The recently proposed left-eigenstate completely renormalized (CR) coupled-cluster (CC) method with singles, doubles, and noniterative triples, termed CR-CC(2,3) Piecuch and Włoch, J Chem Phys, 2005, 123, 224105; Piecuch et al. Chem Phys Lett, 2006, 418, 467 and the companion CR-EOMCC(2,3) methodology, which has been previously applied to singlet excited states of closed-shell molecular systems Włoch et al. Mol Phys, 2006, 104, 2149 and in which relatively inexpensive noniterative corrections due to triple excitations derived from the biorthogonal method of moments of CC equations (MMCC) are added to the CC singles and doubles (CCSD) or equation-of-motion (EOM) CCSD energies, have been extended to excited states of open-shell species. The resulting highly efficient computer codes for the open-shell CR-EOMCC(2,3) approach exploiting the recursively generated intermediates and fast matrix multiplication routines have been developed and interfaced with the GAMESS package, enabling CR-EOMCC(2,3) calculations for singlet as well as nonsinglet ground and excited states of closed- and open-shell systems using the restricted Hartree–Fock or restricted open-shell Hartree–Fock references. A number of important mathematical and algorithmic details related to formal aspects and computer implementation of the CR-EOMCC(2,3) method have been discussed, in addition to overviewing the key concepts behind the CR-EOMCC(2,3) and biorthogonal MMCC methodologies for ground and excited states, and the numerical results involving low-lying states of the CH, CNC, C2N, N3, and NCO species, including states dominated by two-electron transitions, have been presented. The results of the CR-EOMCC(2,3) calculations have been compared with other CC/EOMCC approaches, including the EOMCCSD and EOMCC singles, doubles, and triples methods, and their full and active-space valence counterparts based on the electron-attached and ionized EOMCC methodologies, and the predecessor of CR-EOMCC(2,3) termed CR-EOMCCSD(T) Kowalski and Piecuch, J Chem Phys, 2004, 120, 1715. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

1 aPiecuch, Piotr1 aGour, J., R1 aWloch, M. uhttps://icer.msu.edu/research/publications/left-eigenstate-completely-renormalized-equation-motion-coupled-cluster02100nas a2200181 4500008004100000245008800041210006900129300001000198490000800208520148500216100001401701700001601715700001501731700001401746700001901760700001801779856012101797 2008 eng d00aApplication of Renormalized Coupled- Cluster Methods to Potential Function of Water0 aApplication of Renormalized Coupled Cluster Methods to Potential a59-780 v1203 aThe goal of this paper is to examine the performance of the conventional and renormalized single-reference coupled-cluster (CC) methods in calculations of the potential energy surface of the water molecule. A comparison with the results of the internally contracted multi-reference configuration interaction calculations including the quasi-degenerate Davidson correction (MRCI(Q)) and the spectroscopically accurate potential energy surface of water resulting from the use of the energy switching (ES) approach indicates that the relatively inexpensive completely renormalized (CR) CC methods with singles (S), doubles (D), and a non-iterative treatment of triples (T) or triples and quadruples (TQ), such as CR-CCSD(T), CR-CCSD(TQ), and the recently developed rigorously size extensive extension of CR-CCSD(T), termed CR-CC(2,3), provide substantial improvements in the results of conventional CCSD(T) and CCSD(TQ) calculations at larger internuclear separations. It is shown that the CR-CC(2,3) results corrected for the effect of quadruply excited clusters through the CR-CC(2,3)+Q approach can compete with the highly accurate MRCI(Q) data. The excellent agreement between the CR-CC(2,3)+Q and MRCI(Q) results suggests ways of improving the global potential energy surface of water resulting from the use of the ES approach in the regions of intermediate bond stretches and intermediate energies connecting the region of the global minimum with the asymptotic regions.

