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Small ribozymes cleave their RNA phosphodiester backbone by catalyzing a transphosphorylation reaction wherein a specific O2' functions as the nucleophile. While deprotonation of this alcohol through its acidification would increase its nucleophilicity, little is known about the p K a 's are not readily accessible experimentally. Herein, we turn to molecular dynamics to calculate the p K a 's are not readily accessible experimentally. Herein, we turn to molecular dynamics to calculate the p K a of the nucleophilic O2' in the hairpin ribozyme and to study interactions within the active site that may impact its value. We estimate the p K a of the nucleophilic O2' in the wild-type hairpin ribozyme to be 18.5 ± 0.8, which is higher than the reference compound, and identify a correlation between proper positioning of the O2' for nucleophilic attack and elevation of its p K a . We find that monovalent ions may play a role in depression of the O2' p K a , while the exocyclic amine appears to be important for organizing the ribozyme active site. Overall, this study suggests that the p K a of the O2' is raised in the ground state and lowers during the course of the reaction owing to positioning and metal ion interactions.

Proton-coupled electron transfer (PCET) reactions on metal oxides require coupling between proton transfer at the solid-liquid interface and electron transfer involving defects at or near the band edge. Herein, hybrid functional periodic density functional theory is used to elucidate the impact of proton-coupled defects on the bond dissociation free energies (BDFEs) of O-H bonds on anatase TiO 2 surfaces. These O-H BDFEs are directly related to interfacial PCET thermochemistry. Comparison between geometrically similar O-H bonds associated with different defect types, namely conduction d-band electrons or valence p-band holes, reveals that the BDFEs differ by ∼81 kcal/mol (3.50 eV), comparable to the wide TiO 2 band gap. These differences are shown to be determined primarily by differences in electron transfer driving forces, which are analyzed by using band energies and inner-sphere reorganization energies within a Marcus theory framework. These fundamental insights about the impact of proton-coupled defects on PCET thermochemistry at semiconductor surfaces have broad implications for electrocatalysis.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Proton-coupled electron transfer (PCET) reactions depend on the hydrogen-bond connectivity between sites of proton donors and acceptors. The 2-(2'-hydroxyphenyl) benzimidazole (BIP) based systems, which mimic the natural Tyr Z -His190 pair of Photosystem II, have been useful for understanding the associated PCET process triggered by one-electron oxidation of the phenol. Substitution of the benzimidazole by an appropriate terminal proton acceptor (TPA) group allows for two-proton translocations. However, the prototropic properties of substituted benzimidazole rings and rotation around the bond linking the phenol and the benzimidazole can lead to isomers that interrupt the intramolecular hydrogen-bonded network and thereby prevent a second proton translocation. Herein, a strategic symmetrization of a benzimidazole based system with two identical TPAs yields an uninterrupted network of intramolecular hydrogen bonds regardless of the isomeric form. NMR data confirms the presence of a single isomeric form in the disubstituted system but not in the monosubstituted system in certain solvents. Infrared spectroelectrochemistry demonstrates a two-proton transfer process associated with the oxidation of the phenol occurring at a lower redox potential in the disubstituted system relative to its monosubstituted analogue. Computational studies support these findings and show that the disubstituted system stabilizes the oxidized two-proton transfer product through the formation of a bifurcated hydrogen bond. Considering the prototropic properties of the benzimidazole heterocycle in the context of multiple PCET will improve the next generation of novel, bioinspired constructs built by concatenated units of benzimidazoles, thus allowing proton translocations at nanoscale length., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The computational investigation of photochemical processes often entails the calculation of excited-state geometries, energies, and energy gradients. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons, thereby including the associated nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations. The multicomponent density functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) methods allow efficient calculations of ground and excited states, respectively. Herein, the analytical gradients are derived and implemented for the NEO-TDDFT method and the associated Tamm-Dancoff approximation (NEO-TDA). The programmable equations for these analytical gradients as well as the NEO-DFT analytical Hessian are provided. The NEO approach includes the anharmonic zero-point energy (ZPE) and density delocalization associated with the quantum protons as well as vibronic mixing in geometry optimizations and energy calculations of ground and excited states. The harmonic ZPE associated with the other nuclei can be computed via the NEO Hessian. This approach is used to compute the 0-0 adiabatic excitation energies for a set of nine small molecules with all protons quantized, exhibiting slight improvement over the conventional electronic approach. Geometry optimizations of two excited-state intramolecular proton-transfer systems, [2,2'-bipyridyl]-3-ol and [2,2'-bipyridyl]-3,3'-diol, are performed with one and two quantized protons, respectively. The NEO calculations for these systems produce electronically excited-state geometries with stronger intramolecular hydrogen bonds and similar relative stabilities compared to conventional electronic methods. This work provides the foundation for nonadiabatic dynamics simulations of fundamental processes such as photoinduced proton transfer and proton-coupled electron transfer.

The incorporation of nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations and molecular dynamics simulations is a longstanding challenge. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons with wave function and density functional theory methods. This approach inherently includes nuclear delocalization and zero-point energy in molecular energy calculations, geometry optimizations, reaction paths, and dynamics. It can also provide accurate descriptions of excited electronic, vibrational, and vibronic states as well as nuclear tunneling and nonadiabatic dynamics. Nonequilibrium nuclear-electronic dynamics simulations beyond the Born-Oppenheimer approximation can be used to investigate a wide range of excited state processes. This Perspective provides an overview of the foundational NEO methods and enumerates the prospects for using these methods as building blocks for future developments. The conceptual simplicity and computational efficiency of the NEO approach will enhance its accessibility and applicability to diverse chemical and biological systems.

