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  • 1
    Electronic Resource
    Electronic Resource
    Alternancy symmetry: A unified viewpoint (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 1722-1735 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general formulation of the alternancy symmetry adaptation for the semiempirical Pariser–Parr–Pople (PPP) type Hamiltonians is presented at both the spin-orbital and spin-adapted many-electron levels. The derivation of the general form of the alternancy symmetry conjugation operators is based solely on the tight-binding approximation for the short range one-particle part of the Hamiltonian considered. It starts by a simple formulation of the desired invariance properties of the PPP type Hamiltonian. Using algebraic properties of the unitary group generators and of their particle number nonconserving extensions, it leads to a completely explicit and general form for the alternancy symmetry conjugation operators. In this way the prior descriptions, which become special cases of this general formulation, are interrelated and unified. The spin and quasispin character of certain components of these operators are also pointed out and explicitly derived. The spin-adapted version is based on the unitary group formulation of the valence bond-type approach. A completely general formulation is given which applies to many-electron states of an arbitrary multiplicity of neutral systems, either of the normal kind with an identical number of starred and nonstarred sites, or of the radicaloid character with different numbers of starred and nonstarred sites. An explicit form of the dependence of the relative phase factor of the alternancy symmetry conjugation operator on the total spin, total electron number and on the number of starred and nonstarred sites is also given. General rules for the construction of spin and alternancy symmetry-adapted states are illustrated on a few simple examples. Finally, a brief discussion of the implications of the alternancy symmetry is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449359
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  • 2
    Electronic Resource
    Electronic Resource
    Nonadiabatic corrections for coupled oscillators using Rayleigh–Schrödinger perturbation theory of very high orders (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 8906-8915 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Prospects for higher order perturbation theory in evaluating nonadiabatic corrections to the adiabatic energy levels are investigated by performing calculations on a series of two-dimensional anharmonically coupled oscillators. The convergence properties of the perturbation series are demonstrated for different harmonic frequencies and magnitudes of perturbation. It is found that the perturbation series corresponding to the adiabatic levels which are away from any intersections can accurately be summed, by means of the Padé summation technique, even in the case of "giant'' couplings. The proposed "nondegenerate'' perturbation theory procedure may also provide accurate results, under certain conditions, even in the case of intersecting energy levels. It fails to converge only in the regions around the crossing points. Elsewhere, it converges safely (especially when using high-accuracy arithmetics) and provides the basis for relatively accurate interpolation over the crossing regions. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468944
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  • 3
    Electronic Resource
    Electronic Resource
    Solution of the One-Dimensional Schroedinger Equation by the Combined Use of Symbolic and Numerical Computation (1995)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 15608-15610 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100042a041
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical application of the coupled cluster theory with localized orbitals to polymers. IV. Band structure corrections in model systems and polyacetylene (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 10248-10264 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present the formalism for the correction of the band structure for correlation effects of polymers in the framework of a localized orbital approximation, using the quasiparticle model. For this purpose we use in an ab initio framework Møller–Plesset perturbation theory in second order, the coupled cluster doubles method, and its linear approximation. The formalism is applied to a water stack and two different forms of a water chain as model systems to test the reliability of the approximations involved. From our previous work we know that, e.g., in polyacetylene difficulties due to the localizability of the canonical crystal orbitals do not arise from the π or π* bands, but from bands of σ symmetry. Thus we concentrate in this work again on polyacetylene as an example of a realistic polymer. We find that the localized orbital approximation is quite useful also in the case of band structure corrections due to correlation effects. However, the coupled cluster calculations, in particular, turn out to be computationally very costly for infinite systems. But it seems to us that localized orbital approximations are at the moment the only way to make coupled cluster calculations on realistic polymers with covalent bonds between the unit cells possible at all. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474051
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  • 5
    Electronic Resource
    Electronic Resource
