In this paper we report quantum calculations of the survival probability in linear hydrocarbon chains. We have performed both adiabatic gauge transform calculations and calculations that include corrections beyond the adiabatic approximation. We have managed to perform intermediate steps of the calculations analytically. We require the initial basis set expansion and final summations to be performed numerically. The corrections beyond the adiabatic approximation are shown to be small for this system for multiple time step calculations and large for single time step calculations. We have proved an identity that allows the extension of the calculations for HC2 to longer chains at little computational cost. In particular, we have proved that the quantum solution for any linear hydrocarbon chain can be obtained from the solution of a problem with 3 degrees of freedom. We have performed multi-step adiabatic calculations for HC2 and HC6 that converge at up to 35-40 fs. We have devised a simple diagrammatic scheme that summarizes our method in a very compact form, Finally, we propose an alternative strategy of calculation that might lead to very fast solutions of the quantum dynamics of this system.