  In the present work, a new time-dependent exchange theory is presented
wherein the symmetry constraints, on a multi-electron wavefunction, are
properly accounted for. In so doing, the equations of motion, incorporating the
required symmetry, are derived and a solution algorithm employing an implicit
split-operator procedure is described. A technique (using an orthonormalization
transformation and a unitary rotation), for explicitly enforcing the required
constraints, which render the computations tractible and provide for
non-redundant time evolution, is also presented. This amounts to the
calculation of the appropriate numerically determined guage. The invariance of
the derived orbital equations of motion with respect to the transformations is
explicitly demonstrated.
