An additional charge carrier described as its wave function is propagated in imaginary time using stepwise matrix multiplication and a correction to ensure that the simulation is norm-conserving. The propagation Hamilton operator uses the local ionization energy of a rubrene single crystal, calculated with semiempirical molecular orbital theory, as an external potential for holes to model the interaction with the underlying molecular structure. Virtual electrodes are modeled by setting the potentials in the appropriate areas to constant values with the difference corresponding to the source-drain voltage. Although imaginary time cannot be interpreted directly as time, the simulated gate-dependent imaginary transfer rate is in acceptable qualitative agreement with the experimentally measured gate-dependent hole-transfer rate through a rubrene single crystal.

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.

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