Proton-coupled electron transfer (PCET) is a fundamental step in a wide range of electrochemical processes, including those of interest in energy conversion and storage. Despite its importance, several mechanistic details of such reactions remain unclear. Here, we have combined a proton donor (tertiary ammonium) with a vibrational Stark-shift probe (benzonitrile), to track the process from the entry of the reactants into the electrical double layer (EDL), to the PCET reaction associated with proton donation to the electrode, and the formation of products. We have used operando vibrational spectroscopy and periodic density functional theory under electrochemical bias to assign the reactant and product peaks and their Stark shifts. We have identified three main stages for the progress of the PCET reaction as a function of applied potential. First, we have determined the potential necessary for desolvation of the reactants and their entry into the polarizing environment of the EDL. Second, we have observed the appearance of product peaks prior to the onset of steady state electrochemical current, indicating formation of a stationary population of products that does not turn over. Finally, more negative of the onset potential, the electrode attracts additional reactants, displacing the stationary products and enabling steady state current. This work shows that the integration of a vibrational Stark-shift probe with a proton donor provides critical insight into the interplay between interfacial electrostatics and heterogeneous chemical reactions. Such insights cannot be obtained from electrochemical measurements alone.

The variational quantum eigensolver (VQE) algorithm combined with the unitary coupled cluster (UCC) ansatz has been developed for the quantum computation of molecular energies and wave functions within the Born-Oppenheimer approximation. Herein, this approach is extended to multicomponent systems to enable the quantum mechanical treatment of more than one type of particle, such as electrons and positrons or electrons and nuclei, without invoking the Born-Oppenheimer approximation. Specifically, we introduce the multicomponent unitary coupled cluster (mcUCC) method combined with the VQE algorithm for the calculation of ground-state energies and wave functions as well as the multicomponent equation-of-motion (mcEOM) method for the calculation of excitation energies. These methods are developed within the nuclear-electronic orbital (NEO) framework and are formulated in the qubit basis to enable implementations on quantum computers. Moreover, these methods are used to calculate the ground-state energy and excitation energies of positronium hydride, where both electrons and the positron are treated quantum mechanically, as well as the H 2 molecule, where both electrons and one proton are treated quantum mechanically. These applications validate the implementation and provide benchmark data for future calculations. The errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism, as well as the accompanying computer code, will serve as the basis for applications to more complex multicomponent systems, such as simulations of photoinduced nonadiabatic molecular processes, on both classical and quantum computers.

Ribonucleotide reductase (RNR) is an essential enzyme in DNA synthesis for all living organisms. It reduces ribonucleotides to the corresponding deoxyribonucleotides by a reversible radical transfer mechanism. The active form of E. coli Ia RNR is composed of two subunits, α and β, which form an active asymmetric α 2 β 2 complex. The radical transfer pathway involves a series of proton-coupled electron transfer (PCET) reactions spanning α and β over ∼32 Å. Herein, quantum mechanical/molecular mechanical free energy simulations of PCET between tyrosine residues Y730 and Y731 are performed on the recently solved cryo-EM structure of the active α 2 β 2 complex, which includes a pre-turnover α/β pair with an ordered PCET pathway and a post-turnover α'/β' pair. The free energy surfaces in both the pre- and post-turnover states are computed. According to the simulations, forward radical transfer from Y731 to Y730 is thermodynamically favored in the pre-turnover state, and backward radical transfer is favored in the post-turnover state, consistent with the reversible mechanism. E623, a glutamate residue that is near these tyrosines only in the pre-turnover state, is discovered to play a key role in facilitating forward radical transfer by thermodynamically stabilizing the radical on Y730 through hydrogen-bonding and electrostatic interactions and lowering the free energy barrier via a proton relay mechanism. Introduction of fluorinated Y731 exhibits expected thermodynamic trends without altering the basic mechanism. These simulations suggest that E623 influences the directionality of PCET between Y731 and Y730 and predict that mutation of E623 will impact catalysis.

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semiclassical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool for providing insights and predictions for these processes.

Artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.

Nuclear quantum effects such as zero-point energy are important for describing a wide range of chemical properties. The nuclear-electronic orbital (NEO) approach incorporates such effects into quantum chemistry calculations by treating specified nuclei, typically protons, quantum mechanically on the same level as electrons. Herein, both the traditional and t 1 -transformed NEO coupled cluster with singles and doubles (NEO-CCSD) methods are implemented with a density fitting (DF) scheme for approximating the four-center two-particle integrals. The enhanced computational efficiency enables calculations on larger molecules with multiple quantum protons. The NEO-DF-CCSD method predicts proton affinities within chemical accuracy. Its application to protonated water tetramers with all nine protons treated quantum mechanically produces the qualitatively correct ordering of the isomer energies, which are strongly influenced by the zero-point energy contributions inherently included in NEO energy calculations. This work showcases the capabilities of the NEO-DF-CCSD method and provides the foundation for future developments and applications.

The nuclear-electronic orbital (NEO) method is a multicomponent quantum chemistry theory that describes electronic and nuclear quantum effects simultaneously while avoiding the Born-Oppenheimer approximation for certain nuclei. Typically specified hydrogen nuclei are treated quantum mechanically at the same level as the electrons, and the NEO potential energy surface depends on the classical nuclear coordinates. This approach includes nuclear quantum effects such as zero-point energy and nuclear delocalization directly into the potential energy surface. An extended NEO potential energy surface depending on the expectation values of the quantum nuclei incorporates coupling between the quantum and classical nuclei. Herein, theoretical methodology is developed to optimize and characterize stationary points on the standard or extended NEO potential energy surface, to generate the NEO minimum energy path from a transition state down to the corresponding reactant and product, and to compute thermochemical properties. For this purpose, the analytic coordinate Hessian is developed and implemented at the NEO Hartree-Fock level of theory. These NEO Hessians are used to study the S N 2 reaction of ClCH 3 Cl - and the hydride transfer of C 4 H 9 + . For each system, analysis of the single imaginary mode at the transition state and the intrinsic reaction coordinate along the minimum energy path identifies the dominant nuclear motions driving the chemical reaction. Visualization of the electronic and protonic orbitals along the minimum energy path illustrates the coupled electronic and protonic motions beyond the Born-Oppenheimer approximation. This work provides the foundation for applying the NEO approach at various correlated levels of theory to a wide range of chemical reactions.