1 aZheng, J.1 aGour, J., R1 aLutz, J.J.1 aWloch, M.1 aPiecuch, Piotr1 aTruhlar, D.G. uhttps://icer.msu.edu/research/publications/application-renormalized-coupled-cluster-methods-potential-function-water02156nas a2200181 4500008004100000245022700041210006900268260001200337490000800349520139600357100001401753700001601767700001501783700001401798700001901812700001801831856012501849 2008 eng d00aA Comparative Assessment of the Perturbative and Renormalized Coupled Cluster Theories with a Non-iterative Treatment of Triple Excitations for Thermochemical Kinetics, Including a Study of Basis Set and Core Correlation E0 aComparative Assessment of the Perturbative and Renormalized Coup c01/20080 v1283 aThe CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.

1 aZheng, J.1 aGour, J., R1 aLutz, J.J.1 aWloch, M.1 aPiecuch, Piotr1 aTruhlar, D.G. uhttps://icer.msu.edu/research/publications/comparative-assessment-perturbative-renormalized-coupled-cluster-theories-non02436nas a2200205 4500008004100000245012200041210006900163260001200232300001400244490000800258520172300266100001701989700001602006700001402022700001402036700001902050700001802069700001802087856012502105 2008 eng d00aStereoelectronic Effects on Molecular Geometries and State-Energy Splittings of Ligated Monocopper Diozygen Complexes0 aStereoelectronic Effects on Molecular Geometries and StateEnergy c03/2008 a3754-37670 v1123 aThe relative energies of side-on versus end-on binding of molecular oxygen to a supported Cu(I) species, and the singlet versus triplet nature of the ground electronic state, are sensitive to the nature of the supporting ligands and, in particular, depend upon their geometric arrangement relative to the O2 binding site. Highly correlated ab initio and density functional theory electronic structure calculations demonstrate that optimal overlap (and oxidative charge transfer) occurs for the side-on geometry, and this is promoted by ligands that raise the energy, thereby enhancing resonance, of the filled Cu dxz orbital that hybridizes with the in-plane π* orbital of O2. Conversely, ligands that raise the energy of the filled Cu dz2 orbital foster a preference for end-on binding as this is the only mode that permits good overlap with the in-plane O2 π*. Because the overlap of Cu dz2 with O2 π* is reduced as compared to the overlap of Cu dxz with the same O2 orbital, the resonance is also reduced, leading to generally more stable triplet states relative to singlets in the end-on geometry as compared to the side-on geometry, where singlet ground states become more easily accessible once ligands are stronger donors. Biradical Cu(II)-O2 superoxide character in the electronic structure of the supported complexes leads to significant challenges for accurate quantum chemical calculations that are best addressed by exploiting the spin-purified M06L local density functional, single-reference completely renormalized coupled-cluster theory, or multireference second-order perturbation theory, all of which provide predictions that are qualitatively and quantitatively consistent with one another.

1 aCramer, C.J.1 aGour, J., R1 aKinal, A.1 aWloch, M.1 aPiecuch, Piotr1 aShahi, A.R.M.1 aGagliardi, L. uhttps://icer.msu.edu/research/publications/stereoelectronic-effects-molecular-geometries-state-energy-splittings-ligated01210nas a2200193 4500008004100000245008000041210006900121260001200190300001200202490000700214520059600221100001400817700001600831700001400847700002100861700001800882700001900900856009700919 2007 eng d00aCoupled-Cluster and Configuration-Interaction Calculations for Heavy Nuclei0 aCoupledCluster and ConfigurationInteraction Calculations for Hea c03/2007 a4 pages0 v983 aWe compare coupled-cluster (CC) and configuration-interaction (CI) results for 56Ni obtained in the pf-shell basis, focusing on practical CC approximations that can be applied to systems with dozens or hundreds of correlated fermions. The weight of the reference state and the strength of correlation effects are controlled by the gap between the f7/2 orbit and the f5/2, p3/2, p1/2 orbits. Independent of the gap, the CC method with 1p-1h and 2p-2h clusters and a noniterative treatment of 3p-3h clusters is as accurate as the more demanding CI approach truncated at the 4p-4h level.

