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  • 1
    Electronic Resource
    Electronic Resource
    Explicit expression of the franck-condon factors in terms of the potentials of the two states (1981)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 20 (1981), S. 633-644 
    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 calculus of the overlap integral for two states represented by the vibrational wave functions ψν′a and ψν″b is reduced to that of the Franck-Condon integral ℒ(0, x) = ∫0x ψν′aψν″b (t) dt. It is proved that for “numerical potentials” (as well as for a Dunham potential), this integral is given on each interval by a simple analytic expression in terms of the two potentials. The Franck-Condon factors are well determined by “coupling constants” related uniquely to the coordinates of the turning points of the potentials. An application to the band system BII—XΣ of Nα2 is compared with the usual numerical methods.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560200306
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  • 2
    Electronic Resource
    Electronic Resource
    Vibrational eigenvalues for all levels for the Lennard-Jones potential (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 9 (1988), S. 647-649 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540090610
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  • 3
    Electronic Resource
    Electronic Resource
    Highly accurate vibration-rotation Franck-Condon factors for high levels (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 6 (1985), S. 360-367 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Highly accurate vibration-rotation Franck-Condon factors qab, for a transition between two diatomic electronic states (a) and (b), are sought. When the potentials of states (a) and (b) are of the RKR type, the computation of qab is reduced to that of Franck-Condon integral Iab(i) = ∫riri+1 ψa(r)ψb(r) dr in an interval ri, ri+1. By using convenient interpolations for the potentials Ua and Ub in the considered interval, this integral becomes Iab(i) = ∑n=ON δnab (ri+1 - ri)n+1/(n + 1), where the “coupling constants” δnab depend uniquely on the eigenvalues Ea and Eb of the considered transition and on the potentials Ua and Ub (the number N of terms depends on the desired accuracy). The method used computes the Franck-Condon factors qab without the explicit use of the wave function and by replacing the integrals by simple summations. To test the values of qab obtained by this method, the orthogonality rule ∫0∞ ψv′ψv″ dr = 0 (for v′ ≠ v″) is used for one state or the other. This test, along with other tests, show that the Franck-Condon factors computed by the present method are accurate to nine significant figures for high and low levels.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540060505
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  • 4
    Electronic Resource
    Electronic Resource
    A new treatment of the vibration-Rotation eigenvalue problem for a diatomic molecule (1983)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 4 (1983), S. 218-225 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The problem of the determination of the vibration-rotation eigenvalue in diatomic molecules is considered. An eigenvalue equation totally independent from the eigenfunction is written for any potential, analytical or numerical. This equation uses uniquely the vibration-rotation canonical functions; its resolution is reduced to that of a simple and classical numerical problem. Examples of numerical applications for analytical (Morse) and numerical potentials are presented. It is shown that the vibrational eigenvalues deduced from the eigenvalue equation are within 10-6 cm-1 of the exact values. Comparison with conventional methods are presented and discussed.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540040212
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  • 5
    Electronic Resource
    Electronic Resource
    On the diatomic vibration-rotation eigenvalue equation: Highly accurate results for high levelsOriginal proofs of this paper were lost in the mail. (1984)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 5 (1984), S. 576-580 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Accurate vibration-rotation eigenvalues EvJ are sought for very high levels (up to dissociation) of a diatomic potential. The method used is the recent “eigenvalue equation” method [Kobeissi et al., J. Comput. Chem., 4, 218 (1983)] which dissociates the determination of the eigenvalue from that of the eigenfunction. A new mathematical formulation for any numerical potential is presented, which reduces the problem to the use of a single recurrent formula. A numerical application to the model potential used by Cashion [J. Chem. Phys., 39, 1872 (1963)], up to v = 23, gives results equal to the exact eigenvalues to approximately 10-14 cm-1. Another application to the model potential used by Johnson [J. Chem. Phys., 67, 4086 (1977)], up to v = 60, gives similar results.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540050611
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  • 6
    Electronic Resource
    Electronic Resource
    The true diatomic potential as a perturbed Morse function (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 723-728 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The problem of representing a diatomic (true) Rydberg-Klein-Rees potential Ut by an analytical function Ua is discussed. The perturbed Morse function is in the form Ua = UM + ∑bnyn, where the Morse potential is UM = Dy2, y = 1 -exp(-;a(r - re)). The problem is reduced to determination of the coefficients bn so Ua(r) = Ut(r). A standard least-squares method is used, where the number N of bn is given and the average discrepancy ΔU = |(Ut - Ua)/Ut| is observed over the useful range of r. N is varied until ΔU is stable. A numerical application to the carbon monoxide X1∑ state is presented and compared to the results of Huffaker1 using the same function with N = 9. The comparison shows that the accuracy obtained by Huffaker is reached in one model with N = 5 only and that the best ΔU is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy Ev and the rotational constant Bv, for both potentials, shows that the present method gives values of ΔE and ΔB that are smaller than those found by Huffaker. The dissociation energy obtained here is 2.3% from the experimental value, which is an improvement over Huffaker's results. Applications to other molecules and other states show similar results. © 1995 by John Wiley & Sons, Inc.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540160608
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  • 7
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    On the use of a variable-step method for the computation of diatomic eigenvalues near dissociation: The Lennard-Jones potential (1990)
    Elsevier
    Details
    Publication Date: 1990-02-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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