The cytochrome bc 1 complex is a transmembrane enzymatic protein complex that plays a central role in cellular energy production and is present in both photosynthetic and respiratory chain organelles. Its reaction mechanism is initiated by the binding of a quinol molecule to an active site, followed by a series of charge transfer reactions between the quinol and protein subunits. Previous work hypothesized that the primary reaction was a concerted proton-coupled electron transfer (PCET) reaction because of the apparent absence of intermediate states associated with single proton or electron transfer reactions. In the present study, the kinetics of the primary bc 1 complex PCET reaction is investigated with a vibronically nonadiabatic PCET theory in conjunction with all-atom molecular dynamics simulations and electronic structure calculations. The computed rate constants and relatively high kinetic isotope effects are consistent with experimental measurements on related biomimetic systems. The analysis implicates a concerted PCET mechanism with significant hydrogen tunneling and nonadiabatic effects in the bc 1 complex. Moreover, the employed theoretical framework is shown to serve as a general strategy for describing PCET reactions in bioenergetic systems.

The oxidation of tyrosine to form the neutral tyrosine radical via proton-coupled electron transfer is essential for a wide range of biological processes. The precise measurement of the proton-coupled redox potentials of tyrosine (Y) in complex protein environments is challenging mainly because of the highly oxidizing and reactive nature of the radical state. Herein, a computational strategy is presented for predicting proton-coupled redox potentials in a protein environment. In this strategy, both the reduced Y-OH and oxidized Y-O • forms of tyrosine are sampled with molecular dynamics using a molecular mechanical force field. For a large number of conformations, a quantum mechanical/molecular mechanical (QM/MM) electrostatic embedding scheme is used to compute the free-energy differences between the reduced and oxidized forms, including the zero-point energy and entropic contributions as well as the impact of the protein electrostatic environment. This strategy is applied to a series of fluorinated tyrosine derivatives embedded in a de novo α-helical protein denoted as α 3 Y. The force fields for both the reduced and oxidized forms of these noncanonical fluorinated tyrosine residues are parameterized for general use. The calculated relative proton-coupled redox potentials agree with experimentally measured values with a mean unsigned error of 24 mV. Analysis of the simulations illustrates that hydrogen-bonding interactions between tyrosine and water increase the redox potentials by ∼100-250 mV, with significant variations because of the fluctuating protein environment. This QM/MM approach enables the calculation of proton-coupled redox potentials of tyrosine and other residues such as tryptophan in a variety of protein systems.

The essential role of a well-defined hydrogen-bond network in achieving chemically reversible multiproton translocations triggered by one-electron electrochemical oxidation/reduction is investigated by using pyridylbenzimidazole-phenol models. The two molecular architectures designed for these studies differ with respect to the position of the N atom on the pyridyl ring. In one of the structures, a hydrogen-bond network extends uninterrupted across the molecule from the phenol to the pyridyl group. Experimental and theoretical evidence indicates that an overall chemically reversible two-proton-coupled electron-transfer process (E2PT) takes place upon electrochemical oxidation of the phenol. This E2PT process yields the pyridinium cation and is observed regardless of the cyclic voltammogram scan rate. In contrast, when the hydrogen-bond network is disrupted, as seen in the isomer, at high scan rates (∼1000 mV s -1 ) a chemically reversible process is observed with an E characteristic of a one-proton-coupled electron-transfer process (E1PT). At slow cyclic voltammetric scan rates (<1000 mV s 1/2 characteristic of a one-proton-coupled electron-transfer process (E1PT). At slow cyclic voltammetric scan rates (<1000 mV s -1 ) oxidation of the phenol results in an overall chemically irreversible two-proton-coupled electron-transfer process in which the second proton-transfer step yields the pyridinium cation detected by infrared spectroelectrochemistry. In this case, we postulate an initial intramolecular proton-coupled electron-transfer step yielding the E1PT product followed by a slow, likely intermolecular chemical step involving a second proton transfer to give the E2PT product. Insights into the electrochemical behavior of these systems are provided by theoretical calculations of the electrostatic potentials and electric fields at the site of the transferring protons for the forward and reverse processes. This work addresses a fundamental design principle for constructing molecular wires where protons are translocated over varied distances by a Grotthuss-type mechanism.

Biomolecular hydration is fundamental to biological functions. Using phase-resolved chiral sum-frequency generation spectroscopy (SFG), we probe molecular architectures and interactions of water molecules around a self-assembling antiparallel β-sheet protein. We find that the phase of the chiroptical response from the O-H stretching vibrational modes of water flips with the absolute chirality of the (l-) or (d-) antiparallel β-sheet. Therefore, we can conclude that the (d-) antiparallel β-sheet organizes water solvent into a chiral supermolecular structure with opposite handedness relative to that of the (l-) antiparallel β-sheet. We use molecular dynamics to characterize the chiral water superstructure at atomic resolution. The results show that the macroscopic chirality of antiparallel β-sheets breaks the symmetry of assemblies of surrounding water molecules. We also calculate the chiral SFG response of water surrounding (l-) and (d-) LK 7 β to confirm the presence of chiral water structures. Our results offer a different perspective as well as introduce experimental and computational methodologies for elucidating hydration of biomacromolecules. The findings imply potentially important but largely unexplored roles of water solvent in chiral selectivity of biomolecular interactions and the molecular origins of homochirality in the biological world., Competing Interests: The authors declare no competing interest.

