Modeling time-coincident ultrafast electron transfer and solvation processes at molecule-semiconductor interfaces

Abstract

Kinetic models based on Fermi's Golden Rule are commonly employed to understand photoinduced electron transfer dynamics at molecule-semiconductor interfaces. Implicit in such second-order perturbative descriptions is the assumption that nuclear relaxation of the photoexcited electron donor is fast compared to electron injection into the semiconductor. This approximation breaks down in systems where electron transfer transitions occur on 100-fs time scale. Here, we present a fourth-order perturbative model that captures the interplay between time-coincident electron transfer and nuclear relaxation processes initiated by light absorption. The model consists of a fairly small number of parameters, which can be derived from standard spectroscopic measurements (e.g., linear absorbance, fluorescence) and/or first-principles electronic structure calculations. Insights provided by the model are illustrated for a two-level donor molecule coupled to both (i) a single acceptor level and (ii) a density of states (DOS) calculated for TiO2 using a first-principles electronic structure theory. These numerical calculations show that second-order kinetic theories fail to capture basic physical effects when the DOS exhibits narrow maxima near the energy of the molecular excited state. Overall, we conclude that the present fourth-order rate formula constitutes a rigorous and intuitive framework for understanding photoinduced electron transfer dynamics that occur on the 100-fs time scale.

Light Harvesting and Charge Separation in a π-Conjugated Antenna Polymer Bound to TiO2

“…20 The presence of multiple kinetic components has been observed for other related sensitizers and arises from a number of factors, including the dye-binding motifs, electronic coupling and overlap of the dye donor levels with the TiO 2 acceptor states. [22][23][24] Furthermore, based on the analysis of the transient spectra 25 there is negligible ultrafast (τ<200 fs) electron injection in this complex, and by 1.4 ns the overall injection yield is 45%. 26 Photoexcitation of the PF-Ru-A//TiO 2 film at 450 nm gives rise to similar spectral features as seen for the Model-Ru-A//TiO 2 film at early times (Fig.…”

Ultrafast Spectroscopic Signatures of Coherent Electron-Transfer Mechanisms in a Transition Metal Complex

“…31,35,64 In fact, the derivation of the doorway function in section IIB parallels the derivation of the fourth-order rate function for electron transfer presented in earlier work. 31 The fourth-order rate function can be written as where the only surviving terms are those in which n = k. In other words, the coherence-to-coherence pathway, nk → ul, vanishes when τ is large but the population-to-coherence pathway, nn → ul, survives. This idea can be taken a step further if we let the system establish a Boltzmann distribution of vibrational populations in the excited state before BET.…”

“…In previous work, we showed that a fourth-order perturbative model can be used to simulate time-coincident electron-transfer and solvation dynamics under many of the same approximations made in Marcus' theory. 31 The model takes inspiration from an earlier nonequilibrium version of Fermi's golden rule in which explicit field−matter interactions were not used to establish the initial condition. 32 Similarly motivated models for nonequilibrium electron transfer 33 and nonsecular transitions between vibrational states 34 have been presented in recent literature.…”

“…The point of intersection between free energy surfaces is located at −λ − (ΔG eg + λ) 2 /4λ. The wavepacket initiated by the pump pulse can be written as31…”

Modeling Electron Injection at Semiconductor–Molecule Interfaces using First-Principles Dynamics Simulation: Effects of Nonadiabatic Coupling, Self-energy, and Surface Models

“…of the analytical model expression, as we have demonstrated in the context of a new fourth-order kinetic model in our earlier work. 12 The combined use of the analytical models with first-principles determination of their parameters helps us develop unbiased interpretation and understanding. At the same time, such an approach is still fundamentally limited by some key assumptions of the underlying kinetic model we use, such as having a constant electronic coupling that is independent of the conduction band energy, etc.…”