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  • 1
    Electronic Resource
    Electronic Resource
    Algebraic approach to one- and two-center harmonic oscillator integralsThis work was partially supported by CONACYT-MEXICO PVT/EN/NAL81/1557. (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 57-60 
    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 second-quantization formalism is used to derive closed formulas for one- and two-center matrix elements of two harmonic oscillators with different force constants. The method is based on a linear transformation between the creation and annihilation operators of the two harmonic oscillators, the use of the Baker-Campbell-Hausdorff theorem, and Cauchy's integral formula. As presented, the proposed procedure is considerably simpler than the ones hitherto employed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260809
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  • 2
    Electronic Resource
    Electronic Resource
    Hypervirial theorem and ladder operators. Recurrence relations for harmonic oscillator integrals (1986)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 29 (1986), S. 211-219 
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    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 second-quantization formalism combined with a hypervirial theorem is used to derive new recurrence relations for one-dimensional harmonic oscillator matrix elements. The most general case of 〈m|f(â, â+)|n〉 is considered, and the recurrence relations forf(â, â) = Xk, exp(-βX), and exp(-X2) are given as examples. The relations obtained are considerably simpler than those derived by using only the hypervirial theorem; comparatively, the recurrence relations presented here have the advantage of avoiding the use of the quantum mechanical sum-rules when determining initial matrix elements. The proposed procedure can be used to determine the recurrence relations for other potentials as well as to evaluate the two-center integrals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560290211
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  • 3
    Electronic Resource
    Electronic Resource
    Closed formulas for one- and two-center harmonic oscillator integrals (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 32 (1987), S. 729-735 
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    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: Closed formulas for one- and two-center matrix elements are derived for an analytical arbitrary operator function in the harmonic oscillator basis. The method is based on the Baker-Campbell-Hausdorff (BCH) theorem and Cauchy's integral formula. A table is displayed showing some examples for the two-center case. A pertinent relationship with other works is discussed.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560320771
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  • 4
    Electronic Resource
    Electronic Resource
    Binding energies and peak intensities of light hydrocarbon molecules through TOM I. Methane and acetylene (1986)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 555-561 
    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: Binding energies and peak intensities of methane and acetylene molecules are calculated using the transition operator method (TOM) adapted to ab-initio Hartree-Fock programs. The calculations were done for both systems with and without symmetry restrictions, and the results are analyzed within the framework of TOM. It is found that the symmetry constraints have an important role in the binding energies of the acetylene molecule but none in the methane molecule. The intensities were calculated using the generalized sudden approximation (GSA) and the dipolar approximation; those resulting intensities are compared and discussed for the core and valence orbitals. The results let us conclude that the GSA method is only applicable when comparing photoionization intensities of neighboring ionization energy orbitals.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560300749
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  • 5
    Electronic Resource
    Electronic Resource
    ESCA Peak intensities in the dipole and generalized sudden approximations using fourier transforms of GTO'sWork partially supported by CONACYT (PNCB-1469). (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 417-423 
    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: Analytical expressions for the square of the spherical average of Fourier transforms of Gaussian type orbitals (GTO's) are given. A direct application of these expressions to the calculation of molecular photoionization cross sections is considered under the generalized sudden (GSA) and dipole (DA) Approximations. Numerical calculations were done on the CO molecule using bound orbitals obtained by ab initio LCAO-MO calculations with Gaussian basis sets. The results are in good agreement with experiments. Those obtained by the GSA method however, suggest a limitation in its use: the GSA method is only applicable when comparing photoionization intensities of neighboring ionization energy orbitals. Applications to other molecules are immediate.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230210
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  • 6
    Electronic Resource
    Electronic Resource
    Alternative approach to the factorization method (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 44 (1992), S. 171-179 
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    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 procedure to obtain the operational solutions of second order differential equations related with Sturm-Liouville problems is presented. The method is based on the commutation relation between the ladder operators themselves, with a certain structure, and the position and momentum operators. Even though the creation and annihilation operators, derived by the proposed approach, factorize as expected the corresponding differential equation, the method does not use, as original premise factoring, the differential relation under consideration. That is, the displayed procedure is quite different, simple, and direct when compared with other procedures such as the factorization method of Infeld and Hull. To illustrate the above, the usefulness of the proposed procedure is shown by finding the ladder operators associated to the quantum numbers n and I for various potential wave functions. © 1992 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560440816
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  • 7
    Electronic Resource
    Electronic Resource
    Ladder operators for central potential wave functions from the algebraic representation of orthogonal polynomials (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 155-164 
    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 algebraic procedure that yields to raising and lowering operators for the solutions of second-order differential equations is presented. The method is illustrated by applying it to the differential equations of Hermite and Laguerre polynomials. Taking advantage of the algebraic representation of these polynomials, the ladder operators for harmonic oscillator and hydrogen atom wavefunctions are straightforwardly deduced without resorting to specialized factorizations. The proposed algebraic approach can be extended to the determination of new sets of ladder operators that could be used in the calculation of matrix elements in specific applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560400818
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  • 8
    Electronic Resource
    Electronic Resource
    Theoretical study on Al multiple substitutions in the MFI zeolite (1991)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 659-669 
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    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: In this work we deal with ab initio and semiempirical calculations of single and multiple Al → Si replacements in the ZSM-5 structure. Substitutional energies for single replacements were obtained for cluster models of monomers, hexamers, and for the secondary building unit (SBU) of the zeolite by means of nonempirical SCF calculations, as well as the modified neglect of differential overlap (MNDO) method for extended clusters. The choice of the semiempirical methods for the study of multiple Si replacements by Al in the extended cluster model of the SBU is justified from the results with monomers and hexamers where the replacement energies obtained with MNDO are qualitatively the same as those from ab initio calculations. According to the results, a site occupancy order in the unit cell of the ZSM-5 network is derived from multiple Al → Si substitutions in the SBU, providing a theoretical basis for the Loewenstein-Dempsey Al sitting avoidance rules. Likewise, a Si/Al limit ratio in the Mobil FIve (MFI) zeolite, along with the corresponding Al distribution pattern in the unit cell, are also obtained.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560400858
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  • 9
    Electronic Resource
    Electronic Resource
    Improved recursion formulas for the calculation of two-center central potential integrals (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 339-347 
    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 commutator algebra procedure is used to get improved recurrence relations for the calculation of any f(r) off-diagonal two-center matrix elements in the general case of displaced arbitrary central potential wave functions. As expected, the proposed formulas reduce properly to the generalized recursion equations for the calculation of one-center integrals. Besides, when f(r) = rk, one obtains the equivalent of the Kramer rule for two-center multipolar matrix elements for arbitrary potentials, and when f(r) is constant, the Wu formula (for the calculation of Franck-Condon factors) is ameliorated in the sense that the new relation not necessarily considers equal mass. Furthermore, all diagonal matrix elements as well as all off-diagonal integrals between nondisplaced potentials appear, in our treatment, as particular cases in good agreement with already published results. As a useful application, the corresponding recurrence relations for the calculation of one-center hydrogenic matrix elements and two-center Kratzer potential integrals are given as examples. However, our approach is general and can be easily extended to obtain recursion formulae for other potential wave functions. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560560838
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