated isomers.

%B The Journal of Physical Chemistry A %V 110 %P 3920-3926 %8 2/2006 %G eng %N 11 %0 Journal Article %J Journal of Molecular Structure: THEOCHEM %D 2006 %T Non-Iterative Coupled- Cluster Methods Employing Multi-Reference Perturbation Theory Wave Functions %A Piotr Piecuch %A M.D. Lodriguito %A K. Kowalski %A M. Wloch %K Coupled-cluster theory; Equation-of-motion coupled-cluster methods; Method of moments of coupled-cluster equations; Multi-reference perturbation theory; Non-iterative coupled-cluster methods %XA new class of non-iterative coupled-cluster (CC) methods, which improve the results of standard CC and equation-of-motion (EOM) CC calculations for ground and excited-state potential energy surfaces along bond breaking coordinates and for excited states dominated by two-electron transitions, is explored. The proposed approaches combine the method of moments of coupled-cluster equations (MMCC), in which the a posteriori corrections due to higher-order correlations are added to standard CC/EOMCC energies, with the multi-reference many-body perturbation theory (MRMBPT), which provides information about the most essential non-dynamic and dynamic correlation effects that are relevant to electronic quasi-degeneracies. The performance of the basic MRMBPT-corrected MMCC approximation, in which inexpensive non-iterative corrections due to triple excitations are added to ground- and excited-state energies obtained with the CC/EOMCC singles and doubles approach, is illustrated by the results of a few test calculations, including bond breaking in HF and H2O, and excited states of CH+.

%B Journal of Molecular Structure: THEOCHEM %V 771 %P 89-104 %8 10/2006 %G eng %N 1-3 %0 Journal Article %J Physical Review Letters %D 2005 %T Ab Initio Coupled-Cluster Study of 16O %A M. Włoch %A D. J. Dean %A J. R Gour %A M. {Hjorth-Jensen} %A K. Kowalski %A T. Papenbrock %A P. Piecuch %XWe report converged results for the ground and excited states and matter density of 16O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0+ state. Incorporation of triples has no effect on the latter finding.

%B Physical Review Letters %V 94 %P 212501 %8 06/2005 %G eng %N 21 %0 Journal Article %J Physical Review Letters %D 2005 %T Ab Initio Coupled-Cluster Study of O %A Piotr Piecuch %A M. Wloch %A D. J. Dean %A J. R Gour %A M. {Hjorth-Jensen} %A K. Kowalski %A T. Papenbrock %XWe report converged results for the ground and excited states and matter density of 16O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0+ state. Incorporation of triples has no effect on the latter finding.

%B Physical Review Letters %V 94 %8 06/2005 %G eng %0 Journal Article %J The Journal of Chemical Physics %D 2005 %T Active-Space Coupled-Cluster Study of Electronic States of Be 3 %A Piotr Piecuch %A K. Kowalski %A S. Hirata %A M. Wloch %A T.L. Windus %XThe active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods with all single and double excitations with triple excitations defined via active orbitals (CCSDt, EOMCCSDt), as implemented with TENSOR CONTRACTION ENGINE, are applied to the challenging Be3 system, which is characterized by a large number of low-lying excited states dominated by two-electron transitions and significant high-order correlation effects in the ground electronic state. It is demonstrated that the CCSDt and EOMCCSDt methods provide an excellent description of complicated electronic quasidegeneracies present in the Be3 cluster. Different strategies for defining triple excitations within the CCSDt∕EOMCCSDt approach are discussed.

%B The Journal of Chemical Physics %V 123 %P 6 pages %8 08/2005 %G eng %N 7 %0 Journal Article %J Journal of Chemical Physics %D 2005 %T Comparison of Low-Order Multireference Many-Body Perturbation Theories %A Piotr Piecuch %A R.K. Chaudhuri %A K.F. Freed %A G. Hose %A K. Kowalski %A M. Wloch %A S. Chattopadhyay %A D. Mukherjee %A R. Rolik %A A. Szabados %A G. Toth %A P.R. Surjan %XTests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.

%B Journal of Chemical Physics %V 122 %P 9 pages %8 04/01/2005 %G eng %N 13 %0 Conference Proceedings %B Key Topics in Nuclear Structure, Proceedings of the 8th International Spring Seminar on Nuclear Physics %D 2005 %T Coupled Cluster Approaches to Nuclei, Ground States and Excited States %A Piotr Piecuch %A D. J. Dean %A M. Jhorth-Jensen %A K. Kowalski %A T. Papenbrock %A M. Wloch %XWe present recent coupled-cluster studies of nuclei, with an emphasis on ground state and excited states of closed shell nuclei. Perspectives for future studies are delineated.

%B Key Topics in Nuclear Structure, Proceedings of the 8th International Spring Seminar on Nuclear Physics %C Paestum, Italy %8 2005 %G eng %0 Journal Article %J The Journal of Chemical Physics %D 2005 %T Extension of Renormalized Coupled-Cluster Methods Including Triple Excitations to Electronic States of Open-Shell Molecules %A Piotr Piecuch %A M. Wloch %A J. R Gour %A K. Kowalski %XThe general-purpose open-shell implementation of the completely renormalized equation-of-motion coupled-cluster approach with singles, doubles, and noniterative triples [CR-EOMCCSD(T)] is reported. Benchmark calculations for the low-lying doublet and quartet states of the CH radical show that the CR-EOMCCSD(T) method is capable of providing a highly accurate description of ground and excited states of open-shell molecules. This includes states with strong double excitation character, for which the conventional EOMCCSD approach fails.