1 aHoroi, M.1 aGour, J., R1 aWloch, M.1 aLodriguito, M.D.1 aBrown, B., A.1 aPiecuch, Piotr uhttps://icer.msu.edu/coupled-cluster-and-configuration-interaction-calculations-heavy-nuclei01203nas a2200205 4500008004100000245005500041210005300096260001200149300001300161490000700174520063000181100001400811700001900825700001700844700001600861700001500877700001400892700001900906856007200925 2007 eng d00aCoupled-Cluster Theory for Three-Body Hamiltonians0 aCoupledCluster Theory for ThreeBody Hamiltonians c09/2007 a11 pages0 v763 aWe derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of 4He. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.

1 aHagen, G.1 aPapenbrock, T.1 aDean, D., J.1 aSchwenk, A.1 aNHogga, A.1 aWloch, M.1 aPiecuch, Piotr uhttps://icer.msu.edu/coupled-cluster-theory-three-body-hamiltonians01855nas a2200157 4500008004100000245017000041210006900211260001200280300001600292490000800308520120900316100001401525700001601539700001901555856012301574 2007 eng d00aExtension of the Renormalized Coupled-Cluster Methods Exploiting Left Eigenstates of the Similarity-Transformed Hamiltonian to Open- Shell Systems: A Benchmark Study0 aExtension of the Renormalized CoupledCluster Methods Exploiting c11/2007 a11359-113820 v1113 aThe recently formulated completely renormalized coupled-cluster method with singles, doubles, and noniterative triples, exploiting the biorthogonal form of the method of moments of coupled-cluster equations (Piecuch, P.; Włoch, M. J. Chem. Phys. 2005, 123, 224105; Piecuch, P.; Włoch, M.; Gour, J. R.; Kinal, A. Chem. Phys. Lett. 2006, 418, 467), termed CR-CC(2,3), is extended to open-shell systems. Test calculations for bond breaking in the OH radical and the ion and singlet−triplet gaps in the CH2, HHeH, and (HFH)- biradical systems indicate that the CR-CC(2,3) approach employing the restricted open-shell Hartree−Fock (ROHF) reference is significantly more accurate than the widely used CCSD(T) method and other noniterative triples coupled-cluster approximations without making the calculations substantially more expensive. A few molecular examples, including the activation energies of the C2H4 + H → C2H5 forward and reverse reactions and the triplet states of the CH2 and H2Si2O2 biradicals, are used to show that the dependence of the ROHF-based CR-CC(2,3) energies on the method of canonicalization of the ROHF orbitals is, for all practical purposes, negligible.

