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.

1 aPiecuch, Piotr1 aPimienta, I., S. O.1 aFan, P.-D.1 aKowalski, K. uhttps://icer.msu.edu/new-alternatives-accurate-electronic-structure-calculations-potential-energy-surfaces-involving-bond01273nas a2200205 4500008004100000245008900041210006900130260001200199300001200211490000700223520060600230100001900836700001400855700001700869700001600886700002600902700001900928700001700947856010300964 2006 eng d00aAb Initio Coupled-Cluster Calculations for Nuclei Using Methods of Quantum Chemistry0 aAb Initio CoupledCluster Calculations for Nuclei Using Methods o c09/2005 a485-4880 v253 aWe 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.

1 aPiecuch, Piotr1 aWloch, M.1 aDean, D., J.1 aGour, J., R1 aHjorth-Jensen}, M., {1 aPapenbrock, T.1 aKowalski, K. uhttps://icer.msu.edu/ab-initio-coupled-cluster-calculations-nuclei-using-methods-quantum-chemistry01498nas a2200181 4500008004100000245011900041210006900160260001200229300001200241490000800253520084400261100001901105700001501124700001701139700001501156700002401171856012101195 2006 eng d00aAutomated derivation and parallel computer implementation of renormalized and active-space coupled-cluster methods0 aAutomated derivation and parallel computer implementation of ren c08/2005 a79–970 v1063 aOur 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

1 aPiecuch, Piotr1 aHirata, So1 aKowalski, K.1 aFan, P.-D.1 aWindus, Theresa, L. uhttps://icer.msu.edu/automated-derivation-and-parallel-computer-implementation-renormalized-and-active-space-coupled02232nas a2200253 4500008004100000245008800041210006900129260001100198300001400209490000800223520146400231100001901695700001601714700001401730700001701744700001501761700001801776700001401794700001701808700001401825700001801839700001501857856010601872 2006 eng d00aExperimental and Theoretical UV Characterizations of Acetyloacetone and its Isomers0 aExperimental and Theoretical UV Characterizations of Acetyloacet c2/2006 a3920-39260 v1103 aCryogenic 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.

1 aPiecuch, Piotr1 aCoussan, S.1 aFerro, Y.1 aTrivella, A.1 aRoubin, P.1 aWieczorek, R.1 aManca, C.1 aKowalski, K.1 aWloch, M.1 aKucharski, S.1 aMusial, M. uhttps://icer.msu.edu/experimental-and-theoretical-uv-characterizations-acetyloacetone-and-its-isomers01919nas a2200181 4500008004100000245010400041210006900145260001200214300001100226490000800237520110200245653019501347100001901542700002101561700001701582700001401599856012401613 2006 eng d00aNon-Iterative Coupled- Cluster Methods Employing Multi-Reference Perturbation Theory Wave Functions0 aNonIterative Coupled Cluster Methods Employing MultiReference Pe c10/2006 a89-1040 v7713 aA 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+.

10aCoupled-cluster theory; Equation-of-motion coupled-cluster methods; Method of moments of coupled-cluster equations; Multi-reference perturbation theory; Non-iterative coupled-cluster methods1 aPiecuch, Piotr1 aLodriguito, M.D.1 aKowalski, K.1 aWloch, M. uhttps://icer.msu.edu/non-iterative-coupled-cluster-methods-employing-multi-reference-perturbation-theory-wave-functions01260nas a2200205 4500008004100000245004300041210004200084260001200126300001100138490000700149520068900156100001500845700001700860700001600877700002600893700001700919700001900936700001600955856008300971 2005 eng d00aAb Initio Coupled-Cluster Study of 16O0 aAb Initio CoupledCluster Study of 16O c06/2005 a2125010 v943 aWe 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.

1 aWłoch, M.1 aDean, D., J.1 aGour, J., R1 aHjorth-Jensen}, M., {1 aKowalski, K.1 aPapenbrock, T.1 aPiecuch, P. uhttps://icer.msu.edu/research/publications/ab-initio-coupled-cluster-study-16o01233nas a2200193 4500008004100000245004100041210004000082260001200122490000700134520068900141100001900830700001400849700001700863700001600880700002600896700001700922700001900939856008100958 2005 eng d00aAb Initio Coupled-Cluster Study of O0 aAb Initio CoupledCluster Study of O c06/20050 v943 aWe 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.

1 aPiecuch, Piotr1 aWloch, M.1 aDean, D., J.1 aGour, J., R1 aHjorth-Jensen}, M., {1 aKowalski, K.1 aPapenbrock, T. uhttps://icer.msu.edu/research/publications/ab-initio-coupled-cluster-study-o01316nas a2200181 4500008004100000245006800041210006600109260001200175300001200187490000800199520074000207100001900947700001700966700001500983700001400998700001701012856010501029 2005 eng d00aActive-Space Coupled-Cluster Study of Electronic States of Be 30 aActiveSpace CoupledCluster Study of Electronic States of Be 3 c08/2005 a6 pages0 v1233 aThe 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.

1 aPiecuch, Piotr1 aKowalski, K.1 aHirata, S.1 aWloch, M.1 aWindus, T.L. uhttps://icer.msu.edu/research/publications/active-space-coupled-cluster-study-electronic-states-be-301534nas a2200265 4500008004100000245007500041210006900116260001500185300001200200490000800212520073300220100001900953700002000972700001600992700001301008700001701021700001401038700002201052700001801074700001401092700001701106700001301123700001701136856011501153 2005 eng d00aComparison of Low-Order Multireference Many-Body Perturbation Theories0 aComparison of LowOrder Multireference ManyBody Perturbation Theo c04/01/2005 a9 pages0 v1223 aTests 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.

