A multilevel extension of the local correlation “cluster-in-molecule” (CIM) framework, which enables one to combine different quantum chemistry methods to treat different regions in a large molecular system without splitting it into ad hoc fragments and saturating dangling bonds, is proposed. The resulting schemes combine higher-level methods, such as the completely renormalized coupled-cluster (CC) approach with singles, doubles, and noniterative triples, termed CR-CC(2,3), to treat the reactive part of a large molecular system, and lower-order methods, such as the second-order Møller−Plesset perturbation theory (MP2), to handle the chemically inactive regions. The multilevel CIM-CC/MP2 approaches preserve the key features of all CIM methods, such as the use of orthonormal localized orbitals and coarse-grain parallelism, while substantially reducing the already relatively low costs of the single-level CIM-CC calculations. Illustrative calculations include bond breaking in dodecane and the reactions of the bis(2,4,4-trimethylpentyl)dithiophosphinic acid with one and two water molecules.

1 aLi, Wei1 aPiecuch, Piotr uhttps://icer.msu.edu/research/publications/multi-level-extension-cluster-molecule-local-correlation-methodology-merging00512nas a2200133 4500008004100000245008700041210006900128260001200197490000700209100000500216700001600221700001900237856012200256 2009 eng d00aAb Initio Coupled-Cluster and Configuration Interaction Calculations for O Using V0 aAb Initio CoupledCluster and Configuration Interaction Calculati c05/20090 v791 a1 aGour, J., R1 aPiecuch, Piotr uhttps://icer.msu.edu/research/publications/ab-initio-coupled-cluster-configuration-interaction-calculations-o-using-v01184nas a2200157 4500008004100000245009900041210006900140260001200209300001200221490000800233520062000241100000500861700002200866700001900888856011900907 2009 eng d00aCenter-of-Mass Problem in Truncated Configuration Interaction and Coupled-Cluster Calculations0 aCenterofMass Problem in Truncated Configuration Interaction and c08/2009 a334-3390 v6793 aThe problem of center-of-mass (CM) contaminations in ab initio nuclear structure calculations using configuration interaction (CI) and coupled-cluster (CC) approaches is analyzed. A rigorous and quantitative scheme for diagnosing the CM contamination of intrinsic observables is proposed and applied to ground-state calculations for 4He and 16O. The CI and CC calculations for 16O based on model spaces defined via a truncation of the single-particle basis lead to sizable CM contaminations, while the importance-truncated no-core shell model based on the NmaxΩ space is virtually free of CM contaminations.

1 a1 aGour, Jeffrey, R.1 aPiecuch, Piotr uhttps://icer.msu.edu/research/publications/center-mass-problem-truncated-configuration-interaction-coupled-cluster02843nas a2200157 4500008004100000245022400041210006900265260001200334300001400346490000800360520214900368100001902517700001602536700001402552856011902566 2009 eng d00aLeft-Eigenstate Completely Renormalized Equation-of-motion Coupled-Cluster Methods: Review of Key Concepts, Extension to Excited States of Open-Shell Systems, and Comparison with Electron-Attached and ionized Approaches0 aLeftEigenstate Completely Renormalized Equationofmotion CoupledC c11/2009 a3268-33040 v1093 aThe 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-cluster01687nas a2200157 4500008004100000245009400041210006900135260001200204490000800216520112100224100001201345700001901357700001601376700001501392856012201407 2009 eng d00aLocal Correlation Calculations Using Standard and Renormalized Coupled-Cluster Approaches0 aLocal Correlation Calculations Using Standard and Renormalized C c09/20090 v1313 ahe linear scaling local correlation approach, termed “cluster-in-molecule” (CIM), is extended to the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and noniterative triples, including CCSD(T) and the completely renormalized CR-CC(2,3) approach. The resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods are characterized by (i) the linear scaling of the CPU time with the system size, (ii) the use of orthonormal orbitals in the CC subsystem calculations, (iii) the natural parallelism, (iv) the high computational efficiency, enabling calculations for much larger systems and at higher levels of CC theory than previously possible, and (v) the purely noniterative character of local triples corrections. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is shown that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches accurately reproduce the corresponding canonical CC correlation and relative energies, while offering savings in the computer effort by orders of magnitude.