1 aWloch, M.1 aGour, J., R1 aPiecuch, Piotr uhttps://icer.msu.edu/extension-renormalized-coupled-cluster-methods-exploiting-left-eigenstates-similarity-transformed03587nas a2200145 4500008004100000245011300041210006900154300001100223490000700234520302500241100001903266700001403285700002103299856012103320 2007 eng d00aRenormalized Coupled-Cluster Methods: Theoretical Foundations and Application to Potential Function of Water0 aRenormalized CoupledCluster Methods Theoretical Foundations and a63-1210 v163 aConventional single-reference methods fail when bond breaking and other situations characterized by larger non-dynamical correlation effects are examined. In consequence, the adequate treatment of molecular potential energy surfaces involving signiﬁcant bond rearrangements has been the domain of expert multi-reference methods. The question arises if one can develop practical single-reference procedures that could be applied to at least some of the most frequent multi-reference situations, such as single and double bond dissociations. This question is addressed in the present paper by examining the performance of the conventional and renormalized coupled-cluster (CC) methods in calculations of the potential enery surface of the water molecule. A comparison with the results of the highly accurate internally contracted multi-reference conﬁguration interaction calculations including the quasi-degenerate Davidson correction (MRCI(Q)) and the spectroscopically accurate potential energy surface of water resulting from the use of the energy switching (ES) approach indicates that the relatively inexpensive completely renormalized (CR) CC methods with singles (S), doubles (D), and a non-iterative treatment of triples (T) or triples and quadruples (TQ), such as CR-CCSD(T), CR-CCSD(TQ), and the recently developed rigorously size extensive extension of the CR-CCSD(T), termed CR-CC(2,3), provide considerable improvements in the results of conventional CCSD(T) and CCSD(TQ) calculations at larger internuclear separations. It is shown that the CR-CC(2,3) results a posteriori corrected for the effect of quadruply excited clusters (the CR-CC(2,3)+Q approach) can compete with the highly accurate MRCI(Q) data. The excellent agreement between the CR-CC(2,3)+Q and MRCI(Q) results suggests ways of improving the global potential energy surface of water resulting from the use of the ES approach in the regions of intermediate bond stretches and intermediate and higher energies connecting the region of the global minimum with the asymptotic regions. In addition to the examination of the performance of the CR-CCSD(T), CR-CCSD(TQ), CR-CC(2,3), and CR-CC(2,3)+Q approaches, we provide a thorough review of the method of moments of CC equations (MMCC), as applied to ground electronic states, including the most recent biorthogonal formulation of MMCC theory employing the left eigenstates of the similarity-transformed Hamiltonian, and other mathematical and physical concepts that lie behind all renormalized CC approximations. In particular, we discuss the similarities and differences between the older CR-CCSD(T) and CR-CCSD(TQ) approximations and the recently formulated size extensive renormalized CC methods, such as CR-CC(2,3), and open questions that emerge in the process of designing higher-order schemes based on the biorthogonalMMCC formalism, such as CR-CC(2,4), which describe the combined effect of triples (already present in CR-CC(2,3) calculations) and quadruples in a proper manner.

1 aPiecuch, Piotr1 aWloch, M.1 aVerandas, A.J.C. uhttps://icer.msu.edu/renormalized-coupled-cluster-methods-theoretical-foundations-and-application-potential-function01273nas 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-chemistry00864nas a2200193 4500008004100000245003800041210003800079300001400117490000700131520031100138653006000449100001900509700001700528700001600545700001400561700002600575700001400601856005500615 2006 eng d00aCoupled Cluster Theory for Nuclei0 aCoupled Cluster Theory for Nuclei a5338-53450 v203 aThis presentation focuses on some of the recent developments in low-energy nuclear structure theory, with emphasis on applications of coupled-cluster theory. We report on results for ground and excited states in 4He and 16O, and about extensions of coupled-cluster theory to treat three-body forces.

10aNuclear structure; light nuclei; coupled-cluster theory1 aPapenbrock, T.1 aDean, D., J.1 aGour, J., R1 aHagen, G.1 aHjorth-Jensen}, M., {1 aWloch, M. uhttps://icer.msu.edu/coupled-cluster-theory-nuclei01833nas a2200181 4500008004100000245006500041210006400106260001100170300001300181490000700194520127600201100001901477700001601496700002601512700001401538700001701552856008201569 2006 eng d00aCoupled-Cluster Calculations for Valence Systems around 16 O0 aCoupledCluster Calculations for Valence Systems around 16 O c8/2006 a18 pages0 v743 aWe study the ground and low-lying excited states of 15O, 17O, 15N, and 17F using modern two-body nucleon-nucleon interactions and the suitably designed variants of the ab initio equation-of-motion coupled-cluster theory aimed at an accurate description of systems with valence particles and holes. A number of properties of 15O, 17O, 15N, and 17F, including ways the energies of ground and excited states of valence systems around 16O change as functions of the number of nucleons, are correctly reproduced by the equation-of-motion coupled-cluster calculations performed in up to eight major-oscillator shells. Certain disagreements with experiment are in part because of the degrees of freedom such as three-body interactions not accounted for in our effective two-body Hamiltonians. In particular, the calculated binding energies of 15O/15N and 17O/17F enable us to rationalize the discrepancy between the experimental and recently published [Phys. Rev. Lett. 94, 212501 (2005)] equation-of-motion coupled-cluster excitation energies for the Jπ=3- state of 16O. Our calculations demonstrate the feasibility of the equation-of-motion coupled-cluster methods to deal with valence systems around closed-shell nuclei and to provide results for systems beyond A=16.

