Eigenvalue Methods in Unimolecular Rate Calculations

When the calculation of a unimolecular reaction rate constant is cast in the form of a master equation eigenvalue problem, the magnitude of that rate is often smaller than the rounding error of the trace of the corresponding reaction matrix. Two available methods to overcome this cancellation problem are examined, and it is shown that one of them, the Nesbet procedure, can fail if the master equation relaxation matrix is improperly normalized, or when some time-saving computational approximations are used.