Role of Solvent Dynamics in Ultrafast Photoinduced Proton-Coupled Electron Transfer Reactions in Solution

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Chemovoltaic effect for renewable liquid and vapor fuels on semiconductor surfaces

The chemovoltaic effect - generation of electronic excitation by exergonic redox reactions - has been observed on metallic surfaces of Schottky junctions and is proving to be pivotal in explaining in detail the momentum conservation relations of chemically active collisions. As shown in this work, it can hold keys for direct chemical energy harvesting by semiconductor solar cells. To study the possibilities of chemovoltaic energy conversion by semiconductors, we have modeled and designed an 'electrolyte-free fuel cell' formed by a GaAs diode that can host electrochemical fuel oxidation and oxidant reduction reactions on its conduction and valence bands and as a result convert renewable chemical energy (as well as light) into electricity. The experimental results show that exposing the surface of a suitably designed solar cell to methanol liquid or vapor in the presence of oxygen or hydrogen peroxide leads to the generation of electrical power.

Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency

For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

Modeling Excited-State Proton Transfer Using the Lindblad Equation: Quantification of Time-Resolved Spectroscopy with Mechanistic Insights

The quantum dynamics of excited-state intramolecular proton transfer (ESIPT) is studied using a multilevel vibronic Hamiltonian and the Lindblad master equation. We simulate time-resolved fluorescence spectroscopy of 2-(2'-hydroxyphenyl) benzothiazole (HBT) and 10-hydroxybenzo[h]quinoline (HBQ), which suggests that the underlying mechanism behind the initial ultrafast rise and decay in the spectra is electronic state population that evolves simultaneously with proton wave packet dynamics. The results predict that the initial rise and decay signals at different wavelengths vary significantly with system properties in terms of their shape, the time, and the intensity of the maximum. These findings provide clues for data interpretation, mechanism validation, and control of the dynamics, and the model serves as an attempt toward clarifying ESIPT by direct comparison to time-resolved spectroscopy.

Nuclear Gradient Expressions for Molecular Cavity Quantum ElectrodynamicsSimulations using Mixed Quantum-Classical Methods

We derive a rigorous nuclear gradient for a molecule-cavity hybrid system using the Quantum Electrodynamics Hamiltonian. We treat the electronic-photonic DOFs as the quantum subsystem, and the nuclei as the classical subsystem. Using the adiabatic basis for the electronic DOF and the Fock basis for the photonic DOF, and requiring the total energy conservation of this mixed quantum-classical system, we derived the rigorous nuclear gradient for the molecule-cavity hybrid system, which is naturally connected to the approximate gradient under the Jaynes-Cummings approximation. The nuclear gradient expression can be readily used in any mixed quantum-classical simulations and will allow one to perform the non-adiabatic on-the-fly simulation of polariton quantum dynamics. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the molecule-cavity hybrid system and have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics.

Investigating Tunneling-Controlled Chemical Reactions through Ab Initio Ring Polymer Molecular Dynamics

We use the ab initio ring polymer molecular dynamics (RPMD) approach to investigate tunneling-controlled reactions in methylhydroxycarbene. Nuclear tunneling effects enable molecules to overcome the barriers which cannot be overcome classically. Under low-temperature conditions, intrinsic quantum tunneling effects can facilitate the chemical reaction in a pathway that is favored neither thermodynamically nor kinetically. This behavior is referred to as the tunneling-controlled chemical reaction and is regarded as the third paradigm of chemical reaction controls. In this work, we use the ab initio RPMD approach to incorporate the tunneling effects in our quantum dynamics simulations and investigate the reaction kinetics of two competitive reaction pathways at various temperatures. The reaction rate constants obtained here agree extremely well with the experimentally measured rates. We demonstrate the feasibility of using ab initio RPMD rate calculations in a realistic molecular system and provide an interesting and important example for future investigations of reaction mechanisms dominated by quantum tunneling effects.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Benchmarking the Surface Hopping Method to Include Nuclear Quantum Effects

We have benchmarked the surface hopping method to capture nuclear quantum effects in the spin-Boson model in the deep tunneling regime. The thermal populations and the rate constants calculated using the surface hopping method are compared with those calculated using Boltzmann theory and Fermi's golden rule, respectively. Additionally, we have proposed a simple kinetic model that partially includes nuclear quantum effects within Marcus theory, and the results of the surface hopping method are analyzed under the framework of this simple kinetic model. A broad range of parameters are investigated to identify the regimes for the successes and failures of the surface hopping method. This work shows that with the accurate treatment of decoherence and velocity reversal, surface hopping can generally capture the nuclear quantum effects in the deep tunneling and weak diabatic coupling regime.

