Alkali molecular ion energies and expectation values in a model-potential treatment

Abstract

Success of quantum mechanical approximations for molecular geometries and electron-nuclear attraction expectation values: Gift of the Coulomb potential? J. Chem. Phys. 84, 4519 (1986); 10.1063/1.450024 Interpolated values of spectroscopic constants of asymmetric alkali molecules and molecular ions J. Chem. Phys. 62, 4753 (1975); 10.1063/1.430424Expectation values of the kinetic and potential energy of a diatomic molecule By using Hellman-type model potentials for alkali atoms, the many-electron problem of the alkali molecular ions is reduced to a three-body problem, and the ground state energy of the these ions calculated in the familiar Rayleigh-Ritz variational treatment. All the ions result as being stable. Other physical quantities (equilibrium and mean distances, etc.) are. also calculated. The reported data may be useful in a· variety of scattering problems, such as, for instance, alkali atom-ion collisions. They support the James' suggestion that the dissociation energies of the alkali molecular ions must be greater than those of the corresponding molecules, due to the greater diffuseness of the bonding wavefunctions. Application of the present approach to alkali hydride ions seems to indicate that these ions are not stable. The limitations of the pseudopotential approach for molecular calculations are discussed, and it is concluded that the approach is of simpler use for alkali molecular ions than for the corresponding molecules. Cs 3.88 1.6721. 0.3331. aReference 27. bReference 28.

Simple model potential and model wave functions for (H–alkali)+ and (alkali–alkali)+ ions

“…Our results help in resolving these differences. For example, for the dissociation energy of (KRb) ϩ , the calculations of Bellomonte et al 28 give a value of 0.87 eV and the calculations of Valance 11 give a value of 0.53 eV, whereas our calculated value is 0.794. Generally, our predictions based on a simple, model potential with the correct asymptotic form and a hard core adjusted to incorporate the exchange effects at short distances, are expected to be quite reliable, particularly for systems involving larger atoms.…”

Potential curves of the rare gas alkali ions

“…However, as has been pointed out by Bellomonte et al [4] the influence on the molecular levels is rather small. They depend somewhat on the choice of the states.…”

“…The wavefunction ~ was expressed [4] in elliptical coordinates to be ~(~,fi)=(R2)"exp--(c~2+fi/t)R, whereas 2 = (rA + rRg)/R and # = (r A -rRg)/R. The wavefunction ~ was expressed [4] in elliptical coordinates to be ~(~,fi)=(R2)"exp--(c~2+fi/t)R, whereas 2 = (rA + rRg)/R and # = (r A -rRg)/R.…”

On the Parameters of the Hellman‐like Model Potential

“…basis set (4) used to fit its parameters, just this one has been the starting point for further calculations in several recent papers [13,[15][16][17]. The incorrectness of this M P is shown clearest, however, by comparing it with the results of MCGINN [14] what would have been possible since 1973 and is done in Table 1.…”