In this paper, we present a unified computational method based on
pseudospectral approximations for the design of optimal pulse sequences
in open quantum systems. The proposed method transforms the problem of
optimal pulse design, which is formulated as a continuous-time optimal
control problem, to a finite dimensional constrained nonlinear programming
problem. This resulting optimization problem can then be solved using
existing numerical optimization suites. We apply the Legendre
pseudospectral method to a series of optimal control problems on open
quantum systems that arise in Nuclear Magnetic Resonance (NMR)
spectroscopy in liquids. These problems have been well studied in previous
literature and analytical optimal controls have been found. We find
an excellent agreement between the maximum transfer efficiency produced
by our computational method and the analytical expressions. Moreover, our
method permits us to extend the analysis and address practical concerns,
including smoothing discontinuous controls as well as deriving
minimum-energy and time-optimal controls. The method is not restricted
to the systems studied in this article and is applicable to optimal
manipulation of both closed and open quantum systems.