Magnetically dressed one-electron molecular orbitals

Abstract

A general method for solving the stationary one-electron, two-center Coulomb problem with a superimposed (uniform) strong magnetic field is described and applied. For arbitrary orientation of the field with respect to the line connecting the centers, the pertinent Schrodinger equation is solved by evaluating analytically the Hamiltonian matrix in a basis of (nonorthogonal) Hylleraas functions and solving numerically the generalized eigenvalue problem for this matrix. A detailed study of the properties of "magnetically dressed" (diatomic) one-electron molecular orbitals is performed by calculating energies and wave functions for the H2+ and (H-He)'+ systems for field strengths up to about 10 T. Molecular-orbital correlation diagrams are presented and discussed, in which dressed-orbital energies are displayed as a function of internuclear distance R at fixed angle 9 between field direction and internuclear axis, and as a function of 0 at fixed R. Equilibrium internuclear distances and total binding energies are calculated as functions of field strength for the magnetically dressed H2+ system in its lowest gerade and ungerade states at 0=0 and t9=90'. The influence of the magnetic field on molecular binding properties as well as on the separation behavior of molecular orbitals at large internuclear distances is illustrated by means of wave-function plots. Whenever possible, our results are compared to those of previous investigations. The convergence properties of our method are discussed.

H2+molecular ion in a strong magnetic field: Ground state

“…Thus, we can draw the conclusion that the molecular ion becomes less and less stable monotonically as a function of inclination angle. This confirms the statement made in [9,11,14,16], that the highest molecular stability of the 1 g state of H + 2 occurs for the parallel configuration. Thus, the H + 2 molecular ion is the most stable in parallel configuration.…”

“…It was an underlying reason for the erroneous statement about the existence of the unstable H + 2 ion in this domain with a possibility to dissociate H + 2 → H + p (see [24]). For all magnetic fields studied the total energy is minimal at θ = 0 o (parallel configuration) and then increases monotonically with inclination in complete agreement with statements of other authors [9,11,14,16].…”

“…As seen in Table I, wave function decays asymptotically as a Gaussian function, unlike the Hylleraas functions which decay as the exponential of a linear function. The potential corresponding to the function [14] reproduces correctly the original potential near Coulomb singularities but fails to reproduce ∼ ρ 2 -growth at large distances. This implies a zero radius of convergence of the perturbation theory for which the variational energy represents the first two terms (see discussion in [25]).…”

“…It is worth mentioning that in the calculations [14,16] for B = 1 a.u. and θ = 90 o (and other inclinations) the maximum was not observed in contradiction to our predictions (see Fig.…”

“…However, in spite of all the above-mentioned deficiencies it led to qualitatively correct picture. of [14,16] -for fixed R the potential energy E T grows with inclination. In general, at large R > R eq and for θ > 0 o all the curves behave alike: they reveal a maximum and then tend (from above) to the total energy of the hydrogen atom.…”