We analyze the properties of electron-phonon couplings in K${}_3$ picene by exploiting a molecular-orbital representation derived in the maximally localized Wannier function formalism. This allows us to go beyond the analysis done in Phys. Rev. Lett. 107, 137006 (2011), and separate not only the intra- and intermolecular phonon contributions but also the local and nonlocal electronic states in the electron-phonon matrix elements. Despite the molecular nature of the crystal, we find that the purely molecular contributions (Holstein-like couplings where the local deformation potential is coupled to intramolecular phonons) account for only $20\%$ of the total electron-phonon interaction $\lambda$. In particular, the Holstein-like contributions to $\lambda$ in K${}_3$ picene are four times smaller than those computed for an isolated neutral molecule, as they are strongly screened by the metallic bands of the doped crystal. Our findings invalidate the use of molecular electron-phonon calculations to estimate the total electron-phonon coupling in metallic picene, and possibly in other doped metallic molecular crystals. The major contribution ($80\%$) to $\lambda$ in K${}_3$ picene comes from nonlocal couplings due to phonon-modulated hoppings. We show that the crystal geometry together with the molecular picene structure leads to a strong one-dimensional spatial anisotropy of the nonlocal couplings. Finally, based on the parameters derived from our density-functional theory calculations, we propose a lattice modelization of the electron-phonon couplings in K${}_3$ picene which gives $90\%$ of ab initio $\lambda$.

• Received 21 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.075445