Selective oxidation of alcohols to their corresponding aldehyde or carboxylic acid is one of the most important classes of organic synthesis reactions. In addition, electrochemical alcohol oxidation is considered a viable anode reaction that can be paired with H 2 evolution or other reductive fuel production reactions in electrochemical and photoelectrochemical cells. NiOOH, a material that has been extensively studied as an oxygen evolution catalyst, is among the most promising electrocatalysts for selective alcohol oxidation. Electrochemical alcohol oxidation by NiOOH has been understood since the 1970s to proceed through a hydrogen atom transfer to NiOOH. In this study, we establish that there is a second, more dominant general alcohol oxidation pathway on NiOOH enabled at more positive potentials. Using a three-step electrochemical procedure we developed, we deconvoluted the currents corresponding to these two pathways for various alcohols and aldehydes. The results show that alcohols and aldehydes have a distinct difference in their respective preferences for the two oxidation pathways. Our three-step electrochemical procedure also allowed us to evaluate the Ni valence involved with the different oxidation pathways to elucidate their mechanistic differences. Using these experimental results coupled with a computational investigation, we propose that the new pathway entails hydride transfer from the substrate to Ni 4+ sites in NiOOH. This study offers an essential foundation to understand various oxidative electrochemical dehydrogenation reactions on oxide and hydroxide-based catalytic electrodes.

The recently developed real-time nuclear-electronic orbital (RT-NEO) approach provides an elegant framework for treating electrons and selected nuclei, typically protons, quantum mechanically in nonequilibrium dynamical processes. However, the RT-NEO approach neglects the motion of the other nuclei, preventing a complete description of the coupled nuclear-electronic dynamics and spectroscopy. In this work, the dynamical interactions between the other nuclei and the electron-proton subsystem are described with the mixed quantum-classical Ehrenfest dynamics method. The NEO-Ehrenfest approach propagates the electrons and quantum protons in a time-dependent variational framework, while the remaining nuclei move classically on the corresponding average electron-proton vibronic surface. This approach includes the non-Born-Oppenheimer effects between the electrons and the quantum protons with RT-NEO and between the classical nuclei and the electron-proton subsystem with Ehrenfest dynamics. Spectral features for vibrational modes involving both quantum and classical nuclei are resolved from the time-dependent dipole moments. This work shows that the NEO-Ehrenfest method is a powerful tool to study dynamical processes with coupled electronic and nuclear degrees of freedom.

Interfacial proton-coupled electron transfer (PCET) reactions are central to the operation of a wide array of energy conversion technologies, but molecular-level insights into interfacial PCET are limited. At carbon surfaces, designer sites for interfacial PCET can be incorporated by conjugating organic acid functional groups to graphite edges though aromatic phenazine linkages. At these graphite-conjugated catalysts (GCCs) bearing organic acid moieties, PCET is driven by complex interfacial electrostatic and field gradients that are difficult to probe experimentally. Herein, the spatially inhomogeneous interfacial electrostatic potentials and electric fields of GCC organic acids are computed as functions of applied potential. The calculated proton-coupled redox potentials for the PCET reactions at the GCC phenazine bridges and organic acid sites are in agreement with cyclic voltammetry measurements for a series of GCC acids. The trends in these redox potentials are explained in terms of the acidity of the molecular analogues and continuous conjugation between the acid and the graphite surface. The calculations illustrate that this conjugation is interrupted in a GCC acetic acid system, providing an explanation for the absence of a cyclic voltammetry peak corresponding to PCET at this acid site. This combined theoretical and experimental study demonstrates the critical role of continuous conjugation and strong electronic coupling between the GCC acid site and the graphite to enable interfacial field-driven PCET at the acid site. Understanding the connection between the atomic structure of the surface and the interfacial electrostatic potentials and fields that govern PCET thermochemistry may guide heterogeneous catalyst design.

Hydrogen tunneling is essential for a wide range of chemical and biological processes. The description of hydrogen tunneling with multicomponent quantum chemistry approaches, where the transferring hydrogen nucleus is treated on the same level as the electrons, is challenging due to the importance of both static and dynamical electron-proton correlation. Herein the nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method is presented as a strategy to include both types of correlation. In this approach, two localized nuclear-electronic wave functions obtained with the NEO-DFT method are combined with a nonorthogonal configurational interaction approach to produce bilobal, delocalized ground and excited vibronic states. By including a correction function, the NEO-MSDFT approach can produce quantitatively accurate hydrogen tunneling splittings for fixed geometries of systems such as malonaldehyde and acetoacetaldehyde. This approach is computationally efficient and can be combined with methods such as vibronic coupling theory to describe tunneling dynamics and to compute vibronic couplings in many types of systems.

Blue light using flavin (BLUF) photoreceptor proteins are critical for many light-activated biological processes and are promising candidates for optogenetics because of their modular nature and long-range signaling capabilities. Although the photocycle of the Slr1694 BLUF domain has been characterized experimentally, the identity of the light-adapted state following photoexcitation of the bound flavin remains elusive. Herein hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations of this photocycle provide a nonequilibrium dynamical picture of a possible mechanism for the formation of the light-adapted state. Photoexcitation of the flavin induces a forward proton-coupled electron transfer (PCET) process that leads to the formation of an imidic acid tautomer of Gln50. The calculations herein show that the subsequent rotation of Gln50 allows a reverse PCET process that retains this tautomeric form. In the resulting purported light-adapted state, the glutamine tautomer forms a hydrogen bond with the flavin carbonyl group. Additional ensemble-averaged QM/MM calculations of the dark-adapted and purported light-adapted states demonstrate that the light-adapted state with the imidic acid glutamine tautomer reproduces the experimentally observed spectroscopic signatures. Specifically, the calculations reproduce the red shifts in the flavin electronic absorption and carbonyl stretch infrared spectra in the light-adapted state. Further hydrogen-bonding analyses suggest the formation of hydrogen-bonding interactions between the flavin and Arg65 in the light-adapted state, providing a plausible explanation for the experimental observation of faster photoinduced PCET in this state. These characteristics of the light-adapted state may also be essential for the long-range signaling capabilities of this photoreceptor protein., Competing Interests: The authors declare no competing interest.