Recent progress in approximate quantum dynamics methods for the study of proton-coupled electron transfer reactions

Proton-coupled electron transfer (PCET) reactions are ubiquitous natural processes at the heart of energy conversion reactions in photosynthesis and respiration, DNA repair, and diverse enzymatic reactions. Theoretical formulation and computational method developments have eyed modeling of thermal and photoinduced PCET for the last three decades. The accumulation of these studies, collected in dozens of reviews, accounts, and perspectives, has firmly established the influence of quantum effects, including non-adiabatic electronic transitions, vibrational relaxation, zero-point energy, and proton tunneling, on the rate and mechanism of PCET reactions. Here, we focus on some recently-developed methods, spanning the last eight years, that can quantitatively capture these effects in the PCET context and provide efficient means for their qualitative description in complex systems. The theoretical background of each method and their accuracy with respect to exact results are discussed and the results of relevant PCET simulations based on each method are presented.

Revisiting the Limiting Factors for Overall Water-Splitting on Organic Photocatalysts

In pursuit of inexpensive and earth abundant photocatalysts for solar hydrogen production from water, conjugated polymers have shown potential to be a viable alternative to widely used inorganic counterparts. The photocatalytic performance of polymeric photocatalysts, however, is very poor in comparison to that of inorganic photocatalysts. Most of the organic photocatalysts are active in hydrogen production only when a sacrificial electron donor (SED) is added into the solution, and their high performances often rely on presence of noble metal co-catalyst (e.g. Pt). For pursuing a carbon neutral and cost-effective green hydrogen production, unassisted hydrogen production solely from water is one of the critical requirements to translate a mere bench-top research interest into the real world applications. Although this is a generic problem for both inorganic and organic types of photocatalysts, organic photocatalysts are mostly investigated in the half-reaction, and have so far shown limited success in hydrogen production from overall water-splitting. To make progress, this article exclusively discusses critical factors that are limiting the overall water-splitting in organic photocatalysts. Additionally, we also have extended the discussion to issues related to stability, accurate reporting of the hydrogen production as well as challenges to be resolved to reach 10 % STH (solar-to-hydrogen) conversion efficiency.

Kinetics of Proton Discharge on Metal Electrodes: Effects of Vibrational Nonadiabaticity and Solvent Dynamics

Proton discharge on metal electrodes, also denoted the Volmer reaction, is a critical step in a wide range of electrochemical processes. This electrochemical proton-coupled electron transfer (PCET) reaction is predominantly electronically adiabatic in aqueous solution and is typically treated as fully adiabatic. Recently, a theoretical model for this PCET reaction was developed to generate the vibronic free energy surfaces as functions of a collective solvent coordinate and the distance of the proton-donating acid from the electrode. Herein a unified formulation is devised to describe such PCET reactions in terms of a curve crossing between two diabatic vibronic states corresponding to the lowest two proton vibrational states, employing an interpolation scheme that spans the adiabatic transition state theory, nonadiabatic Fermi golden rule, and solvent-controlled regimes. In contrast to previous treatments, application of this formulation to the aqueous Volmer reaction highlights the importance of vibrational nonadiabaticity and solvent dynamics. The calculated transfer coefficients and kinetic isotope effects are in reasonable agreement with experimental measurements. These fundamental insights have broad implications for understanding electrochemical processes.

Isotopic substitution affects excited state branching in a DNA duplex in aqueous solution

Changing the solvent from H2O to D2O dramatically affects the branching of the initial excited electronic states in an alternating G·C DNA duplex into two distinct decay channels. The slower, multisite PCET channel that deactivates more than half of all excited states in D2O becomes six times weaker in H2O.

Excited state structural dynamics of 4-cyano-4′-hydroxystilbene: deciphering the signatures of proton-coupled electron transfer using ultrafast Raman loss spectroscopy

The photo-initiated proton-coupled electron transfer process in the 4-cyano-4′-hydroxystilbene–tert-butylamine adduct strongly affects the excited-state structural dynamics of CHSB.

