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  • 1
    Electronic Resource
    Electronic Resource
    Orientation of the nitrogen lone-pair electrons in cannivonine (1976)
    s.l. : American Chemical Society
    The @journal of organic chemistry 41 (1976), S. 3321-3322 
    Details
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/jo00882a025
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  • 2
    Electronic Resource
    Electronic Resource
    Diels-Alder reaction of some trimethylsilyloxy 1,3-dienes (1982)
    s.l. : American Chemical Society
    The @journal of organic chemistry 47 (1982), S. 3649-3652 
    Details
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/jo00140a011
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  • 3
    Electronic Resource
    Electronic Resource
    Applicability of valence-universal multireference coupled-cluster theories to quasidegenerate electronic states. I. Models involving at most two-body amplitudes (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 7600-7612 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The recently developed algebraic formulation of valence-universal coupled-cluster (VU-CC) theories [Jeziorski and Paldus, J. Chem. Phys. 90, 2714 (1989)] for open-shell systems has been employed in a systematic derivation of explicit equations defining cluster amplitudes assuming Lindgren's normal ordered exponential ansatz for the wave operator. The latter is approximated by its one- and two-electron components. Various aspects of the applicability of this version of the VU-CC theory to quasidegenerate electronic states are studied for a model system consisting of two slightly stretched, interacting hydrogen molecules. A single parameter that determines the geometry of this system makes it possible to vary the extent of quasidegeneracy of the two lowest-energy states over a wide range. Along with the complete theory, the linear version (VU-LCC) is also examined. The results are compared with the full configuration interaction results as well as with those obtained using other approaches. It was found that, at least in the strongly quasidegenerate region, the VU-CC energies are less accurate than those obtained with other multireference CC theories. It is shown that the VU-CC equations for cluster amplitudes possess multiple solutions representing various pairs of states. The individual solutions that arise for a system possessing n-valence electrons may be characterized in terms of a genealogical scheme that involves states of systems with 0,1,...,n valence electrons.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463480
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  • 4
    Electronic Resource
    Electronic Resource
    Cluster relations for multireference coupled-cluster theories: A model study (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 3549-3561 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The validity of various coupled-cluster conditions, that were recently formulated for both the valence-universal open-shell coupled-cluster theory based on Lindgren's exponential ansatz and the state-universal theory employing the Jeziorski–Monkhorst ansatz, are examined for two model systems consisting of two and four slightly stretched, interacting hydrogen molecules. These cluster conditions ascertain the possibility to represent four-electron terms in the wave operator through appropriate products of two-electron terms and thus justify the truncation of the open-shell cluster operators employed to at most two-electron terms. A single parameter that determines the geometry of the studied model systems makes it possible to continuously vary the extent of quasidegeneracy between the two lowest energy states over a wide range. It is shown that the cluster conditions are relatively well satisfied only in the strongly quasidegenerate region, except for a few very small amplitudes whose effect on the resulting energies should be insignificant. To assess the validity of the often made assumption of negligibility of one-electron amplitudes, the generalized cluster conditions involving these terms were also examined. The role played by these additional terms was shown to be small. Finally, in the valence-universal case, the role of orbital choice was also investigated by performing cluster analysis with both system and core spin orbitals. The effect of using different orbital alternatives was again found to be small.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460857
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  • 5
    Electronic Resource
    Electronic Resource
    Applicability of valence-universal multireference coupled-cluster theories to quasidegenerate electronic states. II. Models involving three-body amplitudes (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 3085-3095 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The reliability study of the valence-universal coupled-cluster (VU-CC) methods [Jankowski et al., J. Chem. Phys. 97, 7600 (1992)] is continued by considering approximations involving one-, two-, and three-electron components of the cluster operator S, S(approximately-equal-to)S1+S2+S3. The explicit equations determining the cluster amplitudes for the quadratic VU-CCSDT approximation were derived and applied to the low lying quasidegenerate states of the model system consisting of two slightly stretched, interacting hydrogen molecules. The degree of quasidegeneracy of the two lowest, totally symmetric, singlet levels of this system may be varied over a wide range by changing its geometry. Along with the quadratic VU-CCSDT theory its linear version (VU-LCCSDT) is also examined. It is found that the effect of the S3 clusters is significant and is mainly due to the spectator part of this operator. The inclusion of this operator increases the number of physically meaningful multiple solutions of the equations for the cluster amplitudes. It also considerably improves the accuracy of the resulting energies, both in the strongly and weakly quasidegenerate regions, but not in the intermediately quasidegenerate region. It is shown that this behavior is a manifestation of an avoided crossing of the lowest excited states of the parent system in the valence-universal genealogy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467621
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  • 6
    Electronic Resource
    Electronic Resource
    Erratum: Applicability of valence-universal multireference coupled-cluster theories to quasidegenerate electronic states. I. Models involving at most two-body amplitudes [J. Chem. Phys. 97, 7600 (1992)] (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 1759-1759 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468519
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  • 7
    Electronic Resource
    Electronic Resource