The coupling between electrons and protons and the long-range transport of protons play important roles throughout biology. Biomimetic systems derived from benzimidazole-phenol (BIP) constructs have been designed to undergo proton-coupled electron transfer (PCET) upon electrochemical or photochemical oxidation. Moreover, these systems can transport protons along hydrogen-bonded networks or proton wires through multiproton PCET. Herein, the nonequilibrium dynamics of both single and double proton transfer in BIP molecules initiated by oxidation are investigated with first-principles molecular dynamics simulations. Although these processes are concerted in that no thermodynamically stable intermediate is observed, the simulations predict that they are predominantly asynchronous on the ultrafast time scale. For both systems, the first proton transfer typically occurs ∼100 fs after electron transfer. For the double proton transfer system, typically the second proton transfer occurs hundreds of femtoseconds after the initial proton transfer. A machine learning algorithm was used to identify the key molecular vibrational modes essential for proton transfer: a slow, in-plane bending mode that dominates the overall inner-sphere reorganization, the proton donor-acceptor motion that leads to vibrational coherence, and the faster donor-hydrogen stretching mode. The asynchronous double proton transfer mechanism can be understood in terms of a significant mode corresponding to the two anticorrelated proton donor-acceptor motions, typically decreasing only one donor-acceptor distance at a time. Although these PCET processes appear concerted on the time scale of typical electrochemical experiments, attaching these BIP constructs to photosensitizers may enable the detection of the asynchronicity of the electron and multiple proton transfers with ultrafast two-dimensional spectroscopy. Understanding the fundamental PCET mechanisms at this level will guide the design of PCET systems for catalysis and energy conversion processes., Competing Interests: The authors declare no competing financial interest., (Copyright © 2020 American Chemical Society.)

Multi-electron, multi-proton transfer is important in a wide spectrum of processes spanning biological, chemical and physical systems. These reactions have attracted significant interest due to both fundamental curiosity and potential applications in energy technology. In this Perspective Review, we shed light on modern aspects of electrode processes in the 21st century, in particular on the recent advances and challenges in multistep electron/proton transfers at solid-liquid interfaces. Ongoing developments of analytical techniques and operando spectrometry at electrode/electrolyte interfaces and reliable computational approaches to simulate complicated interfacial electrochemical reactions enable us to obtain microscopic insights about these complex processes, such as the role of quantum effects in electrochemical reactions. Our motivation in this Perspective Review is to provide a comprehensive survey and discussion of state-of-the-art developments in experiments, materials, and theories for modern electrode process science, as well as to present an outlook for the future directions in this field.

Photoinduced proton-coupled electron transfer (PCET) in anthracene-phenol-pyridine triads exhibits inverted region behavior, where the more thermodynamically favorable process is slower. The long-lived transient charge-separated state (CSS) associated with electron transfer from phenol to anthracene and inverted region behavior were only observed experimentally for certain triads. Herein, excited state molecular dynamics simulations were performed on four different triads to simulate the nonequilibrium dynamics following photoexcitation to the locally excited state (LES) of anthracene. These simulations identified two distinct PCET pathways: the triads exhibiting inverted region behavior transitioned from the LES to the CSS, whereas the other triads transitioned to a local electron-proton transfer (LEPT) state within phenol and pyridine. The simulations suggest that PCET to the LEPT state is slower than PCET to the CSS and provides an alternative relaxation pathway. The mechanistic pathways, as well as the time scales of the electron and proton transfers, can be controlled by tuning the substituents.

Ribonucleotide reductases (RNRs) catalyze the conversion of all four ribonucleotides to deoxyribonucleotides and are essential for DNA synthesis in all organisms. The active form of E. coli Ia RNR is composed of two homodimers that form the active α 2 β 2 complex. Catalysis is initiated by long-range radical translocation over a ∼32 Å proton-coupled electron transfer (PCET) pathway involving Y356β and Y731α at the interface. Resolving the PCET pathway at the α/β interface has been a long-standing challenge due to the lack of structural data. Herein, molecular dynamics simulations based on a recently solved cryogenic-electron microscopy structure of an active α 2 β 2 complex are performed to examine the structure and fluctuations of interfacial water, as well as the hydrogen-bonding interactions and conformational motions of interfacial residues along the PCET pathway. Our free energy simulations reveal that Y731 is able to sample both a flipped-out conformation, where it points toward the interface to facilitate interfacial PCET with Y356, and a stacked conformation with Y730 to enable collinear PCET with this residue. Y356 and Y731 exhibit hydrogen-bonding interactions with interfacial water molecules and, in some conformations, share a bridging water molecule, suggesting that the primary proton acceptor for PCET from Y356 and from Y731 is interfacial water. The conformational flexibility of Y731 and the hydrogen-bonding interactions of both Y731 and Y356 with interfacial water and hydrogen-bonded water chains appear critical for effective radical translocation along the PCET pathway. These simulations are consistent with biochemical and spectroscopic data and provide previously unattainable atomic-level insights into the fundamental mechanism of RNR.

