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  • 1995-1999  (7)
  • 1975-1979  (5)
  • 1970-1974  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Nonadiabatic corrections for coupled Morse oscillators using Hutson and Howard perturbation theory (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 8916-8921 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An adiabatic separation is applied to two coupled Morse oscillators. The resulting approximate energies and wavefunctions are corrected for nonadiabatic interactions by means of the perturbation theory approach of Hutson and Howard supplemented by the "Padé divergent series summation'' technique. The convergence properties of the perturbation series are investigated as functions of the oscillator frequencies and coupling strengths varying over a wide range of values. The rate of convergency and accuracy of summability of the perturbation series depend strongly on the presence of accidental resonances among the adiabatic levels. For relatively well isolated levels, the series either converge strongly or can be summed very accurately for almost any strength of perturbation. In the case of close coincidence of more than two strongly coupled levels, the approach becomes unreliable. The convergency/summability problems faced in the "intermediate'' cases of two "adiabatically crossing'' levels appear to be curable by means of interpolating over the "near-degeneracy'' regions. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468945
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  • 2
    Electronic Resource
    Electronic Resource
    Analytic calculation of second-order perturbatior energy for the one-dimensional Hubbard model in the Hückel limit (1995)
    Springer
    Journal of mathematical chemistry 18 (1995), S. 217-235 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The study of the Hückel limit for the one-dimensional Hubbard model is very complicated. It is necessary to prepare the Lieb-Wu system of equations for expansion and then to initialize the variables which appear in the system, which is not straightforward. However, it is remarkable that, for the second-order contribution to the energy in this limit, it is possible to obtain, after complicated manipulations, quite transparent expressions. The analytical solution is obtained order by order for the variables toβ −2 which appear in the Lieb-Wu solution and theβ −1 coefficient in the energy is calculated using these expansions. The energy can be calculated numerically using these analytic results for the variables for increasing values ofN.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164660
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  • 3
    Electronic Resource
    Electronic Resource
    Correlation effects in the low-lying excited states of the PPP models of alternant hydrocarbons. I. Qualitative rules for the effect of limited configuration interaction (1974)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 951-970 
    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: Simple rules for an estimate of the correlation effects in the low-lying states of alternant hydrocarbons, as described by the Pariser-Parr-Pople Hamiltonian, are formulated. These rules are based on the alternancy and spin symmetry classification of states in both strongly and weakly correlated limits and on the valence bond characteristics of those states in the fully correlated limit. It is shown that the largest effect of the electron correlation will be found for the singlet “minus” states (using Pariser's classification of the alternancy symmetry species), a smaller effect for the triplet “plus” states, and a much smaller effect for the remaining states. These rules are exemplified by limited CI calculations including all monoexcited and all mono- and bi-excited configurations, respectively, for a number of π-electronic systems. In view of these rules the success of the PPP model in the monoexcited CI approximation may be understood.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560080610
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  • 4
    Electronic Resource
    Electronic Resource
    Application of graphical methods of spin algebras to limited CI approaches. II. A simple open shell case (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 849-867 
    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 time independent diagrammatic technique based on the Wick theorem and graphical methods of spin algebras, as outlined in Part I, is applied to a simple open shell case having one unpaired electron in addition to the pure singlet closed shell. Compact explicit expressions for the matrix elements of a spin independent Hamiltonian between conveniently chosen spin symmetry adapted states are given for the ground, mono- and bi-excited configurations.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560110512
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Correlation problems in atomic and molecular systems IIISee [1] for Parts I and II.. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methodstSee [2].Part of this work was carried out at the Institute of Physical Chemistry, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. (1971)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 5 (1971), S. 359-379 
    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 equations of the coupled-pair many-electron theory (CPMET) for the closed shell systems are rederived both in the spin-orbital and orbital forms without the use of second quantization, Wick's theorem or the technique of Feynman-like diagrams. Only the Slater rules are used for the calculation of necessary matrix elements. A comparison with earlier papers shows clearly the usefulness and conceptual simplicity of the mathematical methods of quantum field theory both in the derivation of the CPMET, in spin-orbital form, and in the process of excluding spin variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560050402
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  • 6
    Electronic Resource
    Electronic Resource
    An algebraic approach to bound states of simple one-electron systemsPresented in Part at the Sanibel Workshop 1977. (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 875-896 
