Potential Energy Function For Diatomic Molecules Research Articles

Modified Rosen-Morse potential-energy model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved expression for the generalized Woods-Saxon potential. It is exactly shown that the generalized Woods-Saxon potential and the well-known Rosen-Morse potential are the same empirical potential-energy function for diatomic molecules. Based on the measure of inner-shell radii of two atoms, we propose a modified Rosen-Morse potential-energy model. Evaluation of the average deviations from the experimental data is carried out on six molecules. The modified Rosen-Morse potential is found to be more accurate than the Morse and Rosen-Morse potentials in fitting experimental data for the six molecules examined.

Continued-fraction expansion of the Born-Oppenheimer potential-energy function for diatomic molecules

Expansion of the internuclear Born-Oppenheimer potential for diatomic systems, in the form of a continued fraction, has been investigated. This function satisfies all criteria applicable to a real potential curve of molecules in a stable electronic state; it asymptotically approaches a finite value in the dissociation limit, exhibits a minimum energy at the equilibrium internuclear separation, and approaches a positive value greater than a dissociation energy as the separation decreases. The proposed expansion is applied in quantitative analysis of the infrared, microwave, and Raman spectra of BrCl, NaCl, and ${\mathrm{N}}_{2}.$ The observed transitions are reproduced within experimental errors by making use of fewer fitted parameters than in the approach that employs a power expansion of the potential-energy function.

Extension of a general potential-energy function for diatomic molecules

The conditions applicable at the limits of the united atom and the separate atoms may be applied to any radial function for diatomic molecules based on the argument z≡2(R−Re)/ (R+Re) so as to generate further coefficients in a polynomial representation that thus has the correct asymptotic behavior in the approach to these limits. The appropriate conditions are given for the potential-energy and dipole-moment functions, and the results are illustrated by application to HCl. This type of representation is compared with rational functions.

Accuracy of diatomic potential functions

The accuracy of previously proposed potential-energy functions for diatomic molecules has been tested against known RKR and ab initio data, where these data span a large fraction of the well depth. Systematic testing has revealed several forms which are more accurate than those proposed earlier for a given number of adjustable parameters. The most accurate functions allow the Morse curvature parameter to vary with the internuclear distance. Various higher-order series are also compared with respect to accuracy and stability, leading to general recommendations for the accurate fitting of diatomic potential-energy data.

Comment on Paper by T. Tietz: Potential-Energy Function for Diatomic Molecules

The claim by Tietz to have obtained a new example of a spherically symmetric potential for which the energy levels may be obtained analytically is shown to be unfounded.

Potential-Energy Function for Diatomic Molecules

The purpose of this paper is to give a simple expression for the potential-energy function for diatomic molecules for which one can solve the Schrödinger equation exactly for both discrete and continuous energy parameters E. The analytic expression for this potential curve is illustrated numerically for several diatomic molecules.

Potential energy curves for diatomic molecules

The purpose of this paper is to give a simple expression for the potential-energy function for diatomic molecules for which one can solve exactly the Schrodinger equation for both discrete and continuous energy parameters,E. The analytical expression for this potential curve is illustrated numerically. The possible appearance of the hump and the double-minimum in the potential curve has also been investigated.

Accurate Potential-Energy Function for Diatomic Molecules

A three-parameter potential-energy function for diatomic molecules proposed by Varshni and Shukla, has been modified to improve its accuracy. The modified function is U=De{1−(re/r)exp[−a(rp−rep)]}2, where De is the molecular dissociation energy, re is the equilibrium internuclear distance, and p=2+14(Δ12−4)(Δ12−2)/(Δ12−1), where Δ=½kere2/De, ke being the force constant. This function appears to be more accurate than previously proposed three-parameter functions.

Potential-Energy Function for Diatomic Molecules

The purpose of this paper is to give a simple expression for the potential-energy function for diatomic molecules for which one can solve the Schrodinger equation exactly for both discrete and cont...

Potential-Energy Function for Diatomic Molecules

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