    Physical and mathematical content of coupled-cluster equations. IV. Impact of approximations to the cluster operator on the structure of solutions (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 2952-2959 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The impact of approximations to the form of the cluster operator on the structure and physical significance of the complete set of geometrically isolated solutions to the coupled-cluster (CC) equations has been studied for the first time. To systematically study the correspondence of solutions obtained at various levels of the approximation process, a continuation procedure based on a set of β-nested equations (β-NE) has been proposed and applied. Numerical studies based on a homotopy method for obtaining full solutions to sets of polynomial equations have been performed for the H4 and P4 models which belong to the simplest realistic many-electron model systems. Two examples of approximation procedures have been considered. The first one involved, for the P4 model, the approximation leading from the full CC (FCC) method to the CC method based on double excitations (CCD). As a result of this approximations the number of solutions has increased from 8 to 20. In the second example, for H4, we have studied the approximation leading from the CCSD method to the CCD one. To complete these studies, we have for the first time obtained the full set of geometrically isolated solutions for a CCSD equations which consists of 60 solutions. Only a small subset of this set might have some physical significance. During the approximation process considered, the number of solution decreases from 60 to 12. This radical drop of the numbers of solutions is a consequence of the absence of the third and fourth powers of the unknowns in the CCD equations. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479576
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  • 8
    Electronic Resource
    Electronic Resource
    Physical and mathematical content of coupled–cluster equations: Correspondence between coupled–cluster and configuration–interaction solutions (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 3714-3729 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: To gain more insight into the physical and mathematical content of the equations of the coupled–cluster (CC) method, comprehensive numerical studies have been performed for various geometries of the H4 model which belongs to the simplest and best understood among the realistic many–electron model systems. These studies are for the first time based on the knowledge of the complete sets of geometrically isolated solutions of the relevant equations that are obtained when using a special version of the homotopy methods. The equations of the CC method including two–electron excitations (CCD) both in the spin–orbital and spin–symmetry–adapted versions are considered. To establish the correspondence of the solutions attained with those of the configuration interaction (CID) method, we have for the first time solved the unabridged characteristic equations (CE) of T. P. Zivkovic and H. J. Monkhorst [J. Math. Phys. 19, 1007 (1978)]. The complete sets of solutions to the spin–orbital and spin–symmetry–adapted versions of the CCD equations and CEs consist of 20 and 12 solutions, respectively. Their structures turned out to be unexpectedly simple, which makes it possible to understand the physical and mathematical significance of the individual solutions. Moreover, this simplicity rises hopes that the most serious irregularities previously found for low dimensional simulations of the CEs can be avoided for realistic systems. The present results confirm most of the findings of previous research. Attention is paid to studies of the impact of using mixed–symmetry cluster operators on the structure of solutions to the CC equations. The specific part played by the components of the cluster amplitudes corresponding to other spin–symmetry than that of the reference function has been demonstrated for the first time. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478262
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  • 9
    Electronic Resource
    Electronic Resource
    Physical and mathematical content of coupled-cluster equations. III. Model studies of dissociation processes for various reference states (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 2940-2951 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The structure and physical significance of the full set of solutions to coupled-cluster (CC) equations at various stages of the dissociation process and the impact of the choice of reference functions on these solutions have been studied for the first time. The equations for the CC method involving double excitations (CCD) are obtained for the P4 model consisting of two H2 molecules in a rectangular nuclear configuration determined by a geometry parameter α. We consider equations for the reference states |ΦA〉, |ΦQ〉, and |ΦB〉 corresponding to the lowest, highest, and intermediate Hartree–Fock (HF) energies, respectively. The first two states provide a size-consistent description of the dissociation process. For the compact-molecule geometries (α〈10.0) the sets of complete solutions to the standard CCD equations [based on molecular orbitals (MOs) of D2h symmetry] in the spin–orbital and spin–symmetry-adapted versions always consist of 20 and 12 entries, respectively. For |ΦA〉 and |ΦB〉 in the dissociation limit (α→∞) only for the latter version the solutions can be attained by homotopy method. In this case we have reformulated the standard spin–symmetry-adapted CCD equations to a version based on the use of localized orbitals (LO) which is extremely simple and can be solved analytically providing an understanding of the unexpected peculiarities of the solutions for α→∞. For |ΦA〉 and |ΦQ〉, there are only two regular solutions. For the remaining 10 solutions, the CCD wave functions are meaningless despite the fact that the corresponding CCD energies are equal to the exact values. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479575
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  • 10
    Electronic Resource
    Electronic Resource
    Approximate coupled-cluster methods employing split cluster amplitudes: Implementation of an almost-linear coupled-cluster formalism (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 6255-6263 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new approximation strategy, split-amplitude strategy, useful within the framework of the coupled-cluster (CC) methodology is proposed. It consists in representing the individual cluster amplitudes as a sum of two components, one of fixed value, which may be obtained from external sources, and the other determined from a set of modified CC equations. This approach provides new possibilities of absorbing information concerning the values of cluster amplitudes from independent calculations. By properly choosing the fixed amplitude components, one may substantially reduce the magnitudes of the most significant amplitudes to be determined for the state considered, which in turn causes that the known approximation procedures are more justifiable when applied to the modified CC equations than to the equations of the standard CC approaches. The split-amplitude strategy has been employed to setting up several almost-linear CC (AL-CC) approaches of a single reference type corresponding to the basic CC methods. These low-cost approaches seem to be useful in theories of processes involving nondynamically correlated (quasidegenerate) states. The AL-CC methods have been applied to the ground states for various geometries of the following molecular systems: H8, H2O, BH, and HF. It is found that the energies obtained for a given AL-CC approach are very close to those for the corresponding basic CC method, which is true even for strongly quasidegenerate states. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477266
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