Long-range electron transfer is coupled to proton transfer in a wide range of chemically and biologically important processes. Recently the proton-coupled electron transfer (PCET) rate constants for a series of biomimetic oligoproline peptides linking Ru(bpy) 3 2+ to tyrosine were shown to exhibit a substantially shallower dependence on the number of proline spacers compared to the analogous electron transfer (ET) systems. The experiments implicated a concerted PCET mechanism involving intramolecular electron transfer from tyrosine to Ru(bpy) 3 3+ and proton transfer from tyrosine to a hydrogen phosphate dianion. Herein these PCET systems, as well as the analogous ET systems, are studied with microsecond molecular dynamics, and the ET and PCET rate constants are calculated with the corresponding nonadiabatic theories. The molecular dynamics simulations illustrate that smaller ET donor-acceptor distances are sampled by the PCET systems than by the analogous ET systems. The shallower dependence of the PCET rate constant on the ET donor-acceptor distance is explained in terms of an additional positive, distance-dependent electrostatic term in the PCET driving force, which attenuates the rate constant at smaller distances. This electrostatic term depends on the change in the electrostatic interaction between the charges on each end of the bridge and can be modified by altering these charges. On the basis of these insights, this theory predicted a less shallow distance dependence of the PCET rate constant when imidazole rather than hydrogen phosphate serves as the proton acceptor, even though their p K a values are similar. This theoretical prediction was subsequently validated experimentally, illustrating that long-range electron transfer processes can be tuned by modifying the nature of the proton acceptor in concerted PCET processes. This level of control has broad implications for the design of more effective charge-transfer systems.

The accurate description of excited vibronic states is important for modeling a wide range of photoinduced processes. The nuclear-electronic orbital (NEO) approach, which treats specified protons on the same level as the electrons, can describe excited electronic-protonic states. Herein the multicomponent equation-of-motion coupled cluster with singles and doubles (NEO-EOM-CCSD) method and its time-domain counterpart, TD-NEO-EOM-CCSD, are developed and implemented. The application of these methods to the HCN molecule highlights their capabilities. These methods predict qualitatively reasonable energies and intensities for a combination band corresponding to simultaneous excitation of two vibrational modes, as well as an overtone. These methods also describe states with double excitation character, such as excited electronic-protonic states corresponding to the simultaneous excitation of an electron and a proton. The ability of the NEO-EOM-CCSD method and its time-dependent counterpart to describe combination bands, overtones, and double excitations will enable a wide range of photochemical applications.

Proton-coupled electron transfer (PCET) from tyrosine produces a neutral tyrosyl radical (Y • ) that is vital to many catalytic redox reactions. To better understand how the protein environment influences the PCET properties of tyrosine, we have studied the radical formation behavior of Y 32 in the α 3 Y model protein. The previously solved α 3 Y solution NMR structure shows that Y 32 is sequestered ∼7.7 ± 0.3 Å below the protein surface without any primary proton acceptors nearby. Here we present transient absorption kinetic data and molecular dynamics (MD) simulations to resolve the PCET mechanism associated with Y 32 oxidation. Y 32 • was generated in a bimolecular reaction with [Ru(bpy) 3 ] 3+ formed by flash photolysis. At pH > 8, the rate constant of Y 32 • formation ( k PCET ) increases by one order of magnitude per pH unit, corresponding to a proton-first mechanism via tyrosinate (PTET). At lower pH < 7.5, the pH dependence is weak and shows a previously measured KIE ≈ 2.5, which best fits a concerted mechanism. k PCET is independent of phosphate buffer concentration at pH 6.5. This provides clear evidence that phosphate buffer is not the primary proton acceptor. MD simulations show that one to two water molecules can enter the hydrophobic cavity of α 3 Y and hydrogen bond to Y 32 , as well as the possibility of hydrogen-bonding interactions between Y 32 and E 13 , through structural fluctuations that reorient surrounding side chains. Our results illustrate how protein conformational motions can influence the redox reactivity of a tyrosine residue and how PCET mechanisms can be tuned by changing the pH even when the PCET occurs within the interior of a protein.

The nuclear-electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born-Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.

DNA bases can adopt energetically unfavorable tautomeric forms that enable the formation of Watson-Crick-like (WC-like) mispairs, which have been proposed to give rise to spontaneous mutations in DNA and misincorporation errors in DNA replication and translation. Previous NMR and computational studies have indicated that the population of WC-like guanine-thymine (G-T) mispairs depends on the environment, such as the local nucleic acid sequence and solvation. To investigate these environmental effects, herein G-T mispair tautomerization processes are studied computationally in aqueous solution, in A-form and B-form DNA duplexes, and within the active site of a DNA polymerase λ variant. The wobble G-T (wG-T), WC-like G-T*, and WC-like G*-T forms are considered, where * indicates the enol tautomer of the base. The minimum free energy paths for the tautomerization from the wG-T to the WC-like G-T* and from the WC-like G-T* to the WC-like G*-T are computed with mixed quantum mechanical/molecular mechanical (QM/MM) free energy simulations. The reaction free energies and free energy barriers are found to be significantly influenced by the environment. The wG-T→G-T* tautomerization is predicted to be endoergic in aqueous solution and the DNA duplexes but slightly exoergic in the polymerase, with Arg517 and Asn513 providing electrostatic stabilization of G-T*. The G-T*→G*-T tautomerization is also predicted to be slightly more thermodynamically favorable in the polymerase relative to these DNA duplexes. These simulations are consistent with an experimentally driven kinetic misincorporation model suggesting that G-T mispair tautomerization occurs in the ajar polymerase conformation or concertedly with the transition from the ajar to the closed polymerase conformation. Furthermore, the order of the associated two proton transfer reactions is predicted to be different in the polymerase than in aqueous solution and the DNA duplexes. These studies highlight the impact of the environment on the thermodynamics, kinetics, and fundamental mechanisms of G-T mispair tautomerization, which plays a role in a wide range of biochemically important processes.

