Comparing the electron and hole mobilities in the α and β phases of perylene: role of π-stacking

Abstract

Computational studies are carried out on α and β polymorphs of perylene molecular crystals to estimate their hole and electron mobilities (μ_hole and μ_electron). For both the polymorphs, it is found that the LUMO bandwidhs are larger than the HOMO bandwidth resulting in larger electron conductance, as observed experimentally and which has remained unexplained until now. For a microscopic understanding, we perform quantum chemical calculations for the hole and electron transfer matrix elements (H_mn^hole and H_mn^electron) on some selected unique nearest neighbour pairs of molecules in the crystal geometries. This along with calculations for the hole and electron reorganization energies (λ_hole and λ_electron) within the embedded cluster method reveal that for both the crystals, μ_electron exceeds μ_hole by two orders of magnitude. The electron mobility for the α-phase (μ_electron = 67.2 cm² V^-1 s^-1) is found to be three times that for the β-phase. The major driving force for preferential electron conductance in α-erylene is the slipped parallel π-stacking arrangement of the molecules at short intermolecular distances (d = 3.9 Å) in the crystal. We suggest that experimental strategies that further enhance the percentage of such specific π-stacking dimers in molecular assemblies have the potential to further increase μ_electron. The present theoretical calculations provide a unified understanding of the parameters that optimize an organic crystal for enhanced electron and hole mobilities.