1 aLi, Wei1 aPiecuch, Piotr1 aGour, J., R1 aLi, Shuhua uhttps://icer.msu.edu/research/publications/local-correlation-calculations-using-standard-renormalized-coupled-cluster02324nas a2200157 4500008004100000245021700041210007300258260001200331300001200343490000800355520162000363100001401983700001601997700001902013856013402032 2009 eng d00aLow-Lying Valence Excited States of CNC, C₂N, N₃ and NCO Studied Using the Electron-Attached and Ionized Symmetry-Adapted Cluster Configuration-Interaction and Equation-of-Motion Coupled-Cluster Methodologies0 aLowLying Valence Excited States of CNC C₂N N₃ and NCO Studied Us c04/2009 a871-8800 v1073 aLow-lying valence excited states of four open-shell triatomic molecules, CNC, C2N, N3, and NCO, are investigated using the electron-attached (EA) and ionized (IP) symmetry-adapted-cluster configuration-interaction (SAC-CI) general-R as well as the full and active-space EA and IP equation-of-motion coupled-cluster (EOMCC) methods. A comparison is made with experiment and with the results of the completely renormalized (CR) CC calculations with singles, doubles, and non-iterative triples defining the CR-CC(2,3) approach. Adiabatic excitation energies of the calculated states are in reasonable agreement with the experimental values, provided that the 3-particle-2-hole (3p-2h) components in the electron attaching operator, as in the EA SAC-CI SDT-R and EA EOMCCSD(3p-2h) approaches, are included in the calculations for the excited states of C2N and CNC which have a predominantly two-electron character. The results also reveal that the active-space EA/IP EOMCC schemes with up to 3p-2h/3h-2p excitations are able to accurately reproduce the results of their much more expensive parent methods while requiring significantly less computational effort. Furthermore, the more 'black-box' CR-CC(2,3) approach calculates the lowest state of each symmetry with the same accuracy as that obtained with the EA/IP SAC-CI SDT-R and EA/IP EOMCCSD(3p-2h/3h-2p) methods, confirming the significance of higher-order correlation effects in obtaining an accurate description of excited states of radicals, particularly the valence excited states of the CNC and C2N species dominated by two-electron processes.

1 aEhara, M.1 aGour, J., R1 aPiecuch, Piotr uhttps://icer.msu.edu/research/publications/low-lying-valence-excited-states-cnc-c%E2%82%82n-n%E2%82%83-nco-studied-using-electron01793nas a2200145 4500008004100000245015600041210006900197260001200266300001400278490000800292520118900300100001601489700001901505856012301524 2009 eng d00aMethod of Moments for the Continuous Transition Between the Brillouin-Wigner-Type and Rayleigh-Schrodinger-Type Multireference Coupled Cluster Theories0 aMethod of Moments for the Continuous Transition Between the Bril c01/2009 a1209-12210 v1073 aWe apply the method of moments to the multireference (MR) coupled cluster (CC) formalism representing the continuous transition between the Brillouin-Wigner-type and Rayleigh-Schr\"{o}dinger-type theories based on the Jeziorski-Monkhorst wave function ansatz and derive the formula for the noniterative energy corrections to the corresponding MRCC energies that recover the exact, full configuration interaction energies in the general model space case, including complete and incomplete model spaces. We also extend the relationship between the generalized moments of the state-universal (SU) MRCC equations within the Jeziorski-Monkhorst and Kucharski-Bartlett formulations of the SUMRCC theory to the general model space case. Finally, we argue that in the complete model space case, the relationship between moments of the SUMRCC equations corresponding to the Jeziorski-Monkhorst and Kucharski-Bartlett formulations of the SUMRCC theory, derived in this work, implies an equivalence of these two formulations of the SUMRCC approach, provided that the disconnected linked terms are included in the Kucharski-Bartlett formulation, and verify this statement numerically.

