A Consistent Computational Time-Dependent Electron-Exchange Theory With Non-Redundant Time Evolution

Abstract

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.