    On the use of divergent series in vibrational spectroscopy. Two- and three-dimensional oscillators (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 7331-7336 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Prospects for higher order perturbation theory in evaluating accurate eigenvalues and eigenvectors of the vibrational Hamiltonian are investigated by performing calculations on a series of two- and three-dimensional quartic anharmonic oscillators imitating vibrational motions in the H2O, H2S, NO2, SO2, and HOF triatomic molecules. Despite the fact that most of the corresponding perturbation expansion series diverge strongly they can be summed efficiently using the same methods as in previous studies on one-dimensional oscillators. Hence, higher order perturbation theory appears as a reasonable alternative to accurate variational methods in the case of small molecular systems and as a very promising tool for a proper treatment of larger systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465714
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  • 6
    Electronic Resource
    Electronic Resource
    The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 571-609 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The strongly divergent Rayleigh–Schrödinger perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator and a corresponding renormalized perturbation expansion [F. Vinette and J. Cízek, J. Math. Phys. 32, 3392 (1991)] are summed by Padé approximants, by Levin's sequence transformation [D. Levin, Int. J. Comput. Math. B 3, 371 (1973)], and by a closely related sequence transformation which was suggested recently [E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989)]. It is shown that the renormalized perturbation expansion can be summed much more easily than the original perturbation expansion from which it was derived, and that Levin's sequence transformation diverges and is not able to sum the perturbation expansions. The Padé summation of the renormalized perturbation expansions gives relatively good results in the quartic and sextic case. In the case of the octic anharmonic oscillator, even the renormalized perturbation expansion is not Padé summable. The best results are clearly obtained by the new sequence transformation which, for instance, is able to sum the renormalized perturbation expansions for the infinite coupling limits of the quartic, sextic, and octic anharmonic oscillator, and which produces at least in the quartic and sextic case extremely accurate results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530262
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  • 7
    Electronic Resource
    Electronic Resource
    Origins of coupled cluster technique for atoms and molecules (1991)
    Springer
    Theoretical chemistry accounts 80 (1991), S. 91-94 
    Details
    ISSN: 1432-2234
    Keywords: History of coupled cluster theory ; Correlation problem ; Quantum theory of atoms and molecules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A short description of major events in the study of the correlation problem in the period 1950–1960 is given. The development of coupled cluster theory in the years of 1960–1972 is described. Selected references on the development of coupled cluster theory after 1972 are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01119616
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  • 8
    Electronic Resource
    Electronic Resource
    Eléments matriciels de l'hamiltonien entre les états monoexcités et biexcités singulets (1966)
    Springer
    Theoretical chemistry accounts 6 (1966), S. 292-298 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Abstract Formulas are derived for matrix elements of the hamiltonian between monoexcited singlet states and biexcited singlet states and for matrix elements of the hamiltonian between the biexcited states themselves. The formulas are suitable for computer calculations.
    Abstract: Zusammenfassung Es werden Formeln für die Matrixelemente eines Hamiltonoperators zwischen den einmal angeregten Singulettzuständen und den zweimal angeregten Singulettzuständen sowie den zweimal angeregten Singulettzuständen untereinander abgeleitet. Die Formeln eignen sich für die Anwendung einer vollautomatischen Rechenmaschine.
    Notes: Résumé On a dérivé les formules pour les éléments matriciels de l'hamiltonien entre les états singulets monoexcités et les états biexcités singulets et pour les élements matriciels de l'hamiltonien entre les états biexcités singulets. Les formules sont convenables pour l'usage sur ordinateur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00537275
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  • 9
    Electronic Resource
    Electronic Resource
    On The Tauberian constant in the Ikehara theorem (1999)
    Springer
    Czechoslovak mathematical journal 49 (1999), S. 673-682 
    Details
    ISSN: 1572-9141
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022467830141
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  • 10
    Electronic Resource
    Electronic Resource
    Calcul de l'Énergie de Corrélation pour l'État Fondamental de la Molécule d'Acétylène (1967)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 1 (1967), S. 653-655 
    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
    Description / Table of Contents: Correlation effects in the acetylene molecule are studied by a method using the technique of Feynman-like diagrams. The introduction of the reduced atomic electronic integrals decreases considerably the value of correlation energy.
    Abstract: Die Korrelationseffekte in dem Acetylenmolekül werden mit Hilfe einer Methode, die die Feynmandiagramähnliche Technik benützt, untersucht. Die Einführung der redusierten Atomintegrale erniedrigt wesentlich den Wert der Korrelationsenergie.
    Notes: Les effects de corrélation dans la molécule d'acétylène sont étudiés à partir d'une méthode utilisant une technique de diagrammes analogues à ceux de Feynman. L'introduction de la réduction des intégrales électroniques atomiques diminue considérablement la valeur de l'énergie de corrélation.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560010515
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