1 aPittner, J.1 aPiecuch, Piotr uhttps://icer.msu.edu/research/publications/method-moments-continuous-transition-between-brillouin-wigner-type-rayleigh02667nas a2200157 4500008004100000245008500041210006900126260001200195300001400207490000800221520211000229100001902339700001302358700001802371856012002389 2009 eng d00aThermochemical Kinetics for Multi-reference Systems: Addition Reactions of Ozone0 aThermochemical Kinetics for Multireference Systems Addition Reac c04/2009 a5786-57990 v1133 aThe 1,3-dipolar cycloadditions of ozone to ethyne and ethene provide extreme examples of multireference singlet-state chemistry, and they are examined here to test the applicability of several approaches to thermochemical kinetics of systems with large static correlation. Four different multireference diagnostics are applied to measure the multireference characters of the reactants, products, and transition states; all diagnostics indicate significant multireference character in the reactant portion of the potential energy surfaces. We make a more complete estimation of the effect of quadruple excitations than was previously available, and we use this with CCSDT/CBS estimation of Wheeler et al. (Wheeler, S. E.; Ess, D. H.; Houk, K. N. J. Phys. Chem. A 2008, 112, 1798.) to make new best estimates of the van der Waals association energy, the barrier height, and the reaction energy to form the cycloadduct for both reactions. Comparing with these best estimates, we present comprehensive mean unsigned errors for a variety of coupled cluster, multilevel, and density functional methods. Several computational aspects of multireference reactions are considered: (i) the applicability of multilevel theory, (ii) the convergence of coupled cluster theory for reaction barrier heights, (iii) the applicability of completely renormalized coupled cluster methods to multireference systems, (iv) the treatment by density functional theory, (v) the multireference perturbation theory for multireference reactions, and (vi) the relative accuracy of scaling-type multilevel methods as compared with additive ones. It is found that scaling-type multilevel methods do not perform better than the additive-type multilevel methods. Among the 48 tested density functionals, only M05 reproduces the best estimates within their uncertainty. Multireference perturbation theory based on the complete-active-space reference wave functions constructed using a small number of reaction-specific active orbitals gives accurate forward barrier heights; however, it significantly underestimates reaction energies.

1 aPiecuch, Piotr1 aZhao, Y.1 aTruhlar, D.G. uhttps://icer.msu.edu/research/publications/thermochemical-kinetics-multi-reference-systems-addition-reactions-ozone02100nas 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-ligated02707nas a2200301 4500008004100000245017900041210006900220260001200289300001300301490000800314520164400322653003101966653003301997653002402030653001902054653001802073653001802091653001502109653002202124653002102146653003002167100001602197700001902213700001602232700001402248700001802262856012502280 2007 eng d00aActive-Space Symmetry-Adapted-Cluster Configuration-Interaction and Equation-of-Motion Cluster Methods for High Accuracy Calculations of Potential Energy Surfaces of Radicals0 aActiveSpace SymmetryAdaptedCluster ConfigurationInteraction and c04/2007 a28 pages0 v1263 aThe electron-attached (EA) and ionized (IP) symmetry-adapted-cluster configuration-interaction (SAC-CI) methods and their equation-of-motion coupled-cluster (EOMCC) analogs provide an elegant framework for studying open-shell systems. As shown in this study, these schemes require the presence of higher-order excitations, such as the four-particle-three-hole (4p-3h) or four-hole–three-particle (4h-3p) terms, in the electron attaching or ionizing operator R in order to produce accurate ground- and excited-state potential energy surfaces of radicals along bond breaking coordinates. The full inclusion of the 4p-3h/4h-3p excitations in the EA/IP SAC-CI and EOMCC methods leads to schemes which are far too expensive for calculations involving larger radicals and realistic basis sets. In order to reduce the large costs of such schemes without sacrificing accuracy, the active-space EA/IP EOMCC methodology [ J. R. Gour et al., J. Chem. Phys. 123, 134113 (2005) ] is extended to the EA/IP SAC-CI approaches with 4p-3h/4h-3p excitations. The resulting methods, which use a physically motivated set of active orbitals to pick out the most important 3p-2h/3h-2p and 4p-3h/4h-3p excitations, represent practical computational approaches for high-accuracy calculations of potential energy surfaces of radicals. To illustrate the potential offered by the active-space EA/IP SAC-CI approaches with up to 4p-3h/4h-3p excitations, the results of benchmark calculations for the potential energy surfaces of the low-lying doublet states of CH and OH are presented and compared with other SAC-CI and EOMCC methods, and full CI results.