We investigate rates of proton-coupled electron transfer (PCET) in potential sweep experiments for a generalized Anderson-Holstein model with the inclusion of a quantized proton coordinate. To model this system, we utilize a quantum classical Liouville equation embedded inside of a classical master equation, which can be solved approximately with a recently developed algorithm combining diffusional effects and surface hopping between electronic states. We find that the addition of nuclear quantum effects through the proton coordinate can yield quantitatively (but not qualitatively) different IV curves under a potential sweep compared to electron transfer (ET). Additionally, we find that kinetic isotope effects give rise to a shift in the peak potential, but not the peak current, which would allow for quantification of whether an electrochemical ET event is proton-coupled or not. These findings suggest that it will be very difficult to completely understand coupled nuclear-electronic effects in electrochemical voltammetry experiments using only IV curves, and new experimental techniques will be needed to draw inferences about the nature of electrochemical PCET.

The quantum mechanical treatment of both electrons and nuclei is crucial in nonadiabatic dynamical processes such as proton-coupled electron transfer. The nuclear-electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases show the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving field, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.

In multicomponent quantum chemistry, more than one type of particle is treated quantum mechanically with either density functional theory or wave function based methods. In particular, the nuclear-electronic orbital (NEO) approach treats specified nuclei, typically hydrogen nuclei, on the same level as the electrons. This approach enables the incorporation of nuclear quantum effects, such as nuclear delocalization, anharmonicity, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects directly into quantum chemistry calculations. Such effects impact optimized geometries, molecular vibrational frequencies, reaction paths, isotope effects, and dynamical simulations. Multicomponent density functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) achieve an optimal balance between computational efficiency and accuracy for computing ground and excited state properties, respectively. Multicomponent wave function based methods, such as the coupled cluster singles and doubles (NEO-CCSD) method for ground states and the equation-of-motion counterpart (NEO-EOM-CCSD) for excited states, attain similar accuracy without requiring any parametrization and can be systematically improved but are more computationally expensive. Variants of the orbital-optimized perturbation theory (NEO-OOMP2) method achieve nearly the accuracy of NEO-CCSD for ground states with significantly lower computational cost. Additional approaches for computing excited electronic, vibrational, and vibronic states include the delta self-consistent field (NEO-ΔSCF), complete active space SCF (NEO-CASSCF), and nonorthogonal configuration interaction methods. Multireference methods are particularly important for describing hydrogen tunneling processes. Other types of multicomponent systems, such as those containing electrons and positrons, have also been studied within the NEO framework. The NEO approach allows the incorporation of nuclear quantum effects and non-Born-Oppenheimer effects for specified nuclei into quantum chemistry calculations in an accessible and computationally efficient manner.

Designing molecular platforms for controlling proton and electron movement in artificial photosynthetic systems is crucial to efficient catalysis and solar energy conversion. The transfer of both protons and electrons during a reaction is known as proton-coupled electron transfer (PCET) and is used by nature in myriad ways to provide low overpotential pathways for redox reactions and redox leveling, as well as to generate bioenergetic proton currents. Herein, we describe theoretical and electrochemical studies of a series of bioinspired benzimidazole-phenol (BIP) derivatives and a series of dibenzimidazole-phenol (BI 2 P) analogs with each series bearing the same set of terminal proton-accepting (TPA) groups. The set of TPAs spans more than 6 p K units. These compounds have been designed to explore the role of the bridging benzimidazole(s) in a one-electron oxidation process coupled to intramolecular proton translocation across either two (the BIP series) or three (the BI a units. These compounds have been designed to explore the role of the bridging benzimidazole(s) in a one-electron oxidation process coupled to intramolecular proton translocation across either two (the BIP series) or three (the BI 2 P series) acid/base sites. These molecular constructs feature an electrochemically active phenol connected to the TPA group through a benzimidazole-based bridge, which together with the phenol and TPA group form a covalent framework supporting a Grotthuss-type hydrogen-bonded network. Infrared spectroelectrochemistry demonstrates that upon oxidation of the phenol, protons translocate across this well-defined hydrogen-bonded network to a TPA group. The experimental data show the benzimidazole bridges are non-innocent participants in the PCET process in that the addition of each benzimidazole unit lowers the redox potential of the phenoxyl radical/phenol couple by 60 mV, regardless of the nature of the TPA group. Using a series of hypothetical thermodynamic steps, density functional theory calculations correctly predicted the dependence of the redox potential of the phenoxyl radical/phenol couple on the nature of the final protonated species and provided insight into the thermodynamic role of dibenzimidazole units in the PCET process. This information is crucial for developing molecular "dry proton wires" with these moieties, which can transfer protons via a Grotthuss-type mechanism over long distances without the intervention of water molecules., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The projected decline of available phosphorus necessitates alternative methods to derive usable phosphate for fertilizer and other applications. Phosphite dehydrogenase oxidizes phosphite to phosphate with the cofactor NAD + serving as the hydride acceptor. In addition to producing phosphate, this enzyme plays an important role in NADH cofactor regeneration processes. Mixed quantum mechanical/molecular mechanical free energy simulations were performed to elucidate the mechanism of this enzyme and to identify the protonation states of the substrate and product. Specifically, the finite temperature string method with umbrella sampling was used to generate the free energy surfaces and determine the minimum free energy paths for six different initial conditions that varied in the protonation state of the substrate and the position of the nucleophilic water molecule. In contrast to previous studies, the mechanism predicted by all six independent strings is a concerted but asynchronous dissociative mechanism in which hydride transfer from the phosphite substrate to NAD + occurs prior to attack by the nucleophilic water molecule. His292 is identified as the most likely general base that deprotonates the attacking water molecule. However, Arg237 could also serve as this base if it were deprotonated and His292 were protonated prior to the main chemical transformation, although this scenario is less probable. The simulations indicate that the phosphite substrate is monoanionic in its active form and that the most likely product is dihydrogen phosphate. These mechanistic insights may be helpful for designing mutant enzymes or artificial constructs that convert phosphite to phosphate and NAD + to NADH more effectively.

