Quantum dynamical simulation of photoinduced electron transfer processes in dye-semiconductor systems: theory and application to coumarin 343 at TiO₂

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Photoinduced Carrier Dynamics at the Interface of Black Phosphorus and Bismuth Vanadate

Two-dimensional (2D) heterostructures of black phosphorus (BP)/bismuth vanadate (BVO) have attracted much attention due to their potential uses in photocatalytic water splitting. However, the interfacial photoinduced electron- and hole-transfer dynamics are not explored computationally. Herein, we have used density functional theory (DFT) calculations and DFT-based fewest-switches surface-hopping dynamics simulations to investigate the light-driven electron and hole dynamics taking place at the interface of BP and the BVO(010) surface. Our results show that the BP monolayer is adsorbed on BVO(010) via van der Waals interaction. Upon irradiation, the electron transfer takes place from BP to BVO(010) within 500 fs but with two distinct processes. In the first phase, the electron transfer proceeds adiabatically and is mainly driven by atomic motions. In the second phase, the electron transfer decays very slowly. The hole-transfer dynamics from BVO(010) to BP exhibits a similar ultrafast decay in the first stage followed by a slow decay; however, there is a comparable amount of hole trapped in a BP state due to a large energy gap from its higher state. These insights may be useful for the design of novel photocatalytic water-splitting materials.

A non-perturbative approach to simulate heterogeneous electron transfer dynamics: Effective mode treatment of the continuum electronic states

We propose a non-perturbative method to simulate heterogeneous electron transfer dynamics in systems described by a Newns-Anderson type of model. The coupling between the molecule and the continuum electronic states at the metal or semiconductor surface is represented using a set of effective modes, by employing an exponential expansion of the bath correlation functions. Depending on the nature of the problems, the nuclear degrees of freedom are either treated explicitly using wave functions and density operators or as dissipative modes using the techniques from the hierarchical equations of the motion method. Numerical examples are also presented for applications in problems including (1) photo-induced charge transfer at the molecule-semiconductor interfaces, (2) heterogeneous electron transfer at the molecule-metal interface, and (3) vibrational relaxation on a metal surface.

Theoretical Investigation of the Electron-Transfer Dynamics and Photodegradation Pathways in a Hydrogen-Evolving Ruthenium-Palladium Photocatalyst

Time-dependent density functional theory calculations combined with the Marcus theory of electron transfer (ET) were applied on the molecular photocatalyst [(tbbpy)₂ Ru(tpphz)PdCl₂ ]²⁺ in order to elucidate the light-induced relaxation pathways populated upon excitation in the longer wavelength range of its absorption spectrum. The computational results show that after the initial excitation, metal (Ru) to ligand (tpphz) charge transfer (MLCT) triplet states are energetically accessible, but that an ET toward the catalytic center (PdCl₂ ) from these states is a slow process, with estimated time constants above 1 ns. Instead, the calculations predict that low-lying Pd-centered states are efficiently populated-associated to an energy transfer toward the catalytic center. Thus, it is postulated that these states lead to the dissociation of a Cl^- and are consequently responsible for the experimentally observed degradation of the catalytic center. Following dissociation, it is shown that the ET rates from the MLCT states to the charge separated states are significantly increased (i.e. 10⁴ -10⁶ times larger). This demonstrates that alteration of the catalytic center generates efficient charge separation.

The dynamics of charge transfer with and without a barrier: A very simplified model of cyclic voltammetry

Using the Anderson-Holstein model, we investigate charge transfer dynamics between a molecule and a metal surface for two extreme cases. (i) With a large barrier, we show that the dynamics follow a single exponential decay as expected; (ii) without any barrier, we show that the dynamics are more complicated. On the one hand, if the metal-molecule coupling is small, single exponential dynamics persist. On the other hand, when the coupling between the metal and the molecule is large, the dynamics follow a biexponential decay. We analyze the dynamics using the Smoluchowski equation, develop a simple model, and explore the consequences of biexponential dynamics for a hypothetical cyclic voltammetry experiment.