Analytical first derivatives of the energy in the MNDO half-electron open-shell treatment

Using the Z-vector formalism the analytical gradient of the energy in the half-electron open-shell treatment is derived and implemented for semiempirical MNDO-type methods. The computation time is shown to scale as O(N-3) with the size of the system, with the memory requirements growing as O(N-2). The evaluation of the analytical gradient is significantly faster than the half-electron SCF calculation, so that routine full geometry optimizations become possible for large open-shell systems. The approach can easily be extended to the treatment of the small CI expansions typically encountered in semiempirical computations.