  Singlet fission (SF) is a potential pathway for significant enhancement of
efficiency in organic solar cells (OSC). In this paper, we study singlet
fission in a pair of polyene molecules in two different stacking arrangements
employing exact many-body wave packet dynamics. In the non-interacting model,
the SF yield is absent. The individual molecules are treated within Hubbard and
Pariser-Parr-Pople (PPP) models and the interaction between them involves
transfer terms, intersite electron repulsions and site-charge--bond-charge
repulsion terms. Initial wave packet is constructed from excited singlet state
of one molecule and ground state of the other. Time development of this wave
packet under the influence of intermolecular interactions is followed within
the Schr\"odinger picture by an efficient predictor-corrector scheme. In
unsubstituted Hubbard and PPP chains, $2{}^1A$ excited singlet state leads to
significant SF yield while the $1{}^1B$ state gives negligible fission yield.
On substitution by donor-acceptor groups of moderate strength, the lowest
excited state will have sufficient $2{}^1A$ character and hence results in
significant SF yield. Because of rapid internal conversion, the nature of the
lowest excited singlet will determine the SF contribution to OSC efficiency.
Furthermore, we find the fission yield depends considerably on the stacking
arrangement of the polyene molecules.
