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 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.     

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.     

Study of the geometric structure of the molecules of H2O,Li2O,and LiOH by the method of diatomic fragments in molecules

Conclusion The results of the present work indicate that the DFM method can be used successfully to determine the geometric parameters of the ground states of triatomic molecules. The additional possibilities provided by the method are associated with the variation of the parameters of the theory which are not single-valued, in particular the parameters of the mixing of states of the same symmetry of the diatomic fragments. It has also been shown that the correct choice of the model of the molecule is of considerable importance.Chemistry Department, M. V. Lomonosov Moscow State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 19, No. 5, pp. 771–778, September–October, 1978.     

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     

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.     

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.     

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.     

Commutator perturbation method in the study of vibrational–rotational spectra of diatomic molecules

The commutator perturbation method, an algebraic version of the Van Vleck–Primas perturbation method, expressed in terms of ladder operators, has been applied to solving the eigenvalue problem of the Hamiltonian describing the vibrational–rotational motion of a diatomic molecule. The physical model used in this work is based on Dunham's approach. The method facilitates obtaining both energies and eigenvectors in an algebraic way. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 721–726, 2000     

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.     

A simple method for non-parametric estimation of the probability distribution function of diatomic molecules by electron diffraction

Treating the Debye intensity relationship as a linear Fredholm integral equation of the first kind, a method is developed for a non-parametric estimation of the probability distribution function P/r) for diatomic molecules from electron-diffraction data. Since the problem is an ill-posed one, Tikhonov's regularization procedure was used for the solution. The method was applied to iodine for which the non-parametric P/r) function is obtained. Based on this function the electron-diffraction parameters r_g, r_a and l_a are estimated by the linear least-squares method without a priori assumptions about the form of the vibrational potential. Approximating the potential by the Dunham expansion, the parameters r_e, ω_e, K₃ and K₄ are also estimated. The results are compared with those obtained from conventional analytical representation of an intensity function. Comparison is also made with spectroscopic data for iodine.     

Alignment of diatomic molecules by gaseous transport

Iodine molecules in a flow cell containing helium as a carrier gas appear to be partially aligned. This has been determined by comparison of circular polarisation ratios of rotationally resolved emission lines in the flow cell with those obtained from a similar cell containing 1₂ in an isotropic environment. After all other possibilities have been eliminated, two experimental indicators of alignment remain. One is the reduction of the absolute value of the circular polarisation ratio and the other is the differential reduction of one of the P,R-doublet emission lines.     

Potential energy curves of diatomic molecules from the Hill determinant method

The Hill determinant method is shown to be suitable for constructing potential energy curves of diatomic molecules. Both the Dunham and the perturbed Morse oscillator potentials are used to fit spectroscopic data. Results are shown for ionic and covalent molecules.     

A spline-fitted potential surface for bent triatomic molecules

The rotated-Morse curve cubic spline method developed previously is extended to bent triatomic molecules by using 2D cubic spline. The Yates—Lester potential for bent H₃ is shown to be accurately fitted over the entire range of the three internal coordinates, with a standard deviation of less than 1 kcal mol^?1. The spline method compares favorably in computational speed with the analytical potential.