%B The Journal of Chemical Physics %V 122 %8 06/2005 %G eng %N 21 %0 Journal Article %J The Journal of Chemical Physics %D 2005 %T Extensive Generalization of Renormalized Coupled-Cluster Methods %A Piotr Piecuch %A K. Kowalski %XThe recently developed completely renormalized (CR) coupled-cluster (CC) methods with singles, doubles, and noniterative triples or triples and quadruples [CR-CCSD(T) or CR-CCSD(TQ), respectively], which are based on the method of moments of CC equations (MMCC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], eliminate the failures of the standard CCSD(T) and CCSD(TQ) methods at larger internuclear separations, but they are not rigorously size extensive. Although the departure from strict size extensivity of the CR-CCSD(T) and CR-CCSD(TQ) methods is small, it is important to examine the possibility of formulating the improved CR-CC methods, which are as effective in breaking chemical bonds as the existing CR-CCSD(T) and CR-CCSD(TQ) approaches, which are as easy to use as the CR-CCSD(T) and CR-CCSD(TQ) methods, and which can be made rigorously size extensive. This may be particularly useful for the applications of CR-CC methods and other MMCC approaches in calculations of potential energy surfaces of large many-electron systems and van der Waals molecules, where the additive separability of energies in the noninteracting limit is very important. In this paper, we propose different types of CR-CC approximations, termed the locally renormalized (LR) CCSD(T) and CCSD(TQ) methods, which become rigorously size extensive if the orbitals are localized on nointeracting fragments. The LR-CCSD(T) and LR-CCSD(TQ) methods rely on the form of the energy expression in terms of the generalized moments of CC equations, derived in this work, termed the numerator-denominator-connected MMCC expansion. The size extensivity and excellent performance of the LR-CCSD(T) and LR-CCSD(TQ) methods are illustrated numerically by showing the results for the dimers of stretched HF and LiH molecules and bond breaking in HF and H2O.

%B The Journal of Chemical Physics %V 122 %8 02/09/2005 %G eng %N 7 %0 Journal Article %J Molecular Physics %D 2005 %T Noniterative Corrections to Extended Coupled-Cluster Energies Employing the Generalized Method of Moments of Coupled-Cluster Equations %A Piotr Piecuch %A {P.-D.} Fan %A K. Kowalski %XIt is shown that the extended coupled-cluster method with singles and doubles (ECCSD) does not suffer from the non-variational collapse observed in the standard CCSD calculations when multiple bond breaking is examined. This interesting feature of the single-reference ECCSD theory is used to design the non-iterative CC methods with singles, doubles and non-iterative triples and quadruples, which provide a highly accurate and variational description of potential energy surfaces involving multiple bond breaking with computational steps that scale as with the system size. This is accomplished with the help of the generalized version of the method of moments of coupled-cluster equations (GMMCC), which can be used to correct the results of non-standard CC calculations, such as ECCSD. The theoretical considerations are illustrated by the preliminary results of the ECCSD-based GMMCC calculations for triple bond breaking in N2. Keywords: Coupled-cluster theory; Extended coupled-cluster method; Method of moments of coupled-cluster equations; Non-iterative coupled-cluster approaches; Bond breaking

%B Molecular Physics %V 103 %P 2191-2213 %8 08/2005 %G eng %N 15 & 16 %0 Journal Article %J Nuclear Physics A %D 2005 %T Nuclear Structure Calculations with Coupled-Cluster Methods from Quantum Chemistry %A Piotr Piecuch %A D. J. Dean %A J. R Gour %A G. Hagen %A M. {Hjorth-Jensen} %A K. Kowalski %A T. Papenbrock %A M. Wloch %XWe present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.

%B Nuclear Physics A %V 752 %P 299-308 %8 04/2005 %G eng %0 Journal Article %J Journal of the American Chemical Society %D 2005 %T Where Does the Planar-to-Nonplanar Turnover Occur in Small Gold Clusters %A Piotr Piecuch %A R.M. Olson %A S. Varganov %A M.S. Gordon %A S. Chretien %A H. Metiu %A K. Kowalski %A S. A. Kucharski %A M. Musial %XSeveral levels of theory, including both Gaussian-based and plane wave density functional theory (DFT), second-order perturbation theory (MP2), and coupled cluster methods (CCSD(T)), are employed to study Au6 and Au8 clusters. All methods predict that the lowest energy isomer of Au6 is planar. For Au8, both DFT methods predict that the two lowest isomers are planar. In contrast, both MP2 and CCSD(T) predict the lowest Au8 isomers to be nonplanar.

%B Journal of the American Chemical Society %V 127 %P 1049-1052 %8 12/30/2004 %G eng %N 3 %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