  In this paper we investigate the effect of terminal substituents on the
dynamics of spin and charge transport in donor-acceptor substituted polyenes
($D-(CH)_{x}-A$) chains, also known as push-pull polyenes. We employ long-range
correlated model Hamiltonian for the $D-(CH)_{x}-A$ system, and time-dependent
density matrix renormalization group technique for time propagating the wave
packet obtained by injecting a hole at a terminal site, in the ground state of
the system. Our studies reveal that the end groups do not affect spin and
charge velocities in any significant way, but change the amount of charge
transported. We have compared these push-pull systems with donor-acceptor
substituted polymethine imine (PMI), $D-(CHN)_{x}-A$, systems in which besides
electron affinities, the nature of $p_{z}$ orbitals in conjugation also
alternate from site to site. We note that spin and charge dynamics in the PMIs
are very different from that observed in the case of push-pull polyenes, and
within the time scale of our studies, transport of spin and charge leads to the
formation of a "quasi-static" state.