1 aPiecuch, Piotr1 aGour, J., R1 aHjorth-Jensen}, M., {1 aWloch, M.1 aDean, D., J. uhttps://icer.msu.edu/coupled-cluster-calculations-valence-systems-around-16-o01855nas a2200181 4500008004100000245006400041210006300105260001200168300001100180490000700191520130200198100001601500700001901516700002601535700001401561700001701575856008101592 2006 eng d00aCoupled-cluster calculations for valence systems around O160 aCoupledcluster calculations for valence systems around O16 c08/2006 a0243100 v743 aWe study the ground and low-lying excited states of {15O,} {17O,} {15N,} and {17F} using modern two-body nucleon-nucleon interactions and the suitably designed variants of the ab initio equation-of-motion coupled-cluster theory aimed at an accurate description of systems with valence particles and holes. A number of properties of {15O,} {17O,} {15N,} and {17F,} including ways the energies of ground and excited states of valence systems around {16O} change as functions of the number of nucleons, are correctly reproduced by the equation-of-motion coupled-cluster calculations performed in up to eight major-oscillator shells. Certain disagreements with experiment are in part because of the degrees of freedom such as three-body interactions not accounted for in our effective two-body Hamiltonians. In particular, the calculated binding energies of {15O/15N} and {17O/17F} enable us to rationalize the discrepancy between the experimental and recently published {[Phys.} Rev. Lett. 94, 212501 (2005)] equation-of-motion coupled-cluster excitation energies for the Jπ=3- state of {16O.} Our calculations demonstrate the feasibility of the equation-of-motion coupled-cluster methods to deal with valence systems around closed-shell nuclei and to provide results for systems beyond A=16.

1 aGour, J., R1 aPiecuch, Piotr1 aHjorth-Jensen}, M., {1 aWloch, M.1 aDean, D., J. uhttps://icer.msu.edu/coupled-cluster-calculations-valence-systems-around-o1602232nas 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-isomers01765nas a2200169 4500008004100000245014000041210006900181260001100250300001400261490000800275520098500283653015801268100001901426700001601445700001401461856012001475 2006 eng d00aExtension of the Active-Space Equation-of- Motion Coupled-Cluster Methods to Radical Systems: The EA-EOMCCSDt and IPEOMCCSDt Approaches0 aExtension of the ActiveSpace Equationof Motion CoupledCluster Me c7/2006 a2854-28740 v1063 aThe development of the active-space variants of the electron-attached (EA) and ionized (IP) equation-of-motion coupled-cluster (EOMCC) methods, in which higher-than-doubly excited components of the cluster operator T and higher than 2p-1h or 2h-1p components of the electron attaching and ionizing operators R are defined through the use of active orbitals, is discussed. As shown by preliminary test calculations of adiabatic excitation energies and potential energy curves for the low-lying states of the CH and OH radicals, the basic active-space EA-EOMCC and IP-EOMCC methods, referred to as the EA-EOMCCSDt and IP-EOMCCSDt approaches, are capable of accuratelydescribing the ground and excited states of open-shell systems, even at the moderately stretched nuclear geometries and even for states with a strong multi-determinantal or doubly excited character, at the low costs that are on the order of those characterizing the standard EOMCC singles and doubles method.

