We present a new, fully ab initio approach for computing intramolecular charge- and energy-transfer rates. Using a time-convolutionless master equation approach and parametrizing using couplings obtained using an accurate quantum chemical approach, we benchmark the approach against experimental results and Marcus theory rates for triplet energy transfer for a series of donor-bridge-acceptor systems. An important component of our analysis is the use of a projection operator scheme that parses out specific internal nuclear motions that accompany the electronic transition. Using an iterative Lanczos approach, we concentrate the coupling between the electronic and nuclear degrees of freedom into a small number of reduced harmonic modes. We find that by using only a single reduced mode termed the "primary mode", one obtains an accurate evaluation of the golden rule rate constant and insight into the nuclear motions responsible for coupling the initial and final electronic states. In particular, the primary mode reflects the irreducible representation of the donor and acceptor excited states.