Theoretical-computational modeling of charge transfer and intersystem crossing reactions in complex chemical systems

In this paper we present a theoretical-computational methodology specifically aimed at describing processes involving internal conversion or intersystem crossing, from atomistic (semiclassical) simulations and, hence, very suitable for treating complex atomic-molecular systems. The core of the presented approach is the evaluation of the diabatic perturbed energy surfaces of a portion of the whole system, treated at the quantum level and therefore preventively selected, in semi-classical interaction with the atomic-molecular environment. Subsequently, the estimation of the coupling between the diabatic surfaces and the inclusion of the obtained observables within a properly designed kinetic model allows the reconstruction of the whole phenomenology directly comparable to the experimental (typically kinetic) data. Application to two systems has demonstrated that the proposed approach can represent a valuable tool, somewhat complementary to other methods based on explicit quantum-dynamical approaches, for the theoretical-computational investigations of large and complex atomic-molecular systems.

Proton-Coupled Electron Transfer: Moving Together and Charging Forward

Proton-coupled electron transfer (PCET) is ubiquitous throughout chemistry and biology. This Perspective discusses recent advances and current challenges in the field of PCET, with an emphasis on the role of theory and computation. The fundamental theoretical concepts are summarized, and expressions for rate constants and kinetic isotope effects are provided. Computational methods for calculating reduction potentials and pKa's for molecular electrocatalysts, as well as insights into linear correlations and non-innocent ligands, are also described. In addition, computational methods for simulating the nonadiabatic dynamics of photoexcited PCET are discussed. Representative applications to PCET in solution, proteins, electrochemistry, and photoinduced processes are presented, highlighting the interplay between theoretical and experimental studies. The current challenges and suggested future directions are outlined for each type of application, concluding with an overall view to the future.

Excited-state proton coupled charge transfer modulated by molecular structure and media polarization

Charge and proton transfer reactions in the excited states of organic dyes can be coupled in many different ways. Despite the complementarity of charges, they can occur on different time scales and in different directions of the molecular framework. In certain cases, excited-state equilibrium can be established between the charge-transfer and proton-transfer species. The interplay of these reactions can be modulated and even reversed by variations in dye molecular structures and changes of the surrounding media. With knowledge of the mechanisms of these processes, desired rates and directions can be achieved, and thus the multiple emission spectral features can be harnessed. These features have found versatile applications in a number of cutting-edge technological areas, particularly in fluorescence sensing and imaging.

Neutral carotenoid radicals in photoprotection of wild-type Arabidopsis thaliana

The deprotonation of naturally occurring zeaxanthin (Zea) radical cations (Zea(•+)) to form neutral radicals (#Zea(•)) and their involvement in the qE portion of nonphotochemical quenching (NPQ) was examined. The radical cations are weak acids, and readily deprotonate to a long-lived neutral radical (#Zea(•)) that could serve as long-lived quenching sites. When #Zea(•) is eventually neutralized and Zea is reformed in the presence of D2O, the Zea has an opportunity to undergo H/D exchange. This paper examines evidence for H/D exchange specific to qE activity in Arabidopsis thaliana . We demonstrate that Zea(•+) formed chemically via oxidation of Zea by Fe(III) in the presence of D2O undergoes H/D exchange with a significant intensity increase of the M+1 (d1Zea) and M+2 (d2Zea) mass peaks in the mass spectrum. Then leaves from wild-type A. thaliana were infiltrated with either D2O or H2O and exposed to light. The carotenoids were extracted and analyzed via electrospray ionization liquid chromatography/mass spectrometry (LC/MS) to examine the mass peak distribution of Zea. Only leaves exposed to light intensity that triggers qE in A. thaliana (>300 μE m(-2)s(-1)) showed H/D exchange. This result suggests that #Zea(•) can form by the deprotonation of the weak acid Zea(•+) during qE, and its possible impact on qE must be considered.

