Propagation of Holes and Electrons in Metal-Organic Frameworks

Charge transport in two zinc metal-organic frameworks (MOFs) has been investigated using periodic semiempirical molecular orbital calculations with the AM1∗ Hamiltonian. Restricted Hartree-Fock calculations underestimate the band gap using Koopmans theorem (ca. 2 eV compared to the experimental value of 2.8 eV). However, it almost doubles when the constraint on the wave function to remain spin-restricted is removed and the energies of the UHF Natural Orbitals are used. Charge-transport simulations using propagation of the electron- or hole-density in imaginary time allow charge-transport paths and mechanisms to be determined. The calculated relative mobilities in the directions of the three crystal axes agree with experimental expectations, but the absolute values are not reliable using the current technique. Hole-mobility along the crystal c-axis (along the metal stacks) is found to be 13 times higher in the zinc MOF with anthracene linker (Zn-ANMOF-74) than in the other directions, whereas the factor is far smaller (1.7) for electron mobility. Directional preferences are far less distinct in the equivalent structure with phenyl linkers (Zn-MOF-74). The imaginary-time simulation technique does not give quantitative mobilities. The simulations reveal a change in mechanism between the different directions: Coherent polaron migration is observed along the stacks but tunneling hops between them.