10aoupled-cluster theory;equation-of-a motion coupled-cluster method;active-space coupled-cluster approaches;electronic-attached and ionized states;radicals1 aPiecuch, Piotr1 aGour, J., R1 aWloch, M. uhttps://icer.msu.edu/extension-active-space-equation-motion-coupled-cluster-methods-radical-systems-ea-eomccsdt-and01919nas 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-functions00503nas a2200145 4500008004100000245007200041210006900113300001100182490000700193100001900200700001400219700001900233700001600252856008900268 2006 eng d00aNon-iterative Coupled-Cluster Methods for Excited Electronic States0 aNoniterative CoupledCluster Methods for Excited Electronic State a45-1060 v151 aPiecuch, Piotr1 aWloch, M.1 aLodriguito, M.1 aGour, J., R uhttps://icer.msu.edu/non-iterative-coupled-cluster-methods-excited-electronic-states01338nas a2200169 4500008004100000245011100041210006900152260001200221300001400233490000800247520073400255100001900989700001401008700001601022700001401038856011601052 2006 eng d00aSingle-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals0 aSinglereference sizeextensive noniterative coupledcluster approa c02/2006 a467–4740 v4183 aWe propose the non-iterative, completely renormalized (CR) coupled-cluster (CC) approaches, including the CR-CC(2, 3) method which offers considerable improvements over the CCSD(T) approach without a significant increase in the computer effort. The CR-CC(2, 3) method, in which the CCSD (CC singles and doubles) energy is corrected for the effect of triples, is size extensive, competitive with CCSD(T) in calculations for non-degenerate states, and as accurate as the expensive CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving trimethylene suggest that CR-CC(2, 3) may be applicable to biradicals.

1 aPiecuch, Piotr1 aWloch, M.1 aGour, J., R1 aKinal, A. uhttps://icer.msu.edu/single-reference-size-extensive-non-iterative-coupled-cluster-approaches-bond-breaking-and01465nas a2200181 4500008004100000245010100041210006900142260001500211300001600226490000800242520084100250100001701091700001401108700001401122700001901136700001801155856011001173 2006 eng d00aTheoretical Characterization of End-on and Side-on Peroxide Coordination in Ligated Cu2O2 Models0 aTheoretical Characterization of Endon and Sideon Peroxide Coordi c09/15/2006 a11557-115680 v1103 aThe relative energetics of μ-η1:η1 (trans end-on) and μ-η2:η2 (side-on) peroxo isomers of Cu2O2 fragments supported by 0, 2, 4, and 6 ammonia ligands have been computed with various density functional, coupled-cluster, and multiconfigurational protocols. There is substantial disagreement between the different levels for most cases, although completely renormalized coupled-cluster methods appear to offer the most reliable predictions. The significant biradical character of the end-on peroxo isomer proves problematic for the density functionals, while the demands on active space size and the need to account for interactions between different states in second-order perturbation theory prove challenging for the multireference treatments. In the latter case, it proved impossible to achieve any convincing convergence.

1 aCramer, C.J.1 aKinal, A.1 aWloch, M.1 aPiecuch, Piotr1 aGagliardi, L. uhttps://icer.msu.edu/theoretical-characterization-end-and-side-peroxide-coordination-ligated-cu2o2-models02131nas a2200181 4500008004100000245012100041210006900162260001200231300001600243490000800259520146800267100001701735700001401752700001901766700002401785700001801809856012201827 2006 eng d00aTheoretical Models on the Cu2O2 Torture Track. Mechanistic Implications for Oxytyrosinase and Small-molecule Analogs0 aTheoretical Models on the Cu2O2 Torture Track Mechanistic Implic c06/2007 a1991–20040 v1103 aAccurately describing the relative energetics of alternative bis(mu-oxo) and mu-eta2:eta2 peroxo isomers of Cu2O2 cores supported by 0, 2, 4, and 6 ammonia ligands is remarkably challenging for a wide variety of theoretical models, primarily owing to the difficulty of maintaining a balanced description of rapidly changing dynamical and nondynamical electron correlation effects and a varying degree of biradical character along the isomerization coordinate. The completely renormalized coupled-cluster level of theory including triple excitations and extremely efficient pure density functional levels of theory quantitatively agree with one another and also agree qualitatively with experimental results for Cu2O2 cores supported by analogous but larger ligands. Standard coupled-cluster methods, such as CCSD(T), are in most cases considerably less accurate and exhibit poor convergence in predicted relative energies. Hybrid density functionals significantly underestimate the stability of the bis(mu-oxo) form, with the magnitude of the error being directly proportional to the percentage Hartree-Fock exchange in the functional. Single-root CASPT2 multireference second-order perturbation theory, by contrast, significantly overestimates the stability of bis(mu-oxo) isomers. Implications of these results for modeling the mechanism of C-H bond activation by supported Cu2O2 cores, like that found in the active site of oxytyrosinase, are discussed.