10aconfiguration interactions10acoupled cluster calculations10aelectron attachment10aexcited states10afree radicals10aground states10aionisation10aorganic compounds10aoxygen compounds10apotential energy surfaces1 aOhtsuka, Y.1 aPiecuch, Piotr1 aGour, J., R1 aEhara, M.1 aNakatsuji, H. uhttps://icer.msu.edu/active-space-symmetry-adapted-cluster-configuration-interaction-and-equation-motion-cluster-methods01936nas a2200157 4500008004100000245009100041210006900132260001200201300001200213490000800225520137300233100001101606700001701617700001901634856012501653 2007 eng d00aBreaking Bonds with the Left Eigenstate Completely Renormalized Coupled-Cluster Method0 aBreaking Bonds with the Left Eigenstate Completely Renormalized c11/2007 a6 pages0 v1273 aThe recently developed [ P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 (2005) ] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2SiSiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R = 1–3Re for all of the studied single bond-breaking reactions, where R and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R = 1–3Re of the H–SiH3, H–Cl, H3Si–SiH3, Cl–CH3, H–CH3, and H3C–SiH3 bonds. The maximum errors are −2.1, 1.6, and 1.6 mhartree in the R = 1–3Re region of the H3C–CH3, Cl–Cl, and H3Si–Cl bonds, respectively, while the discrepancy for the H2SiSiH2 double bond-breaking reaction is 6.6 (8.5) mhartree at R = 2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T).

1 aGe, Y.1 aGordon, M.S.1 aPiecuch, Piotr uhttps://icer.msu.edu/research/publications/breaking-bonds-left-eigenstate-completely-renormalized-coupled-cluster-method03686nas a2200145 4500008004100000245018100041210006900222260001200291300001200303490000800315520305800323100001403381700001903395856012603414 2007 eng d00aComputational Investigation of the Conrotatory and Disrotatory Isomerization Channels of Bicyclo[1.1.0]butane to Buta-1,3-diene: A Completely Renormalized Coupled-Cluster Study0 aComputational Investigation of the Conrotatory and Disrotatory I c01/2007 a734-7420 v1113 aThe conrotatory and disrotatory mechanisms of the isomerization of bicyclo[1.1.0]butane to trans-buta-1,3-diene have been computationally investigated with the CASSCF, MCQDPT2, (U)B3LYP, CCSD(T), CR-CCSD(T), and CR-CC(2,3) approaches. The coupled-cluster (CC) methods, including the CC approach with singles, doubles, and noniterative triples (CCSD(T)), and its completely renormalized (CR) extensions called CR-CCSD(T) and CR-CC(2,3), and the density functional theory B3LYP approach do an excellent job of correctly predicting the activation barrier for the conrotatory pathway, which corresponds to a weakly biradical transition state (TS), producing values within experimental error bars. In particular, the recently developed CR-CC(2,3) method gives 40.8 or 41.1 kcal/mol, in perfect agreement with the experimental value of 40.6 ± 2.5 kcal/mol. The complete-active-space self-consistent-field (CASSCF) approach and the second-order multireference perturbation theory (MCQDPT2) are less accurate in describing the conrotatory barrier than CR-CC(2,3). The higher energy disrotatory pathway, which has not been characterized experimentally and which involves a strongly biradical TS, poses a great challenge for many methods. CCSD(T) fails, predicting the activation barrier for the disrotatory pathway significantly below the conrotatory barrier, contradicting the experimental result that the conrotatory pathway describes the mechanism. The strongly biradical character of the disrotatory TS, spin contamination, and the proximity of singlet and triplet potential energy surfaces cause difficulties for B3LYP, which does not link this TS with gauche-buta-1,3-diene. No such difficulties occur in the CASSCF calculations, which offer a proper description of the structure of the disrotatory TS that links it with the reactant and product molecules. The CR-CC(2,3) approach, which accurately balances dynamical and nondynamical correlations in systems containing closed-shell and biradical structures, predicts the activation enthalpy for the disrotatory mechanism of 66 kcal/mol. CR-CCSD(T) gives 69 kcal/mol. In agreement with experiment and earlier multireference configuration interaction calculations of Nguyen and Gordon, CR-CCSD(T) and CR-CC(2,3) favor the conrotatory mechanism. The CASSCF, MCQDPT2, and B3LYP methods correctly place the disrotatory barrier above the conrotatory one, but, on the basis of a comparison with the accurate CR-CC(2,3) results, they underestimate the activation energy for the disrotatory pathway. All CC approaches employed in this study produce very good estimates of the enthalpy of isomerization of bicyclo[1.1.0]butane into buta-1,3-diene, the experimental value of which is −25.9 ± 0.4 kcal/mol, giving about −28 kcal/mol, when trans-buta-1,3-diene is used as a product, and −25 kcal/mol, when the nearly isoenergetic gauche-buta-1,3-diene rotamer is used as a product. The CC reaction enthalpies are more accurate than those obtained with CASSCF, MCQDPT2, and B3LYP.

