Thanks to the connection proposed here between model Hamiltonian and mobility we can look specifically on the effect on charge mobility of the transfer integral magnitude since it has been proposed that small transfer integral could be (counterintuitively) beneficial for transport. Indeed, over the last thirty years, the stateof-the-art organic polymers have seen a steady decrease in electronic bandwidth (MEH-PPV > P3HT > PBTTT > IDTBT) and it was suggested this was due to the reduced activation energy for transport in narrower bands. There must be a limit to this trend as the mobility should vanish for vanishing transfer integrals. To clarify this matter, we consider the parameters corresponding to polymer #36 (highest mobility polymer screened; Ref. ) and compute the mobility as function of 𝜏 (0) (Fig. ). In agreement with Ref. , we find that increasing 𝜏 (0) is detrimental to charge transport due to the trapping of the charge-carrier at deep trap states away from the band edge, and in effect from the reduced number of longer range hopping; yet, we also find that the at very small 𝜏 (0) the effective coupling strength between localized states (|𝑀 𝑖𝑗 | 2 ) diminishes significantly, and this mutual interplay dictates the optimal electronic coupling strength for high-mobility polymers. The range of coupling which is close to ideal is 0.15-1.25 eV which is very similar to that observed for the high mobility polymers in our screening. Therefore, the most suitable bandwidth for high charge-carrier mobility has moreor-less been achieved and this parameter does not play too critical a role during further optimization of modular polymers.