Magnetically dressed one-electron molecular orbitals

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 Schrödinger 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 ${\mathrm{H}}_2^{+}$ and (H-He${)}^{2+}$ systems for field strengths up to about ${10}^8$ 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 θ between field direction and internuclear axis, and as a function of θ at fixed R. Equilibrium internuclear distances and total binding energies are calculated as functions of field strength for the magnetically dressed ${\mathrm{H}}_2^{+}$ system in its lowest gerade and ungerade states at θ=0 and θ=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.