The 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.

VL - 112 IS - 16 ER - TY - JOUR T1 - Computational Investigation of the Conrotatory and Disrotatory Isomerization Channels of Bicyclo[1.1.0]butane to Buta-1,3-diene: A Completely Renormalized Coupled-Cluster Study JF - Journal of Physical Chemistry A Y1 - 2007 A1 - A. Kinal A1 - Piotr Piecuch AB -The 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.

VL - 111 IS - 4 ER - TY - CHAP T1 - New Alternatives for Accurate Electronic Structure Calculations of Potential Energy Surfaces Involving Bond Breaking T2 - Electron Correlation Methodology Y1 - 2007 A1 - Piotr Piecuch A1 - I. S. O. Pimienta A1 - P.-D. Fan A1 - K. Kowalski AB -The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches.

JF - Electron Correlation Methodology T3 - ACS Symposium Series PB - American Chemical Sociegy CY - Washington, DC VL - 958 SN - ISBN13: 9780841238435 ER - TY - JOUR T1 - Ab Initio Coupled-Cluster Calculations for Nuclei Using Methods of Quantum Chemistry JF - European Physics Journal A Y1 - 2006 A1 - Piotr Piecuch A1 - M. Wloch A1 - D. J. Dean A1 - J. R Gour A1 - M. {Hjorth-Jensen} A1 - T. Papenbrock A1 - K. Kowalski AB -We 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.

VL - 25 IS - 1 ER - TY - JOUR T1 - Ab initio studies of the electronic structure of defects in {PbTe} JF - Physical Review B Y1 - 2006 A1 - Salameh Ahmad A1 - S. D. Mahanti A1 - Khang Hoang A1 - M. G. Kanatzidis AB -Understanding the detailed electronic structure of deep defect states in narrow band-gap semiconductors has been a challenging problem. Recently, self-consistent ab initio calculations within density functional theory using supercell models have been successful in tackling this problem. In this paper, we carry out such calculations in {PbTe,} a well-known narrow band-gap semiconductor, for a large class of defects: cationic and anionic substitutional impurities of different valence, and cationic and anionic vacancies. For the cationic defects, we study the chemical trends in the position of defect levels by looking at series of compounds {RPb2n−1Te2n,} where R is vacancy or monovalent, divalent, or trivalent atom. Similarly, for anionic defects, we study compounds {MPb2nTe2n−1,} where M is vacancy, S, Se or I. We find that the density of states near the top of the valence band and the bottom of the conduction band get significantly modified for most of these defects. This suggests that the transport properties of {PbTe} in the presence of impurities may not always be interpreted by simple carrier doping (from bound impurity states in the gap) concepts, confirming such ideas developed from qualitative and semiquantitative arguments.

VL - 74 IS - 15 N1 - Copyright {(C)} 2010 The American Physical Society; Please report any problems to prola@aps.org ER - TY - JOUR T1 - Automated derivation and parallel computer implementation of renormalized and active-space coupled-cluster methods JF - International Journal of Quantum Chemistry Y1 - 2006 A1 - Piotr Piecuch A1 - So Hirata A1 - K. Kowalski A1 - P.-D. Fan A1 - Theresa L. Windus AB -Our 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

VL - 106 IS - 1 ER - TY - JOUR T1 - Experimental and Theoretical UV Characterizations of Acetyloacetone and its Isomers JF - The Journal of Physical Chemistry A Y1 - 2006 A1 - Piotr Piecuch A1 - S. Coussan A1 - Y. Ferro A1 - A. Trivella A1 - P. Roubin A1 - R. Wieczorek A1 - C. Manca A1 - K. Kowalski A1 - M. Wloch A1 - S. Kucharski A1 - M. Musial AB -Cryogenic 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.

VL - 110 IS - 11 ER - TY - JOUR T1 - Is the Mechanism of the [2+2] Cycloaddition of Cyclopentyne to Ethylene Concerted or Biradical? A Completely Renormalized Coupled Cluster Study JF - The Journal of Physical Chemistry Y1 - 2006 A1 - Piotr Piecuch A1 - A. Kinal AB -The 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.

VL - 110 IS - 2 ER - TY - JOUR T1 - Non-Iterative Coupled- Cluster Methods Employing Multi-Reference Perturbation Theory Wave Functions JF - Journal of Molecular Structure: THEOCHEM Y1 - 2006 A1 - Piotr Piecuch A1 - M.D. Lodriguito A1 - K. Kowalski A1 - M. Wloch KW - Coupled-cluster theory; Equation-of-motion coupled-cluster methods; Method of moments of coupled-cluster equations; Multi-reference perturbation theory; Non-iterative coupled-cluster methods AB -A 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+.

VL - 771 IS - 1-3 ER - TY - JOUR T1 - Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals JF - Chemical Physics Letters Y1 - 2006 A1 - Piotr Piecuch A1 - M. Wloch A1 - J. R Gour A1 - A. Kinal AB -We 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.

