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

Exact Wave Packet Dynamics of Singlet Fission in Unsubstituted and Substituted Polyene Chains within Long-Range Interacting Models