Real-Time CASSCF (Ehrenfest) Modeling of Electron Dynamics in Organic Semiconductors. Dynamics Reaction Paths Driven by Quantum Coherences. Application to a Radical Organic Semiconductor

Abstract

We present a strategy for the modeling of charge carrier dynamics in organic semiconductors using conventional quantum chemistry methods, including the analytic gradient for nuclear motion. The theoretical approach uses real-time CASSCF (Ehrenfest) all-electron dynamics coupled to classical nuclear dynamics for the special case of a small number (4–8) of molecular units. The objective is to obtain mechanistic/atomistic insight at the electronic structure level, relating to spin density dynamics, to the effect of crystal structure (e.g., slippage between spin/charge carriers), and to ferromagnetic and antiferromagnetic effects. The initial conditions for our simulations use the equilibrium structures of all the molecular units. At this geometry, a localized hole on one of the units corresponds to a coherent superposition of adiabatic states. We thus generate a dynamics reaction path driven by quantum coherences. Our aim is to inform experiment and to compare with parametrized theoretical models. The methodology is demonstrated for a perfectly π-stacked ethylene model (up to 8 eclipsed molecular units) for both hole transfer and localized exciton transfer. An application for hole transfer is presented for bisdithiazolyl (S,S) and bisdiselenazolyl (Se,Se) radicals for the special case of ferromagnetic coupling. For these examples, the embedded pyridine radical model organic chromophore (up to 6 eclipsed π-stacked molecular units) has been studied on its own as well as the target bisdithiazolyl (S,S) and bisdiselenazolyl (Se,Se) systems. A significant difference between these systems and the ethylene and pyridine stacks is that the (S,S) and (Se,Se) systems exhibit molecular slippage rather than being perfectly eclipsed. This slippage may result from crystal defects or intermolecular vibrations. For the model systems, the electron dynamics is dominated by the initial and final molecular units, irrespective of the length of the chain. The intervening units act as a “superexchange bridge”. Our simulations reveal that, in the presence of slippage, charge migration cannot propagate across the entire system; instead, the coherence length is limited to 3 molecular units. The results also suggest that the mechanism of charge transport is different for bisdiselenazolyl (Se,Se) (superexchange-like A –[B]→ C) and bisdithiazolyl (S,S) (direct A → C). An analysis of the spin density suggests that, in the charge carrier dynamics, the additional charge carried by the Se versus S in the “scaffold” is small. Since we use a small number of molecular units, the coupled nuclear dynamics is seen to be complementary to the electron dynamics (i.e., creating a hole causes bond length contraction while filling a hole with an electron lengthens the bond). In all the cases studied, the mechanism of charge mobility is wave-like, rather than hopping, because we use the time dependent Schrödinger equation to propagate the electronic wave function.