Electric fields control chemical reactivity in a wide range of systems, including enzymes and electrochemical interfaces. Characterizing the electric fields at electrode-solution interfaces is critical for understanding heterogeneous catalysis and associated energy conversion processes. To address this challenge, recent experiments have probed the response of the nitrile stretching frequency of 4-mercaptobenzonitrile (4-MBN) attached to a gold electrode to changes in the solvent and applied electrode potential. Herein, this system is modeled with periodic density functional theory using a multilayer dielectric continuum treatment of the solvent and at constant applied potentials. The impact of the solvent dielectric constant and the applied electrode potential on the nitrile stretching frequency computed with a grid-based method is in qualitative agreement with the experimental data. In addition, the interfacial electrostatic potentials and electric fields as a function of applied potential were calculated directly with density functional theory. Substantial spatial inhomogeneity of the interfacial electric fields was observed, including oscillations in the region of the molecular probe attached to the electrode. These simulations highlight the microscopic inhomogeneity of the electric fields and the role of molecular polarizability at electrode-solution interfaces, thereby demonstrating the limitations of mean-field models and providing insights relevant to the interpretation of vibrational Stark effect experiments., Competing Interests: The authors declare no competing financial interest., (Copyright © 2020 American Chemical Society.)

Multicomponent quantum chemistry methods such as the nuclear-electronic orbital (NEO) method allow the consistent quantum mechanical treatment of electrons and nuclei. The development of computationally practical, accurate, and robust multicomponent wave function methods is challenging because of the importance of orbital relaxation effects. Herein the variational orbital-optimized coupled cluster with doubles (NEO-OOCCD) method and the orbital-optimized second-order Møller-Plesset perturbation theory (NEO-OOMP2) method with scaled-opposite-spin (SOS) versions are developed and applied to molecular systems in which a proton and all electrons are treated quantum mechanically. The results highlight the importance of orbital relaxation in multicomponent wave function methods. The NEO-SOS'-OOMP2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electronic correlation energy, is found to achieve nearly the same level of accuracy as the NEO-OOCCD method for proton densities, proton affinities, and optimized geometries. An advantage of the NEO-SOS'-OOMP2 method is that it can be implemented with N 4 scaling, where N is a measure of the system size. This method will enable future multicomponent wave function calculations of structures, energies, reaction paths, and dynamics for substantially larger chemical systems.

Inverted region behavior for concerted proton-coupled electron transfer (PCET) was recently demonstrated for biomimetic anthracene-phenol-pyridine molecular triads. Photoexcitation of the anthracene to a locally excited state (LES) is followed by concerted electron transfer from the phenol to the anthracene and proton transfer from the phenol to the pyridine, forming a relatively long-lived charge separated state (CSS). The long-lived CSS and the inverted region behavior associated with the decay from the CSS to the ground state through charge recombination were experimentally observed only for triads with certain substituents on the anthracene and the pyridine. To explain this distinction, we computed the proton potential energy curves in four substituted triads using the complete active space self-consistent-field method and multireference perturbation theory, including solvent effects with a dielectric continuum model. The calculations revealed a local electron-proton transfer (LEPT) state, in which both the electron and proton transfer from the phenol to the pyridine. When the LEPT state is lower in energy than the CSS, it may provide an alternative pathway for fast decay from the LES to the ground state and thereby preclude detection of the CSS and the inverted region behavior. These calculations predict that substituents stabilizing negative charge on the pyridine and destabilizing negative charge on the anthracene will favor the LEPT pathway, while substituents with the reverse effects will favor the CSS pathway, which could exhibit inverted region behavior. These insights about the stabilization of energy-storing charge-separated states have implications for designing and controlling PCET reactions in artificial photosynthetic systems and other energy conversion processes.

Blue-light using flavin (BLUF) photoreceptor proteins are essential to many biological processes and are attractive candidates for use in optogenetics. To understand the photocycle mechanism in the Slr1694 BLUF photoreceptor, adiabatic excited-state quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations are performed using Tamm-Dancoff time-dependent density functional theory. These simulations elucidate the roles of protein dynamics, conformational changes, and electrostatics. After photoexcitation to a locally excited state of the flavin, protein reorganization drives electron transfer from Tyr8 to the flavin. The movement of certain charged residues and a decrease in the distance between Tyr8 and the flavin are found to play important roles in facilitating this charge transfer. The formation of this charge-transfer state drives sequential double proton transfer: Tyr8 transfers a proton to the intervening Gln50, which then relays a second proton to the flavin. Although the second proton transfer involves the formation of a singlet diradical ground state, which requires multireference methods, the photocycle dynamics can be continued in an approximate manner by switching to a spin-flip approach. The resulting trajectories trace out the mechanism of photoinduced proton-coupled electron transfer (PCET) in the Slr1694 BLUF photocycle. Propagating the trajectories beyond the PCET reaction identifies possible pathways involving different tautomers of Gln50 that will eventually lead to the light-adapted state. These simulations provide insights into the nonequilibrium dynamics of photoinduced PCET in the Slr1694 BLUF photocycle that have not been attainable with previous simulations.

Quantum mechanical phenomena such as coherence, spin dynamics, and tunneling have been observed in biological, electrochemical, polymeric, and many other condensed phase processes. This paper summarizes the diverse contributions to the Faraday Discussion on quantum effects in complex systems. Various processes exhibiting quantum mechanical behavior were examined using advanced spectroscopic and theoretical methods. An emerging theme was the critical importance of feedback between experiment and theory, particularly in the form of experimental testing of theoretical predictions.