A new approximation method to obtain vibration eigenfunctions suitable for a new oscillator model

Navati, B. S.; Korwar, V. M.

doi:10.1007/bf02846281

Cited by 6 publications

References 10 publications

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Generalized morse analytic function for the “true” diatomic potential of the RKR type

et al. 1993

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The problem of the representation of the RKR (or IPA) diatomic potential by a simple analytic function is considered. This old problem has for a fairly good solution the Coxon-Hajigeorgiou function U(x) = D(lexp( -fn(x)I2 withf,(x) = Ck=, a,P. The problem of the determination of the disposable parameters al, . . . a,, [in order that U(r) fits the given RKR potential] is reduced to that of a set of linear equations in a, where a standard least-squares technique is used. The application to several states (ground or excited) of several molecules shows that a fairly "good' fit is obtained for n -10, even for the state X0,-12 bounded by 109 vibrational levels, for which the RKR potential is defiied by the coordinates of 219 points. It is shown that the percentage deviation IU(r)RKR -U(r)l throughout the range of r values is about 0.04% for XX-Li2, 0.0005% for XS--HC1,0.06% for XO,-I,, and 0.05% for B0,-12 (as examples). This approach shows the same success for deep and shallow potentials. The comparison of the computed E, (vibrational energy) and B,,

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Generalized morse analytic function for the “true” diatomic potential of the RKR type

et al. 1993

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The true diatomic potential as a perturbed Morse function

Dagher¹,

Kobersi²,

Kobeissi³

1995

J Comput Chem

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The problem of representing a diatomic (true) Rydberg-Klein-Rees potential U ' by an analytical function U" is discussed. The perturbed Morse function is in the form U" = U M + Cb, y", where the Morse potential is U M = Dy2, y = 1 -exp( -a(r -re)). The problem is reduced to determination of the coefficients b, so UYr) = U ' ( r ) . A standard least-squares method is used, where the number N of b, is given and the average discrepancy n = I(U' -U a ) / U ' I is observed over the useful range of r. N is varied until n is stable. A numerical application to the carbon monoxide X 'C state is presented and compared to the results of Huffaker' 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 is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy E, and the rotational constant B,, for both potentials, shows that the present method gives values of and a 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. 0 1995 by John Wiley & Sons, Inc.In the early decades of quantum mechanics, the rotationless potential U ( r ) was given by an analytical function. The functions of Durham3

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Interpolation and fitting of potential energy surfaces: Concepts, recipes and applications

Jaquet

1999

Lecture Notes in Chemistry

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A new approximation method to obtain vibration eigenfunctions suitable for a new oscillator model

Cited by 6 publications

References 10 publications

Generalized morse analytic function for the “true” diatomic potential of the RKR type

Generalized morse analytic function for the “true” diatomic potential of the RKR type

The true diatomic potential as a perturbed Morse function

Interpolation and fitting of potential energy surfaces: Concepts, recipes and applications

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