A model potential for vibrational excitation of diatomic molecules

A model interaction potential for the vibrational excitation of H₂ by Li⁺ of the form C exp(−αx+βy) is studied using non-iterative integral techniques. The results show that vibrational excitation is sensitive to small quantitative change in qualitatively similar surfaces.     

Variable-screening model for diatomic molecules

An effective hamiltonian method based on a one-electron potential is proposed. The potential is represented by a sum of two coulombic interactions with effective nuclear charges depending upon the internuclear distance. This potential preserves the separability of Schrödinger equation. The method can be usefully applied to various atom (ion)-atom collision problems. Calculations are carried out for some states of HeH⁺ and HeH using one configuration built up from a minimal basis set chosen to ensure correct dissociation.     

Improved multiparameter exponential-type potential for diatomic molecules

We report an improved multiparameter exponential-type potential (MPETP) energy model for diatomic molecules. It is found that this potential is identical to the Tietz potential in the realm of diatomic molecules. The efficiency of the improved MPETP is clarified by simulating the internuclear interaction potential curve for the A (³Π₁) state of the chlorine monofluoride molecule.     

Nonbonded potential energy functions based on the dumbbell model of diatomic molecules

Summary The potential energy functions commonly used in calculating crystal packing are in poor agreement when applied to the interaction of a spherically symmetric atom and diatomic molecule or to the interaction of two diatomic molecules. The attractive components of potential energy functions of these interactions, however, are known from quantum mechanics. New potential energy functions for these interactions, based on a dumbbell model, are proposed. In addition, the goodness of fit of the repulsion term is discussed.

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Zusammenfassung Potentielle Energiefunktionen, die gewöhnlich bei der Berechnung der Packung von Molekülen in Kristalliten Verwendung finden, stimmen nicht mit der bekanntenvan der W aals-Wechselwirkung eines kugelsymmetrischen Atoms und eines zweiatomigen Moleküls oder der Wechselwirkung zweier zweiatomigen Moleküle überein. Neue potentielle Energiefunktionen für die Atom-Atom-Wechselwirkung von Molekülen werden vorgeschlagen und die Güte der Anpassung des abstoßenden Terms einesBuckingham-Potentials diskutiert.

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Dedicated to Prof.R. Hosemann on the occasion of his 60th birthday.     

Rydberg-London potential for diatomic molecules and unbonded atom pairs

We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form.     

The generalized potential energy function for diatomic molecules

A new generalized potential energy function is suggested for diatomic molecules. The Dunham, Simons—Parr—Finlan, Thakkar and Ogilvie potentials are shown to be particular cases of the generalized potential energy function. It is also shown that the function suggested may reproduce the path of the potential curve with sufficient accuracy even for the cases of small expansion length.     

Generalized double exponential potential functions for diatomic molecules

Two variants of the double exponential potential function and their virial modifications are proposed and tested. The first in reduced variables is F(t)=e^−mt{[m(m²−1)^−1/2−1]exp[−(m²−1)^1/2t]−[m(m²−1)^−1/2+1]exp[(m²−1)^1/2t]} where t=κs=κ(R−R_e))/R_e, κ is a scaling constant, and m is a parameter. The second is G(t)=e^−mt{e^−mt−exp[(m²−1)^1/2t]+exp[−(m²−1)^1/2t]}. For m<1, F(t) and G(t) are expressible in terms of trigonometric functions. A new procedure [multiplication by e^s/(1+s)] is illustrated that modifies potential functions so that they necessarily satisfy the molecular virial theorem. The generalized double exponential functions generate scaled first and second Dunham coefficients that well describe the experimental results for both ground and excited states. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 1–8, 1997     

Three-dimensional bond-charge models for potential curves of diatomic molecules

Several simple three-dimensional Fermi-gas models for potential energy curves of diatomic molecules are suggested. Bond-charge parameters close to those predicted by the earlier point bondcharge model of Borkman, Simons and Parr [J. Chem. Phys. 49, 1055 (1968); 50, 58 (1969)] are obtained for models assuming uniform spherical or elliptical electron distributions in the bond region.Aided by a research grant to The Johns Hopkins University from the National Science Foundation.     

