All-Atom Photoinduced Charge Transfer Dynamics in Condensed Phase via Multistate Nonlinear-Response Instantaneous Marcus Theory

Abstract

Photoinduced charge transfer (CT) in the condensed phase is an essential component in solar energy conversion, but it is challenging to simulate such a process on the all-atom level. The traditional Marcus theory has been utilized for obtaining CT rate constants between pairs of electronic states but cannot account for the nonequilibrium effects due to the initial nuclear preparation. The recently proposed instantaneous Marcus theory (IMT) and its nonlinear-response formulation allow for incorporating the nonequilibrium nuclear relaxation to electronic transition between two states after the photoexcitation from the equilibrium ground state and provide the time-dependent rate coefficient. In this work, we extend the nonlinear-response IMT method for treating photoinduced CT among general multiple electronic states and demonstrate it in the organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent. All-atom molecular dynamics simulations were employed to obtain the time correlation functions of energy gaps, which were used to generate the IMT-required time-dependent averages and variances of the relevant energy gaps. Our calculations show that the multistate IMT could capture the significant nonequilibrium effects due to the initial nuclear state preparation, and this is corroborated by the substantial differences between the population dynamics predicted by the multistate IMT and the Marcus theory, where the Marcus theory underestimates the population transfer. The population dynamics by multistate IMT is also shown to have a better agreement with the all-atom nonadiabatic mapping dynamics than the Marcus theory does. Because the multistate nonlinear-response IMT is straightforward and cost-effective in implementation and accounts for the nonequilibrium nuclear effects, we believe this method offers a practical strategy for studying charge transfer dynamics in complex condensed-phase systems.

Figure 1

Geometries of triad conformations 3 (a) and 5 (b).

Figure 2

Time correlation function C₁^NL(t) of CPC₆₀ triad conformation 3 for different transitions j → k obtained from all-atom equilibrium MD simulations on the V_j potential surface at 300 K.

Figure 3

Time correlation function C₂^NL(t) of CPC₆₀ triad conformation 3 for different transitions j → k obtained from all-atom equilibrium MD simulations on the V_j potential surface at 300 K.

Figure 4

Time-depenent average energy gap of CPC₆₀ triad conformation 3 for different transitions j → k obtained from all-atom equilibrium MD simulations on the V_j potential surface at 300 K.

Figure 5

Time-dependent energy gap variance of CPC₆₀ triad conformation 3 for different transitions j → k obtained from all-atom equilibrium MD simulations on the V_j potential surface at 300 K.

Figure 6

Time-dependent distribution of U_jk(t) of CPC₆₀ triad conformation 3 for different transitions j → k obtained from all-atom equilibrium MD simulations on the V_j potential surface at 300 K.

Figure 7

Time-dependent distribution of U_jk(t) of CPC₆₀ triad conformation 5 for different transitions j → k obtained from all-atom equilibrium MD simulations on the V_j potential surface at 300 K.

Figure 8

Instantaneous Marcus theory (IMT) CT rate coefficient k_j→k(t) of different transitions j → k of CPC₆₀ triad conformation 3 dissolved in THF solvent at 300 K obtained using the nonlinear-response formulation of IMT.

Figure 9

Instantaneous Marcus theory (IMT) CT rate coefficient k_j→k(t) of different transitions j → k of CPC₆₀ triad conformation 5 dissolved in THF solvent at 300 K obtained using the nonlinear-response formulation of IMT.

Figure 10

Population dynamics of CPC₆₀ triad conformation 3 obtained by integrating the time-dependent IMT rate coefficient. The top, middle, and bottom panels correspond to the initial electronic states of ππ*, CT1, and CT2, respectively. In all cases, the initial nuclear state is in thermal equilibrium with the ground-state potential surface. Left and right panels are short and long-time dynamics, respectively.

Figure 11

Population dynamics of CPC₆₀ triad conformation 5 obtained by integrating the time-dependent IMT rate coefficient. The top, middle, and bottom panels correspond to the initial electronic state of ππ*, CT1, and CT2, respectively. In all cases, the initial nuclear state is in thermal equilibrium with the ground-state potential surface. Left and right panels are short- and long-time dynamics, respectively.

Figure 12

Comparison of population dynamics of CPC₆₀ triad conformation 3 dissolved in explicit THF solvent at 300 K with the initial electronic state on ππ* obtained with (a) instantaneous Marcus theory (IMT, solid) and traditional Marcus theory (dashed) and (b) nonadiabatic mapping dynamics using the symmetrical quasiclassical method with a triangle window (SQC, triangle symbol) and the linearized semiclassical methods 1 (LSC1, circle symbol) and 2 (LSC2, square symbol). Data of the all-atom nonadiabatic SQC and LSC dynamics were obtained from ref (69).

Figure 13

Comparison of population dynamics of CPC₆₀ triad conformation 5 dissolved in explicit THF solvent at 300 K with the initial electronic state on ππ* obtained with (a) instantaneous Marcus theory (IMT, solid) and traditional Marcus theory (dashed) and (b) nonadiabatic mapping dynamics using the symmetrical quasiclassical method with a triangle window (SQC, triangle symbol) and the linearized semiclassical methods 1 (LSC1, circle symbol) and 2 (LSC2, square symbol).