In this paper we describe a new technique that enables us to study vibrational energy transfer in linear hydrocarbon chains significantly more efficiently than by earlier approaches. The principal feature of our method is that the conjugate momentum operators that appear in the coupling terms in the Hamiltonian for the system are projected in the complete set of momentum states of the bonds. This allows us to express the expectation values of the time evolution operator in various energy eigenstates as one-dimensional momentum integrals which can be performed very rapidly and stored. All survival probabilities can then be expressed in terms of these stored integrals. We have evaluated the survival probability for HC2 and HC6 for up to eight time steps. Finally, we indicate how our approach may be extended to more general coupling terms.