  A Galerkin method is developed to solve the time-dependent Dirac equation in
prolate spheroidal coordinates for an electron-molecular two-center system. The
initial state is evaluated from a variational principle using a kinetic/atomic
balanced basis, which allows for an efficient and accurate determination of the
Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain
high accuracy. This numerical method is used to compute the energy spectrum of
the two-center problem and then the evolution of eigenstate wavefunctions in an
external electromagnetic field.
