In the present work, we have critically examined the origin of strong two-photon transition probability of a donor-acceptor substituted bisanthene molecule that imitates a small piece of edge passivated (4, 4) graphene nanoribbon. In our calculations, we have considered -OMe, and -NH(2) as donors and -NO(2) as an acceptor. The one- and two-photon absorption parameters are evaluated using state-of-the-art linear and quadratic response theory, respectively, and all these calculations are carried out within the framework of time dependent density functional theory. To give a proper judgment on our findings, we have used the long-range corrected CAMB3LYP functional for all of the time dependent calculations. The present investigation reveals that the bisanthene molecule with three pairs of donor/acceptor moiety has a lower two-photon transition probability than that of a suitably designed bisanthene with only a single pair of donor/acceptor moiety. This in silico observation is consistent for all of the donor/acceptor moieties chosen in the present work. A comprehensive analysis at the two state model level of theory clearly offers us a verdict that by placing the donor/acceptor moiety in a suitable position of bisanthene, we can create a significant asymmetry in the electron density in the first excited state, which eventually leads to a significant difference in the ground and excited state dipole moment and is attributed to the higher two-photon transition probability of a particular bisanthene with a single pair of donor/acceptor moiety than bisanthene with three pairs of donor/acceptor.