1 aKinal, A.1 aPiecuch, Piotr uhttps://icer.msu.edu/computational-investigation-conrotatory-and-disrotatory-isomerization-channels-bicyclo110butane-buta01210nas 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-transformed01291nas a2200169 4500008004100000020002600041245012100067210006900188260004600257490000800303520060900311100001900920700002400939700001500963700001700978856012600995 2007 eng d aISBN13: 978084123843500aNew Alternatives for Accurate Electronic Structure Calculations of Potential Energy Surfaces Involving Bond Breaking0 aNew Alternatives for Accurate Electronic Structure Calculations aWashington, DCbAmerican Chemical Sociegy0 v9583 aThe 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-bond03587nas 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-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-coupled01833nas 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-o1601911nas a2200193 4500008004100000245014700041210006900188260001200257300001300269490000800282520117900290653003301469653001801502653002201520653002201542100001601564700001901580856011801599 2006 eng d00aEfficient Formulation and Computer Implementation of the Active-Space Electron-Attached and Ionized Equation-of-Motion Coupled-Cluster Methods0 aEfficient Formulation and Computer Implementation of the ActiveS c12/2006 a17 pages0 v1253 aThe efficient, general-purpose implementations of the active-space electron-attached (EA) and ionized (IP) equation-of-motion coupled-cluster (EOMCC) methods including up to 3p-2h and 3h-2p excitations, called EA-EOMCCSDt and IP-EOMCCSDt, respectively, are discussed. The details of the algorithm that enables one to achieve a high degree of code vectorization for the active-space methods and the factorized forms of the EA- and IP-EOMCCSDt equations that maximize the benefits of using active orbitals in the process of selecting the dominant 3p-2h and 3h-2p excitations are presented. The results of benchmark calculations for the low-lying doublet and quartet states of the CH and SH radicals reveal that the active-space EA-EOMCCSDt and IP-EOMCCSDt methods are capable of producing results for the electronic excitations in open-shell systems that match the high accuracy of EA- and IP-EOMCC calculations with a full treatment of 3p-2h and 3h-2p excitations, even when the excited states of interest display a manifestly multideterminantal nature, with the costs that can be on the same order of those characterizing the basic EOMCC singles and doubles approach.

10acoupled cluster calculations10afree radicals10aorganic compounds10asulphur compounds1 aGour, J., R1 aPiecuch, Piotr uhttps://icer.msu.edu/efficient-formulation-and-computer-implementation-active-space-electron-attached-and-ionized02232nas 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-and00839nas a2200145 4500008004100000245009700041210006900138260001500207300001200222490000800234520030100242100002100543700001900564856011000583 2006 eng d00aExtrapolating Potential Energy Surfaces by Scaling Electron Correlation at a Single Geometry0 aExtrapolating Potential Energy Surfaces by Scaling Electron Corr c10/30/2006 a448-4530 v4303 aIt is shown that the molecular potential energy surface corresponding to a high level of ab initio theory can be accurately predicted by performing calculations with smaller basis sets and then scaling the electron correlation at a single point calculated with the larger target basis set.

1 aVarandas, A.J.C.1 aPiecuch, Piotr uhttps://icer.msu.edu/extrapolating-potential-energy-surfaces-scaling-electron-correlation-single-geometry01624nas a2200145 4500008004100000245014800041210006900189260001100258300001200269490000800281520103500289100001901324700001401343856012101357 2006 eng d00aIs the Mechanism of the [2+2] Cycloaddition of Cyclopentyne to Ethylene Concerted or Biradical? A Completely Renormalized Coupled Cluster Study0 aMechanism of the 22 Cycloaddition of Cyclopentyne to Ethylene Co c6/2005 a367-3780 v1103 aThe mechanism of the [2+2] cycloaddition reaction of cyclopentyne to ethylene has been studied using the completely renormalized coupled cluster method with singles, doubles, and noniterative triples (CR−CCSD(T)). In agreement with the experimentally observed stereochemistry, the CR−CCSD(T) method favors the concerted pathway involving a [2+1] transition state, whereas the popular CCSD(T) method, which is often regarded as the “gold standard” of electronic structure theory, and low-order multireference methods support the less probable biradical mechanism. In addition, the CCSD(T) approach produces an erroneous description of some transition states and intermediates, particularly those which have a significant biradical character. The CR−CCSD(T) calculations indicate that the reaction is a highly exothermic (Δ = −68 kcal/mol), predominantly concerted process with a relatively low activation barrier on the order of 13−16 kcal/mol which permits its thermal occurrence.

