Effects of the target time in controlling molecular motion: The role of errors in the field and in the model

This paper examines the effects of random errors in the electric field and errors inherent in the model on the choice of a target time, T, in designing an optimal field to achieve site-selective excitation in molecular systems. A formalism is presented for control of classically modeled systems which includes additional costs due to these errors. In applying this formalism to a linear coupled harmonic system, it is demonstrated that, for errors in the model, the additional cost terms approach asymptotic values. In contrast, for a constant magnitude of error in the field, the added terms manifest consistent growth behavior with increasing target times due to accumulation of phase errors in the controlled dynamics. In the present illustration, a reasonable level of field and force constant error had a minimal influence on the practical choice of a final target time. Although other systems may behave differently and must be assessed on their own merit, some general conclusions are drawn regarding the factors influencing the choice of a target time T.