Calculation from First-Principles of Golden Rule Rate Constants for Photoinduced Subphthalocyanine/Fullerene Interfacial Charge Transfer and Recombination in Organic Photovoltaic Cells

Abstract

The rates of interfacial charge transfer and recombination between the donor and acceptor layers play a key role in determining the performance of organic photovoltaic cells. The time scale and mechanism of these processes are expected to be impacted by the structure of the interface. In this paper we model the kinetics of those processes within the framework of a subphthalocyanine/fullerene donor/acceptor dimer model. Two likely configurations (on-top and hollow) in which the interfacial charge transfer and recombination may occur are studied. The corresponding rate constants are calculated within the fully quantum-mechanical framework of Fermi's golden rule. All the input parameters (excitation energies, electronic coupling coefficients, normal-mode frequencies and coordinates, and Huang−Rhys factors) are obtained from density functional theory calculations with density functionals designed to yield accurate results in the case of noncovalently bound systems and charge transfer states. Multiple π−π* and charge-transfer excited states are identified and assigned. The kinetics of photoinduced charge transfer is obtained by solving a master equation using Fermi's golden rule rate constants for the electronic transitions between the various excited states. Our results suggest that the hollow configuration may be superior to the on-top configuration and that maximizing its prevalence may improve the performance of subphthalocyanine/fullerene-based photovoltaic cells.

Efficient Charge Generation via Hole Transfer in Dilute Organic Donor–Fullerene Blends

“…Transition rate constants for each pair of dyad states are calculated based on Fermi's golden rule and invoking the harmonic approximation (13), which is presented in detail in Section S4 of the SI and which was widely benchmarked in our previous studies [22][23][24][25] . The rate expression is based upon the energetic and structural difference between minima of the initial and the target state.…”

“…Recently, it has been used to uncover mechanisms of electron transfer in conjugated polymer/fullerene blends, (10) although studies on hole transfer are still lacking. TD-DFT electronic structure calculations of dyad models have also been used to simulate complex interfacial processes in OPVs (13,14). In this context, long-range interactions and polarization effects must be accounted for to achieve a reliable description of interfacial CT states (15).…”

Equilibrium Fermi’s Golden Rule Charge Transfer Rate Constants in the Condensed Phase: The Linearized Semiclassical Method vs Classical Marcus Theory

“…They can occur spontaneously, as in redox reactions, 6,7,11,18,19 or can be induced by electron injection, as in electrochemical devices, or by photoexcitation, as in photochemical reactions and photovoltaic devices. 14,[24][25][26][27][28][29][30][31][32][33] The rates of CT processes can vary on an extremely wide dynamical range and can be very sensitive to the underlying molecular structure, molecular environment, temperature, etc. Molecular level untem is assumed to start out with the nuclear degrees of freedom (DOF) at thermal equilibrium on the diabatic donor state potential energy surface (PES) and when the electronic coupling between the donor and acceptor electronic states can be assumed weak.…”

“…Another example corresponds to the inverted region, where the enhanced overlap between nuclear wavefunctions can make nuclear tunneling, as opposed to the classical activated process underlying classical Marcus theory, into the dominant CT pathway. 9,[31][32][33]40 This scenario is particularly relevant to organic photovoltaic devices, where the rigid solid state environment and low dielectric constant of the organic host conspire to give rise to relatively small reorganization energies. [31][32][33] A third example corresponds to cases where the electronic coupling autocorrelation function decays on sufficiently slow time scales so as to make it sensitive to the underlying nuclear dynamics.…”

“…9,[31][32][33]40 This scenario is particularly relevant to organic photovoltaic devices, where the rigid solid state environment and low dielectric constant of the organic host conspire to give rise to relatively small reorganization energies. [31][32][33] A third example corresponds to cases where the electronic coupling autocorrelation function decays on sufficiently slow time scales so as to make it sensitive to the underlying nuclear dynamics. 31 Lastly, the validity of the Condon approximation can become questionable, for example in cases where the transition between electronic states occurs through a conical intersection.…”