Photoinduced proton-coupled electron transfer of hydrogen-bonded p-nitrophenylphenol-methylamine complex in solution

Proton-coupled electron transfer can occur through concerted (electron-proton transfer, EPT) or sequential mechanisms, but this distinction becomes less well-defined for photoinduced reactions. These issues have been examined with transient absorption experiments on a hydrogen-bonded complex consisting of p-nitrophenylphenol and t-butylamine. These experiments revealed two spectroscopically distinct states: the higher-energy excited state was interpreted to be a conventional intramolecular charge transfer (ICT) state within the p-nitrophenylphenol, whereas the lower-energy state was interpreted to be an ICT-EPT state, where photoexcitation resulted in both ICT and the shifting of electronic density corresponding to effective proton transfer from the phenol to the amine. In the present work, the singlet excited states of the hydrogen-bonded p-nitrophenylphenol-methylamine complex in 1,2-dichloroethane are studied with time-dependent density functional theory and higher-level ab initio methods. The calculations suggest that the ππ* state, which is the S(1) state at the Franck-Condon geometry, corresponds to the state denoted ICT-EPT in the experimental analysis, whereas the nπ* state, which is the S(2) state at this geometry, likely corresponds to the state denoted ICT in the experimental analysis. According to the calculations, the ππ* state has charge-transfer character, as well as a change in electronic density on the amine, with the minimum-energy structure corresponding to the proton bonded to the nitrogen acceptor, consistent with proton transfer. The nπ* state has little charge-transfer character, as well as negligible change in electronic density on the amine, with the minimum-energy structure corresponding to the proton bonded to the oxygen donor. The calculations also provide evidence of an avoided crossing between these two states located energetically close to the Franck-Condon point. These calculations provide the foundation for future nonadiabatic molecular dynamics studies of the relaxation process.

Nonadiabatic dynamics of photoinduced proton-coupled electron transfer: comparison of explicit and implicit solvent simulations

Theoretical approaches for simulating the ultrafast dynamics of photoinduced proton-coupled electron transfer (PCET) reactions in solution are developed and applied to a series of model systems. These processes are simulated by propagating nonadiabatic surface hopping trajectories on electron-proton vibronic surfaces that depend on the solute and solvent nuclear coordinates. The PCET system is represented by a four-state empirical valence bond model, and the solvent is treated either as explicit solvent molecules or as a dielectric continuum, in which case the solvent dynamics is described in terms of two collective solvent coordinates corresponding to the energy gaps associated with electron and proton transfer. The explicit solvent simulations reveal two distinct solvent relaxation time scales, where the faster time scale relaxation corresponds to librational motions of solvent molecules in the first solvation shell, and the slower time scale relaxation corresponds to the bulk solvent dielectric response. The charge transfer dynamics is strongly coupled to both the fast and slow time scale solvent dynamics. The dynamical multistate continuum theory is extended to include the effects of two solvent relaxation time scales, and the resulting coupled generalized Langevin equations depend on parameters that can be extracted from equilibrium molecular dynamics simulations. The implicit and explicit solvent approaches lead to qualitatively similar charge transfer and solvent dynamics for model PCET systems, suggesting that the implicit solvent treatment captures the essential elements of the nonequilibrium solvent dynamics for many systems. A combination of implicit and explicit solvent approaches will enable the investigation of photoinduced PCET processes in a variety of condensed phase systems.

Probing quantum and dynamic effects in concerted proton-electron transfer reactions of phenol-base compounds

The oxidation of three phenols, which contain an intramolecular hydrogen bond to a pendent pyridine or amine group, has been shown, in a previous experimental study, to undergo concerted proton-electron transfer (CPET). In this reaction, the electron is transferred to an outer-sphere oxidant, and the proton is transferred from the oxygen to nitrogen atom. In the present study, this reaction is studied computationally using a version of Hammes-Schiffer's multistate continuum theory where CPET is formulated as a transmission frequency between neutral and cation vibrational-electronic states. The neutral and cation proton vibrational wave functions are computed from one-dimensional potential energy surfaces (PESs) for the transferring proton in a fixed heavy atom framework. The overlap integrals for these neutral/cation wave functions, considering several initial (i.e., neutral) and final (i.e., cation) vibrational states, are used to evaluate the relative rates of oxidation. The analysis is extended to heavy atom configurations with various proton donor-acceptor (i.e., O-N) distances to assess the importance of heavy atom "gating". Such changes in d(ON) dramatically affect the nature of the proton PESs and wave functions. Surprisingly, the most reactive configurations have similar donor-acceptor distances despite the large (~0.2 Å) differences in the optimized structures. These theoretical results qualitatively reproduce the experimental faster reactivity of the reaction of the pyridyl derivative 1 versus the CH(2)-pyridyl 2, but the computed factor of 5 is smaller than the experimental 10(2). The amine derivative is calculated to react similarly to 1, which does not agree with the experiments, likely due to some of the simplifying assumptions made in applying the theory. The computed kinetic isotope effects (KIEs) and their temperature dependence are in agreement with experimental results.