A simplified model for the predissociation of diatomic molecules

A model consisting of a harmonic oscillator well and a repulsive inverse square potential, coupled by a delta function, is solved. We find the S-function for this case and study its poles as a function of the coupling strength. These poles show how the harmonic levels shift and broaden as the two potential curves couple and predissociation occurs. A “new state” is found when the energy threshold is just below the first excited state of the harmonic oscillator.     

Improved Pöschl–Teller potential energy model for diatomic molecules

By employing the dissociation energy and the equilibrium internuclear distance for a diatomic molecule as explicit parameters, we construct an improved Pöschl–Teller potential energy model. We analyze the average absolute deviations of the improved Pöschl–Teller and Morse potentials from the experimental Rydberg–Klein–Rees (RKR) potentials for six diatomic molecules. It is found that the improved Pöschl–Teller potential is more accurate than the Morse potential in fitting experimental RKR potential curves over a large range of internuclear distances for six molecules examined.     

A realistic model for curve crossing in diatomic molecules

We present a model system for the study of curve-crossing situations in diatomic molecules. All model parameters are determined by the potential energy topology. No coupling functions are fitted. The standard approximation schemes (Born–Oppenheimer approximation, adiabatic approximation, and the generator coordinate approximation) are then applied. The result of these numerical experiments suggest that the generator coordinate approximation is able to remove 80%–90% of the nonadiabatic effect on all levels throughout the crossing region.     

Application of the spline-function method to determination of potential constants for diatomic molecules

We describe a new technique for calculating force constants for diatomic molecules, making significnat use of approximate information on derivatives of the function of the total energy of the molecule given in tables. The proposed procedure is applied to determine the potential constants for the LiH molecule.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 98–101, January–February, 1985.     

Coefficient interrelatedness among polynomial potential functions of diatomic molecules

It is shown that the diatomic potential energy functions of Dunham, SPF and Ogilvie can be easily converted from one another when their coefficients are related. Through Maclaurin expansion and comparison of terms, the coefficients can be related by using the Pascal Triangle. In this paper, the coefficients were related up to the tenth order of δr/R for HX (X = H, Ga, Cl, I). Comparison of all three potential energy curves shows very good agreement for r ≤ 1.5R, thereby verifying the formulated relations. Observation of the plotted potential energy curves for r > 1.5R shows that the difference of the three potential function definitions is not reflected as any consistent trend arising from the related potential functions.     

Static charge distributions which generate exact potential curves for diatomic molecules

For a diatomic molecule, there exists a charge density which can be used to generate the exact potential energy curve for the molecule, by integration of the classical Poisson equation. This density is displayed for H⁺₂, H₂ and LiH, and it is shown to be similar in shape to the united-atom electron density.     

Semiclassical three-dimensional model for vibrational energy transfer in diatomic molecules

A semiclassical model for calculation of rate constants for vibrational excitation in diatomic gases at low temperatures (below 1000 K) is suggested. The model has been tested by its ability to predict the relaxation times of hydrogen (τ_H1 in the temperature region 40–1000 K. The agreement with experimental values is excellent. The isotopic ratio τ_D2/τ_H2 as a function of temperature is predicted.     

Variable-screening method for diatomic molecules

A variable-screening method is proposed for the calculation of electronic energies of diatomic molecules. This new method is applied to the ground state of HeH⁺ in order to investigate its utility.     

Relativistic and nonrelativistic solutions for diatomic molecules in the presence of double ring-shaped Kratzer potential

The authors investigate solutions of the three dimensional Klein-Gordon and Schrodinger equations in the presence of a new exactly solvable potential of V(r,theta)=-2De(re/r-(1/2)(re2/r2))+b/r2 sin2 theta+a/r2 cos2 theta type, the so-called double ring-shaped Kratzer potential. For a diatomic molecule system in double ring-shaped Kratzer potential, the exact bound state energy eigenvalues and corresponding wave functions have been determined within the framework of the asymptotic iteration method. Bound state eigenfunction solutions used in applications related to molecular spectroscopy are obtained in terms of confluent hypergeometric function and Jacobi polynomial. This new formulation is tested by calculating the energies of rovibrational states of a number of diatomic molecules. Also, the author-prove that in the nonrelativistic limit c-->infinity, where c is the speed of light, solutions of the Klein-Gordon system converge to those of the Schrodinger system.