    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 very general realization of the so(2, 1) algebra, which easily follows from the basic commutation relations that are satisfied by any pair of mutually conjugate generalized coordinates and momenta, is constructed. Using special cases of this general realization, and closely following the well known derivation of the eigenvalue spectra of the angular-momentum operators, based on the so(3) algebra, we derive the energy spectrum for the N-dimensional isotropic harmonic oscillator, and for both the nonrelativistic and the relativistic N-dimensional hydrogen atom. Special attention is given to a simple derivation of the form of these Hamiltonians in terms of the so(2, 1) algebra generators. In particular, the usually exploited tilting transformation is avoided, and the whole derivation is presented in an extremely simple and straightforward way. The present approach stresses the similarity and mutual relationship between the systems studied and, in addition to introducing some novel techniques and providing considerable insight into the overall structure of these problems, also has a definite pedagogical value.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560120510
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  • 7
    Electronic Resource
    Electronic Resource
    Correlation effects in the PPP model of alternant π-electronic systems: two-point Padé approximant approach (1975)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 9 (1975), S. 987-1007 
    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 general procedure, based on the two-point Padé approximant technique, is formulated, enabling an interpolation of the low-lying energy levels of the PPP (Pariser-Parr-Pople) Hamiltonian over the divergency gap separating the asymptotic perturbation expansions in both strongly and weakly correlated limits. The methods for the determination of the first few terms of the perturbation expansions in both limits are also briefly outlined. The procedure is applied to the five lowest singlet energy levels of the PPP model of the benzene molecule and the results are compared with the exact solutions for this model. The advantages as well as the shortcoming of this approach are pointed out and illustrated on the model calculation for benzene. The applicability of this technique to larger π-electronic systems is discussed and a feasible procedure for its implementation is formulated.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560090607
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  • 8
    Electronic Resource
    Electronic Resource
    Application of graphical methods of spin algebras to limited CI approaches. I. Closed shell case (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 813-848 
    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 time independent diagrammatic technique based on the mathematical methods of quantum electrodynamics (second quantization, Wick's theorem, Feynman-like diagrams) is combined with graphical techniques of spin algebras to derive general expressions for the matrix elements of spin independent one- and two-particle operators between spin symmetry adapted ground, mono- and bi-excited configurations of a closed shell system. Two coupling schemes are considered for bi-excited states and their relative merits are discussed. Finally, the results are used to derive compact expressions for the coupling coefficients of the direct configuration interaction from molecular integrals (CIMI) method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560110511
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  • 9
    Electronic Resource
    Electronic Resource
    Correlation problems in atomic and molecular systems. VII. Application of the open-shell coupled-cluster approach to simple π-electron model systems (1979)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 15 (1979), S. 463-479 
    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 coupled-cluster variational-like direct approach to the calculation of ionization and electron attachment energies and of excitation energies is applied to several π-electron model systems, using the PPP Hamiltonian with various parametrizations. A simple approximation, which represents the triexcited clusters in terms of disconnected W1T2 terms, is employed. All the necessary diagrams for both excitation energy and ionization potential (electron affinity) calculations are given in the compact Hugenholtz nonoriented form. The results of the calculations for benzene, trans-butadiene, all-trans-hexatriene, and fulvene are compared with the corresponding full CI results, and the conclusions about the validity and efficiency of this approach are drawn.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560150503
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  • 10
    Electronic Resource
    Electronic Resource
    Perturbation expansion of the ground-state energy for the one-dimensional cyclic Hubbard system in the Hückel limit (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 53 (1995), S. 457-466 
    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 perturbation expansion coefficients for the ground-state energy of the half-filled one-dimensional Hubbard model with N = 4ν + 2, (ν = 1, 2,…) sites and satisfying cyclic boundary conditions were calculated in the Hückel limit (U/β → 0), where β designates the one-electron hopping or resonance integral, and U, the two-electron on-site Coulomb integral. This was achieved by solving - order by order - the Lieb-Wu equations, a system of transcendental equations that determines the set of quasi-momenta {ki} and spin variables {τα} for this model. The exact values for these quantities were found for the N = 6 member ring up to the 20th order in terms of the coupling constant B = U/2β, as well as numerically for 10 ≤ N ≤ 50, and the N = 6 Lieb-Wu system was reduced to a system of sextic algebraic equations. These results are compared with those of the infinite system derived analytically by Misurkin and Ovchinnikov [Teor. Mat. Fiz. 11, 127 (1972)]. It is further shown how the results of this article can be used for the interpolation by the root of a polynomial. It is demonstrated that a polynomial of relatively small degree provides a very good approximation for the energy in the intermediate coupling region. © 1995 John Wiley & Sons, Inc.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560530502
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