We describe an independent trajectory implementation of semiclassical Lionville method for simulating quantum processes using classical trajectories. In this approach, a single ensemble of trajectories describes all semiclassical density matrix elements of a coupled electronic state problem, with the ensemble evolving classically under a single reference Hamiltonian chosen on the basis of physical grounds. In this paper, we introduce an additional uncoupled trajectory approximation, allowing the members of the ensemble to evolve independently of one another and eliminating the major computational costs of our previous coupled trajectory implementation. The accuracy of the method is demonstrated for model one-dimensional problems. In addition, the approach is applied to the chemical reaction dynamics of a collinear triatomic system, yielding excellent agreement with exact calculations. This method allows molecular dynamics involving coupled electronic surfaces to be modeled with essentially the same effort as classical molecular dynamics and ensemble averaging.