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  • Computational Chemistry and Molecular Modeling  (10)
  • Many-electron correlation problem  (4)
  • Unitary group approach  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Clifford algebra and unitary group formulations of the many-electron problem (1988)
    Springer
    Theoretical chemistry accounts 73 (1988), S. 81-103 
    Details
    ISSN: 1432-2234
    Keywords: Many-electron correlation problem ; Spin-adaption ; Unitary group approach ; Coupled-pair approach ; Configuration interaction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract An essential role of Clifford algebras for quantum-chemical finite-dimensional orbital models of many-electron systems is pointed out. The relationship between Clifford algebra matric units, the generators of the unitary group approach (UGA) and the higher order replacement or excitation operators, as well as between their first and second quantized realizations, is elucidated. The usefulness of higher order replacement operators in the spin-adaptation of various many-body theories is briefly outlined and illustrated on the orthogonally spin-adapted coupled-pair approach. A natural connection with the Clifford algebra UGA is explored and new possibilities for its exploitation in large scale configuration interaction calculations are suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00528196
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation (1992)
    Springer
    Theoretical chemistry accounts 83 (1992), S. 69-103 
    Details
    ISSN: 1432-2234
    Keywords: Many-electron correlation problem ; Coupled-cluster approach ; Multi-reference formalism ; Spin-adaptation ; Graphical methods of spin algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The problem of spin-adaptation of the multi-reference (MR) coupled-cluster (CC) formalism, employing Jeziorski-Monkhorst ansatz, is addressed. The diagrammatic technique based on graphical methods of spin algebras is generalized to the MR case, so that both direct and coupling terms can be determined. Usefulness of this fully diagrammatic spin-adaptation approach is illustrated on a derivation of explicit expressions for the linear and bilinear coupling terms that are required in the special two-reference MR-CC theory involving singly and doubly excited states (MR-CCSD formalism). Results obtained with the diagrammatic approach are compared with those derived earlier using the algebraic technique and relative advantages of both procedures are compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113244
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Method of moments approach and coupled cluster theory (1991)
    Springer
    Theoretical chemistry accounts 80 (1991), S. 223-243 
    Details
    ISSN: 1432-2234
    Keywords: Coupled cluster approach ; Method of moments approach ; Many-electron correlation problem ; Intruder states ; Quasi-degeneracy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The single reference coupled cluster (CC) approach to the many-electron correlation problem is examined from the viewpoint of the method of moments (MM). This yields generally an inconsistent (overcomplete) set of equations for cluster amplitudes, which can be solved either in the least squares sense or by selective projection process restricting the number of equations to that of the unknowns. These resulting generalized MM-CC equations always contain the standard CC equations as a special case. Since, in the MM-CC formalism, the Schrödinger equation will be approximately satisfied on a subspace spanned by non-canonical configurations, this procedure may be helpful in extending the standard single reference CC theory to quasi-degenerate situations. To examine the potential usefulness of this idea, we explore the linear version of the CC approach for systems with a quasi-degenerate reference, in which case the standard linear theory is plagued with singularities due to the intruder states. Implications of this analysis for the structure of the wavefunction are also briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01117411
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  • 4
    Electronic Resource
    Electronic Resource
    Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique (1990)
    Springer
    Theoretical chemistry accounts 78 (1990), S. 65-128 
    Details
    ISSN: 1432-2234
    Keywords: Many-electron correlation problem ; Spin-adaptation ; Coupled cluster approach ; Optimized inner projection ; Graphical methods of spin algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01119191
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  • 5
    Electronic Resource
    Electronic Resource
    Explicit representation of Gel'fand-Tsetlin states in clifford algebra unitary group approach (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 36 (1989), S. 127-140 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A explicit expression for the unitary group Clebsch-Gordan coefficients, which couple two fully antisymmetric single-column states into the two-column Gel'fand-Tsetlin states, is given in terms of isoscalar factors for the canonical subgroup chain U(n) ⊃ U(n - 1) ⊃ … ⊃ U(1). The isoscalar factors are expressed through the step numbers labeling canonical basis states and enable a straightforward construction of Gel'fand-Tsetlin states in the Clifford algebra unitary group approach, without the use of the tables for the symmetric group outer-product reduction coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560360205
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Orthogonally spin-adapted coupled-cluster equations involving singly and doubly excited clusters. Comparison of different procedures for spin-adaptation (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 36 (1989), S. 429-453 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A particularly compact form of the orthogonally spin-adapted coupled-cluster equations involving all singly and doubly excited clusters is derived for the general case of a non-Hartree-Fock closed-shell reference determinant. The diagrammatic approach based on the graphical methods of spin algebras is applied. The relationship of different diagrammatic procedures for spin-adaptation, employing both bare and spin-adapted two-electron interaction vertices, is discussed. A comparison with the results obtained with algebraic spin-adaption approaches is also given.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560360402
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  • 7
    Electronic Resource
    Electronic Resource
    Numerical estimates of the convergence of the Rayleigh-Schrödinger perturbation expansions for the energy levels of various models of the benzene molecule (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 147-151 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We estimate radii of convergence of the Rayleigh-Schrödinger perturbation expansions for various energy levels of the π-electron model of the benzene molecule, described by the Hubbard Hamiltonian in both weakly and strongly correlated limits. They are determined using a “generalized” Cauchy criterion applied to the numerically determined coefficients of the pertinent expansions.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210111
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  • 8
    Electronic Resource
    Electronic Resource
    Convergence radii of the perturbation expansions for the ground-state energies of finite Hubbard models (1988)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 407-415 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ground state energies of finite Hubbard molecules are calculated by numerically solving the Lieb-Wu equations for a complex Hubbard repulsion parameter U. From the positions of the singular points located in the complex plane, the radii of convergence of the perturbation expansions for the ground state energies are determined.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560340502
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  • 9
    Electronic Resource
    Electronic Resource
    On the solution of coupled-cluster equations in the fully correlated limit of cyclic polyene model (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 9-34 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that the exact pair-cluster coefficients corresponding to the fully correlated limit of cyclic polyene model satisfy the equations of the approximate coupled-pair theory with quadruples (ACPQ) approach, but do not represent any solution of the standard coupled-cluster method with doubles (CCD) equations. Implications of this result for the performance of various coupled-cluster (CC) approaches, when applied to cyclic polyene model, are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560400807
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  • 10
    Electronic Resource
    Electronic Resource
    Valence bond approach exploiting Clifford algebra realization of Rumer-Weyl basis (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 117-146 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A detailed algorithm is described that enables an implementation of a general valence bond (VB) method using the Clifford algebra unitary group approach (CAUGA). In particular, a convenient scheme for the generation and labeling of classical Rumer-Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin-independent operator, in this basis. The case of both orthogonal and nonrothogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N-electron basis-set truncation than is possible with the standard Gel'fand-Tsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser-Parr-Pople (PPP)-type Hamiltonian and nonorthogonal overlap-enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560410112
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