1 aCramer, C.J.1 aWloch, M.1 aPiecuch, Piotr1 aPuzzarini, Cristina1 aGagliardi, L. uhttps://icer.msu.edu/theoretical-models-cu2o2-torture-track-mechanistic-implications-oxytyrosinase-and-small-molecule00614nas a2200157 4500008004100000245012500041210006900166260001100235300001400246490000800260100001900268700001400287700002100301700001600322856011800338 2006 eng d00aTwo New Classes of Non-Iterative Coupled-Cluster Methods Derived from the Method of Moments of Coupled-Cluster Equations0 aTwo New Classes of NonIterative CoupledCluster Methods Derived f c7/2006 a2149-21720 v1041 aPiecuch, Piotr1 aWloch, M.1 aLogriguito, M.D.1 aGour, J., R uhttps://icer.msu.edu/two-new-classes-non-iterative-coupled-cluster-methods-derived-method-moments-coupled-cluster01233nas 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-300613nas a2200145 4500008004100000245014900041210006900190260001200259300001300271490000800284100001900292700001600311700001400327856012600341 2005 eng d00aActive-Space Equation-of=Motion Coupled-Cluster Methods for Excited States of Radicals and Other Open-Shell Systems: EA-EOMCCSDt and IP-EOMCCSDt0 aActiveSpace EquationofMotion CoupledCluster Methods for Excited c10/2005 a14 pages0 v1231 aPiecuch, Piotr1 aGour, J., R1 aWloch, M. uhttps://icer.msu.edu/research/publications/active-space-equation-ofmotion-coupled-cluster-methods-excited-states-radicals02028nas a2200193 4500008004100000245012400041210006900165260005600234300001000290490000800300520128900308100001901597700001401616700001601630700001701646700002601663700001901689856012601708 2005 eng d00aBridging Quantum Chemistry and Nuclear Structure Theory: Coupled-Cluster Calculations for Closed- and Open-Shell Nuclei0 aBridging Quantum Chemistry and Nuclear Structure Theory CoupledC aMelville, NYbAmerican Institute of Physicsc7/2005 a28-450 v7773 aWe review basic elements of the single-reference coupled-cluster theory and discuss large scale ab initio calculations of ground and excited states of 15O, 16O, and 17O using coupled-cluster methods and algorithms developed in quantum chemistry. By using realistic two-body interactions and the renormalized form of the Hamiltonian obtained with a no-core G-matrix approach, we obtain the converged results for 16O and promising preliminary results for 15O and 17O at the level of two-body interactions. The calculated properties other than energies include matter density, charge radius, and charge form factor. The relatively low costs of coupled-cluster calculations, which are characterized by the low-order polynomial scaling with the system size, enable us to probe large model spaces with up to 7 or 8 major oscillator shells, for which non-truncated shell-model calculations for nuclei with A = 15 17 active particles are presently not possible. We argue that the use of coupled-cluster methods and computer algorithms developed by quantum chemists to calculate properties of nuclei is an important step toward the development of accurate and affordable many-body theories that cross the boundaries of various physical sciences. ©2005 American Institute of Physics

1 aPiecuch, Piotr1 aWloch, M.1 aGour, J., R1 aDean, D., J.1 aHjorth-Jensen}, M., {1 aPapenbrock, T. uhttps://icer.msu.edu/bridging-quantum-chemistry-and-nuclear-structure-theory-coupled-cluster-calculations-closed-and-open01534nas 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-excitations01746nas 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-chemistry