1 aPiecuch, Piotr1 aChaudhuri, R.K.1 aFreed, K.F.1 aHose, G.1 aKowalski, K.1 aWloch, M.1 aChattopadhyay, S.1 aMukherjee, D.1 aRolik, R.1 aSzabados, A.1 aToth, G.1 aSurjan, P.R. uhttps://icer.msu.edu/research/publications/comparison-low-order-multireference-many-body-perturbation-theories00768nas a2200169 4500008004100000245007500041210006900116260002500185520018800210100001900398700001700417700002200434700001700456700001900473700001400492856009200506 2005 eng d00aCoupled Cluster Approaches to Nuclei, Ground States and Excited States0 aCoupled Cluster Approaches to Nuclei Ground States and Excited S aPaestum, Italyc20053 aWe 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.

1 aPiecuch, Piotr1 aDean, D., J.1 aJhorth-Jensen, M.1 aKowalski, K.1 aPapenbrock, T.1 aWloch, M. uhttps://icer.msu.edu/coupled-cluster-approaches-nuclei-ground-states-and-excited-states01156nas a2200157 4500008004100000245012800041210006900169260001200238490000800250520055100258100001900809700001400828700001600842700001700858856012300875 2005 eng d00aExtension of Renormalized Coupled-Cluster Methods Including Triple Excitations to Electronic States of Open-Shell Molecules0 aExtension of Renormalized CoupledCluster Methods Including Tripl c06/20050 v1223 aThe 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.

1 aPiecuch, Piotr1 aWloch, M.1 aGour, J., R1 aKowalski, K. uhttps://icer.msu.edu/research/publications/extension-renormalized-coupled-cluster-methods-including-triple-excitations02334nas a2200133 4500008004100000245006900041210006800110260001500178490000800193520185400201100001902055700001702074856010902091 2005 eng d00aExtensive Generalization of Renormalized Coupled-Cluster Methods0 aExtensive Generalization of Renormalized CoupledCluster Methods c02/09/20050 v1223 aThe 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.

1 aPiecuch, Piotr1 aKowalski, K. uhttps://icer.msu.edu/research/publications/extensive-generalization-renormalized-coupled-cluster-methods01726nas a2200157 4500008004100000245013900041210006900180260001200249300001400261490000800275520111600283100001901399700001701418700001701435856011601452 2005 eng d00aNoniterative Corrections to Extended Coupled-Cluster Energies Employing the Generalized Method of Moments of Coupled-Cluster Equations0 aNoniterative Corrections to Extended CoupledCluster Energies Emp c08/2005 a2191-22130 v1033 aIt 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

1 aPiecuch, Piotr1 aFan, {P.-D.}1 aKowalski, K. uhttps://icer.msu.edu/research/publications/noniterative-corrections-extended-coupled-cluster-energies-employing01746nas a2200217 4500008004100000245008700041210006900128260001200197300001200209490000800221520103700229100001901266700001701285700001601302700001401318700002601332700001701358700001901375700001401394856012001408 2005 eng d00aNuclear Structure Calculations with Coupled-Cluster Methods from Quantum Chemistry0 aNuclear Structure Calculations with CoupledCluster Methods from c04/2005 a299-3080 v7523 aWe 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.

1 aPiecuch, Piotr1 aDean, D., J.1 aGour, J., R1 aHagen, G.1 aHjorth-Jensen}, M., {1 aKowalski, K.1 aPapenbrock, T.1 aWloch, M. uhttps://icer.msu.edu/research/publications/nuclear-structure-calculations-coupled-cluster-methods-quantum-chemistry01158nas a2200229 4500008004100000245007700041210006900118260001500187300001400202490000800216520046200224100001900686700001600705700001700721700001700738700001700755700001400772700001700786700002200803700001500825856008800840 2005 eng d00aWhere Does the Planar-to-Nonplanar Turnover Occur in Small Gold Clusters0 aWhere Does the PlanartoNonplanar Turnover Occur in Small Gold Cl c12/30/2004 a1049-10520 v1273 aSeveral 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.

1 aPiecuch, Piotr1 aOlson, R.M.1 aVarganov, S.1 aGordon, M.S.1 aChretien, S.1 aMetiu, H.1 aKowalski, K.1 aKucharski, S., A.1 aMusial, M. uhttps://icer.msu.edu/where-does-planar-nonplanar-turnover-occur-small-gold-clusters02386nas a2200241 4500008004100000245015000041210006900191260001200260300001400272490000800286520138300294653017701677100001901854700001701873700002401890700001501914700002101929700002301950700002201973700001301995700001502008856012102023 2004 eng d00aMethod of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states0 aMethod of moments of coupledcluster equations a new formalism fo c07/2004 a349–3930 v1123 aThe 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.

10aCoupled-cluster theory - Method of moments of coupled-cluster equations - Renormalized coupled-cluster methods - extended coupled cluster theory - Potential energy surfaces1 aPiecuch, Piotr1 aKowalski, K.1 aPimienta, I., S. O.1 aFan, P.-D.1 aLodriguito, M.D.1 aMcGuire}, M., J. {1 aKucharski, S., A.1 aKuś, T.1 aMusial, M. uhttps://icer.msu.edu/research/publications/method-moments-coupled-cluster-equations-new-formalism-designing-accurate