VL - 418 ER - TY - JOUR T1 - Theoretical Characterization of End-on and Side-on Peroxide Coordination in Ligated Cu2O2 Models JF - The Journal of Physical Chemistry A Y1 - 2006 A1 - C.J. Cramer A1 - A. Kinal A1 - M. Wloch A1 - Piotr Piecuch A1 - L. Gagliardi AB -The 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.

VL - 110 IS - 40 ER - TY - JOUR T1 - Ab Initio Coupled-Cluster Study of 16O JF - Physical Review Letters Y1 - 2005 A1 - M. Włoch A1 - D. J. Dean A1 - J. R Gour A1 - M. {Hjorth-Jensen} A1 - K. Kowalski A1 - T. Papenbrock A1 - P. Piecuch AB -We 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.

VL - 94 IS - 21 ER - TY - JOUR T1 - Ab Initio Coupled-Cluster Study of O JF - Physical Review Letters Y1 - 2005 A1 - Piotr Piecuch A1 - M. Wloch A1 - D. J. Dean A1 - J. R Gour A1 - M. {Hjorth-Jensen} A1 - K. Kowalski A1 - T. Papenbrock AB -We 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.

VL - 94 ER - TY - JOUR T1 - Active-Space Coupled-Cluster Study of Electronic States of Be 3 JF - The Journal of Chemical Physics Y1 - 2005 A1 - Piotr Piecuch A1 - K. Kowalski A1 - S. Hirata A1 - M. Wloch A1 - T.L. Windus AB -The 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.

VL - 123 IS - 7 ER - TY - JOUR T1 - Comparison of Low-Order Multireference Many-Body Perturbation Theories JF - Journal of Chemical Physics Y1 - 2005 A1 - Piotr Piecuch A1 - R.K. Chaudhuri A1 - K.F. Freed A1 - G. Hose A1 - K. Kowalski A1 - M. Wloch A1 - S. Chattopadhyay A1 - D. Mukherjee A1 - R. Rolik A1 - A. Szabados A1 - G. Toth A1 - P.R. Surjan AB -Tests 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.

VL - 122 IS - 13 ER - TY - Generic T1 - Coupled Cluster Approaches to Nuclei, Ground States and Excited States T2 - Key Topics in Nuclear Structure, Proceedings of the 8th International Spring Seminar on Nuclear Physics Y1 - 2005 A1 - Piotr Piecuch A1 - D. J. Dean A1 - M. Jhorth-Jensen A1 - K. Kowalski A1 - T. Papenbrock A1 - M. Wloch AB -We 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.

JF - Key Topics in Nuclear Structure, Proceedings of the 8th International Spring Seminar on Nuclear Physics CY - Paestum, Italy ER - TY - JOUR T1 - Extension of Renormalized Coupled-Cluster Methods Including Triple Excitations to Electronic States of Open-Shell Molecules JF - The Journal of Chemical Physics Y1 - 2005 A1 - Piotr Piecuch A1 - M. Wloch A1 - J. R Gour A1 - K. Kowalski AB -The 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.

VL - 122 IS - 21 ER - TY - JOUR T1 - Extensive Generalization of Renormalized Coupled-Cluster Methods JF - The Journal of Chemical Physics Y1 - 2005 A1 - Piotr Piecuch A1 - K. Kowalski AB -The 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.

VL - 122 IS - 7 ER - TY - JOUR T1 - Noniterative Corrections to Extended Coupled-Cluster Energies Employing the Generalized Method of Moments of Coupled-Cluster Equations JF - Molecular Physics Y1 - 2005 A1 - Piotr Piecuch A1 - {P.-D.} Fan A1 - K. Kowalski AB -It 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

VL - 103 IS - 15 & 16 ER - TY - JOUR T1 - Nuclear Structure Calculations with Coupled-Cluster Methods from Quantum Chemistry JF - Nuclear Physics A Y1 - 2005 A1 - Piotr Piecuch A1 - D. J. Dean A1 - J. R Gour A1 - G. Hagen A1 - M. {Hjorth-Jensen} A1 - K. Kowalski A1 - T. Papenbrock A1 - M. Wloch AB -We 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.

VL - 752 ER - TY - JOUR T1 - Where Does the Planar-to-Nonplanar Turnover Occur in Small Gold Clusters JF - Journal of the American Chemical Society Y1 - 2005 A1 - Piotr Piecuch A1 - R.M. Olson A1 - S. Varganov A1 - M.S. Gordon A1 - S. Chretien A1 - H. Metiu A1 - K. Kowalski A1 - S. A. Kucharski A1 - M. Musial AB -Several 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.

VL - 127 IS - 3 ER - TY - JOUR T1 - Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states JF - Theoretical Chemistry Accounts: Theory, Computation, and Modeling Y1 - 2004 A1 - Piotr Piecuch A1 - K. Kowalski A1 - I. S. O. Pimienta A1 - P.-D. Fan A1 - M.D. Lodriguito A1 - M. J. {McGuire} A1 - S. A. Kucharski A1 - T. Kuś A1 - M. Musial KW - Coupled-cluster theory - Method of moments of coupled-cluster equations - Renormalized coupled-cluster methods - extended coupled cluster theory - Potential energy surfaces AB -The 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.

VL - 112 ER -