1 aPiecuch, Piotr1 aKinal, A. uhttps://icer.msu.edu/mechanism-22-cycloaddition-cyclopentyne-ethylene-concerted-or-biradical-completely-renormalized01919nas 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-cluster02773nas a2200145 4500008004100000245019000041210006900231260001200300300000900312490000700321520214700328100001502475700001902490856011802509 2006 eng d00aThe Usefulness of Exponential Wave Function Expansions Employing One- and Two-Body Cluster Operators in Electronic Structure Theory: The Extended and Generalized Coupled-Cluster Methods0 aUsefulness of Exponential Wave Function Expansions Employing One c12/2006 a1-570 v513 aIn 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.

1 aFan, P.-D.1 aPiecuch, Piotr uhttps://icer.msu.edu/usefulness-exponential-wave-function-expansions-employing-one-and-two-body-cluster-operators01233nas 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-radicals01392nas a2200181 4500008004100000245015300041210006900194300001600263490000800279520065800287653003300945653001800978653003200996100002201028700001901050700001701069856012401086 2005 eng d00aActive-space equation-of-motion coupled-cluster methods for excited states of radicals and other open-shell systems: {EA-EOMCCSDt} and {IP-EOMCCSDt}0 aActivespace equationofmotion coupledcluster methods for excited a134113–140 v1233 aThe previously developed active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods are extended to radicals and other open-shell systems by combining them with the electron attached (EA) and ionized (IP) EOMCC approaches. As illustrated by the calculations for the CH and OH radicals, the resulting EA-EOMCCSDt and IP-EOMCCSDt theories are capable of providing a highly accurate description of the electronic spectra of radical systems, including excited states displaying a manifestly multideterminantal nature, with the low costs that are not much greater that those characterizing the standard EOMCC singles and doubles method.

10acoupled cluster calculations10afree radicals10amolecular electronic states1 aGour, Jeffrey, R.1 aPiecuch, Piotr1 aWloch, Marta uhttps://icer.msu.edu/research/publications/active-space-equation-motion-coupled-cluster-methods-excited-states-radicals01208nas a2200145 4500008004100000245017600041210006900217260001500286300001400301490000800315520057100323100001900894700002300913856012600936 2005 eng d00aBalancing Dynamic and Non-Dynamic Correlation for Diradical and Aromatic Transition States: A Renormalized Coupled-Cluster Study of the Cope Rearrangement of 1,5-Hexadiene0 aBalancing Dynamic and NonDynamic Correlation for Diradical and A c02/05/2005 a2608-26140 v1273 aSingle-reference coupled-cluster calculations employing the completely renormalized CCSD(T) (CR-CCSD(T)) approach have been used to examine the mechanism of the Cope rearrangement of 1,5-hexadiene. In agreement with multireference perturbation theory, the CR-CCSD(T) method favors the concerted mechanism of the Cope rearrangement involving an aromatic transition state. The CCSD(T) approach, which is often regarded as the “gold standard” of electronic structure theory, seems to fail in this case, favoring pathways through diradical structures.

1 aPiecuch, Piotr1 aMcGuire}, M., J. { uhttps://icer.msu.edu/research/publications/balancing-dynamic-non-dynamic-correlation-diradical-aromatic-transition-states02028nas 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-open01552nas a2200169 4500008004100000245026000041210006900301260001200370300001600382490000800398520078000406100001901186700001501205700001801220700002301238856012101261 2005 eng d00aCan a Single-Reference Approach Provide a Balanced Description of Ground and Excited States? A Comparison of the Completely Renormalized Equation-of-the-Motion Coupled-Cluster Method with Multi-Reference Quasi-Degenerate Perturbation Theory Near a Conical0 aCan a SingleReference Approach Provide a Balanced Description of c11/2005 a11643-116460 v1093 aWe calculated the two lowest electronically adiabatic potential energy surfaces of ammonia in the region of the conical intersection and at a sequence of geometries along which one of the N-H bonds is broken. We employed both a multireference (MR) method and a single-reference (SR) method. The MR calculations are based on multiconfiguration quasidegenerate perturbation theory (MC-QDPT) with a 6-311+G(3df,3pd) basis set. The SR calculations, carried out with the same basis, employ the completely renormalized equation-ofmotion coupled-cluster method with singles and doubles, and a noniterative treatment of triples, denoted CR-EOMCCSD(T). At 91 geometries used for comparison, including geometries near a conical intersection, the surfaces agree to 7% on average.

