Photoinduced Charge Transfer Dynamics in the Carotenoid–Porphyrin–C₆₀ Triad via the Linearized Semiclassical Nonequilibrium Fermi’s Golden Rule

Abstract

The nonequilibrium Fermi's golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions, when the nuclear degrees of freedom start out in a nonequilibrium state. In this paper, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer (CT) rates in the carotenoidporphyrin-C 60 molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground-state to the ππ * state, and the porphyrin-to-C 60 and the carotenoid-to-C 60 CT rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C 60 CT process. We also derive an instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcuslike expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

Direct Nonadiabatic Simulations of the Photoinduced Charge Transfer Dynamics

“…On the other hand, for the synthesized CPC triad, the formation of the CT state is within 10 ps . Recent work based on the linearized semiclassical nonequilibrium Fermi’s Golden Rule (as well as the instantaneous Marcus theory) suggest that 90% of the CT occurs during the first 0.6 ps of the simulation for the bent configuration of CTC, agreeing with what we find from our direct simulation. Together, all the above results clearly demonstrate that the current direct simulation approach is both efficient and accurate to investigate the photoinduced charge transfer dynamics.…”

“…Figure presents the CT dynamics in the CPC triad model system, which is another well-studied prototypical artificial light-harvesting system. ,,, Earlier experimental investigations , have shown photoinduced charge separation in this system. Recent theoretical work suggests that the simple Marcus theory is unable to properly predict the photoinduced electron-transfer time-scales in this system. , Here, we use direct nonadiabatic simulations to investigate the charge transfer dynamics. Figure A, presents the time-dependent transferring charge density of the corresponding active state along a given nuclear trajectory at t = 0 fs, t = 94.2 fs, and t = 600 fs, respectively.…”

“…Our approach uses the fewest switches surface hopping algorithm , to capture the influence of nuclear vibrations on the electronic nonadiabatic transitions, and the single-particle time-dependent Kohn–Sham (TDKS) approach ,, to describe the quantum mechanical state of the transferring electron. With this approach, we investigate the nonadiabatic PICT dynamics in the phthalocyanine dimer/fullerene system ,, and the carotenoid–porphyrin–C 60 (CPC) triad system, ,,,,− which are model systems for understanding the CT dynamics in organic photovoltaics. Our results are in excellent agreement with both experimental measurements and high-level (yet expensive) theoretical calculations.…”

CTRAMER: An open-source software package for correlating interfacial charge transfer rate constants with donor/acceptor geometries in organic photovoltaic materials

“…Module 5 evaluates CT rates at different levels. Transition rate constants are calculated following a Marcus-level linearized semi-classical (LSC) 1, 19,21,22 approximation to Fermi's Golden Rule, where the donor-to-acceptor transition rate constant (k M ) is given by: 19,21,23,24 , but is referred to as "Marcus-level" as the reorganization energy, 𝐸 E , the reaction free energy, ∆𝐸, and the activation energy, 𝐸 G , can be calculated from 〈𝑈〉 and 𝜎 8 : 𝐸 E = 𝜎 8 -/(2𝑘 K 𝑇), ∆𝐸 = −𝐸 E − 〈𝑈〉, and 𝐸 G = 𝑘 K 𝑇〈𝑈〉 -/(2𝜎 8 -). These parameters allow for the analysis of rates calculated using Marcus Theory.…”

“…The CT rate constants are calculated within the framework of Fermi's golden rule (FGR) and based on the linearized semiclassical (LSC) approximation. [19][20][21][22][23][24][25][26] Support for other levels of CT theory is planned to be added in future versions. Each of the methods used in CTRAMER have been chosen due to being well-studied and performing well in benchmarks.…”