1 aPiecuch, Piotr1 aNangia, S.1 aTruhlar, D.G.1 aMcGuire}, M., J. { uhttps://icer.msu.edu/research/publications/can-single-reference-approach-provide-balanced-description-ground-excited01534nas 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-theories01895nas a2200133 4500008004100000245012300041210006900164260001400233490000800247520134500255100001901600700001901619856012301638 2005 eng d00aA Comparison of Renormalized Coupled-Cluster and Multireference Methods with Full Configuration Interaction Benchmarks0 aComparison of Renormalized CoupledCluster and Multireference Met c3/22/20050 v1223 aUnusual bonding and electronic near degeneracies make the lowest-lying singlet states of the C2 molecule particularly challenging for electronic structure theory. Here we compare two alternative approaches to modeling bond-breaking reactions and excited states: sophisticated multireference configuration interaction and multireference perturbation theory methods, and a more "black box," single-reference approach, the completely renormalized coupled-cluster method. These approximate methods are assessed in light of their ability to reproduce the full configuration interaction potential energy curves for the X1Sigmag+, B1Deltag, and B' 1Sigmag+ states of C2, which are numerically exact solutions of the electronic Schrodinger equation within the space spanned by a 6-31G* basis set. Both the multireference methods and the completely renormalized coupled-cluster approach provide dramatic improvements over the standard single-reference methods. The multireference methods are nearly as reliable for this challenging test case as for simpler reactions which break only single bonds. The completely renormalized coupled-cluster approach has difficulty for large internuclear separations R in this case, but over the wide range of R=1.0-2.0 A, it compares favorably with the more complicated multireference methods.

1 aPiecuch, Piotr1 aSherrill, C.D. uhttps://icer.msu.edu/comparison-renormalized-coupled-cluster-and-multireference-methods-full-configuration-interaction00768nas 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-chemistry02915nas a2200313 4500008004100000245011100041210006900152260001200221300001600233490000800249520189000257653002102147653003102168653003302199653001302232653001902245653001302264653001802277653002102295653002302316653001802339653002202357653002202379653002902401653001002430100001902440700001702459856012502476 2005 eng d00aRenormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian0 aRenormalized coupledcluster methods exploiting left eigenstates c12/2005 a224105–100 v1233 aCompletely renormalized (CR) coupled-cluster (CC) approaches, such as CR-CCSD(T), in which one corrects the standard CC singles and doubles (CCSD) energy for the effects of triply (T) and other higher-than-doubly excited clusters [ K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000) ], are reformulated in terms of the left eigenstates 〈Φ∣L of the similarity-transformed Hamiltonian of CC theory. The resulting CR-CCSD(T)L or CR-CC(2,3) and other CR-CCL methods are derived from the new biorthogonal form of the method of moments of CC equations (MMCC) in which, in analogy to the original MMCC theory, one focuses on the noniterative corrections to standard CC energies that recover the exact, full configuration-interaction energies. One of the advantages of the biorthogonal MMCC theory, which will be further analyzed and extended to excited states in a separate paper, is a rigorous size extensivity of the basic ground-state CR-CCL approximations that result from it, which was slightly violated by the original CR-CCSD(T) and CR-CCSD(TQ) approaches. This includes the CR-CCSD(T)L or CR-CC(2,3) method discussed in this paper, in which one corrects the CCSD energy by the relatively inexpensive noniterative correction due to triples. Test calculations for bond breaking in HF, F2, and H2O indicate that the noniterative CR-CCSD(T)L or CR-CC(2,3) approximation is very competitive with the standard CCSD(T) theory for nondegenerate closed-shell states, while being practically as accurate as the full CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving the trimethylene biradical as a transition state show that the noniterative CR-CCSD(T)L approximation is capable of providing activation enthalpies which perfectly agree with experiment.

10abonds (chemical)10aconfiguration interactions10acoupled cluster calculations10aenthalpy10aexcited states10afluorine10aground states10aheat of reaction10ahydrogen compounds10aisomerisation10amethod of moments10aorganic compounds10areaction kinetics theory10awater1 aPiecuch, Piotr1 aWloch, Marta uhttps://icer.msu.edu/renormalized-coupled-cluster-methods-exploiting-left-eigenstates-similarity-transformed-hamiltonian01158nas 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