Long-range electrostatic effects from intramolecular Lewis acid binding influence the redox properties of cobalt-porphyrin complexes.

A CoII-porphyrin complex (1) with an appended aza-crown ether for Lewis acid (LA) binding was synthesized and characterized. NMR spectroscopy and electrochemistry show that cationic group I and II LAs (i.e., Li+, Na+, K+, Ca2+, Sr2+, and Ba2+) bind to the aza-crown ether group of 1. The binding constant for Li+ is comparable to that observed for a free aza-crown ether. LA binding causes an anodic shift in the CoII/CoI couple of between 10 and 40 mV and also impacts the CoIII/CoII couple. The magnitude of the anodic shift of the CoII/CoI couple varies linearly with the strength of the LA as determined by the pKa of the corresponding metal-aqua complex, with dications giving larger shifts than monocations. The extent of the anodic shift of the CoII/CoI couple also increases as the ionic strength of the solution decreases. This is consistent with electric field effects being responsible for the changes in the redox properties of 1 upon LA binding and provides a novel method to tune the reduction potential. Density functional theory calculations indicate that the bound LA is 5.6 to 6.8 Å away from the CoII ion, demonstrating that long-range electrostatic effects, which do not involve changes to the primary coordination sphere, are responsible for the variations in redox chemistry. Compound 1 was investigated as a CO2 reduction electrocatalyst and shows high activity but rapid decomposition.

Nuclear-Electronic Orbital Time-Dependent Configuration Interaction Method.

Combining real-time electronic structure with the nuclear-electronic orbital (NEO) method has enabled the simulation of complex nonadiabatic chemical processes. However, accurate descriptions of hydrogen tunneling and double excitations require multiconfigurational treatments. Herein, we develop and implement the real-time NEO time-dependent configuration interaction (NEO-TDCI) approach. Comparison to NEO-full CI calculations of absorption spectra for a molecular system shows that the NEO-TDCI approach can accurately capture the tunneling splitting associated with the electronic ground state as well as vibronic progressions corresponding to double electron-proton excitations associated with excited electronic states. Both of these features are absent from spectra obtained with single reference real-time NEO methods. Our simulations of hydrogen tunneling dynamics illustrate the oscillation of the proton density from one side to the other via a delocalized, bilobal proton wave function. These results indicate that the NEO-TDCI approach is highly suitable for studying hydrogen tunneling and other inherently multiconfigurational systems.

Hydrogen on Colloidal Gold Nanoparticles.

Colloidal gold nanoparticles (AuNPs) have myriad scientific and technological applications, but their fundamental redox chemistry is underexplored. Reported here are titration studies of oxidation and reduction reactions of aqueous AuNP colloids, which show that the AuNPs bind substantial hydrogen (electrons + protons) under mild conditions. The 5 nm AuNPs are reduced to a similar extent with reductants from borohydrides to H2 and are reoxidized back essentially to their original state by oxidants, including O2. The reactions were monitored via surface plasmon resonance (SPR) optical absorption, which was shown to be much more sensitive to surface H than to changes in solution conditions. Reductions with H2 occurred without pH changes, demonstrating that hydrogenation forms surface H rather than releasing H+. Computational studies suggested that an SPR blueshift was expected for H atom addition, while just electron addition likely would have caused a redshift. Titrations consistently showed a maximum redox change of the 5 nm NPs, independent of the reagent, corresponding to 9% of the total gold or ∼30% hydrogen surface coverage (∼370 H per AuNP). Larger AuNPs showed smaller maximum fractional surface coverages. We conclude that H binds to the edge, corner, and defect sites of the AuNPs, which explains the stoichiometric limitation and the size effect. The finding of substantial and stable hydrogen on the AuNP surface under mild reducing conditions has potential implications for various applications of AuNPs in reducing environments, from catalysis to biomedicine. This finding contrasts with the behavior of bulk gold and with the typical electron-focused perspective in this field.

A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters.

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

Switching the proton-coupled electron transfer mechanism for non-canonical tyrosine residues in a de novo protein.

The proton-coupled electron transfer (PCET) reactions of tyrosine (Y) are instrumental to many redox reactions in nature. This study investigates how the local environment and the thermodynamic properties of Y influence its PCET characteristics. Herein, 2- and 4-mercaptophenol (MP) are placed in the well-folded α3C protein (forming 2MP-α3C and 4MP-α3C) and oxidized by external light-generated [Ru(L)3]3+ complexes. The resulting neutral radicals are long-lived (>100 s) with distinct optical and EPR spectra. Calculated spin-density distributions are similar to canonical Y˙ and display very little spin on the S-S bridge that ligates the MPs to C32 inside the protein. With 2MP-α3C and 4MP-α3C we probe how proton transfer (PT) affects the PCET rate constants and mechanisms by varying the degree of solvent exposure or the potential to form an internal hydrogen bond. Solution NMR ensemble structures confirmed our intended design by displaying a major difference in the phenol OH solvent accessible surface area (≤∼2% for 2MP and 30-40% for 4MP). Additionally, 2MP-C32 is within hydrogen bonding distance to a nearby glutamate (average O-O distance is 3.2 ± 0.5 Å), which is suggested also by quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations. Neither increased exposure of the phenol OH to solvent (buffered water), nor the internal hydrogen bond, was found to significantly affect the PCET rates. However, the lower phenol pKa values associated with the MP-α3C proteins compared to α3Y provided a sufficient change in PT driving force to alter the PCET mechanism. The PCET mechanism for 2MP-α3C and 4MP-α3C with moderately strong oxidants was predominantly step-wise PTET for pH values, but changed to concerted PCET at neutral pH values and below when a stronger oxidant was used, as found previously for α3Y. This shows how the balance of ET and PT driving forces is critical for controlling PCET mechanisms. The presented results improve our general understanding of amino-acid based PCET in enzymes.

Theoretical basis for interpreting heterodyne chirality-selective sum frequency generation spectra of water.

Chirality-selective vibrational sum frequency generation (chiral SFG) spectroscopy has emerged as a powerful technique for the study of biomolecular hydration water due to its sensitivity to the induced chirality of the first hydration shell. Thus far, water O-H vibrational bands in phase-resolved heterodyne chiral SFG spectra have been fit using one Lorentzian function per vibrational band, and the resulting fit has been used to infer the underlying frequency distribution. Here, we show that this approach may not correctly reveal the structure and dynamics of hydration water. Our analysis illustrates that the chiral SFG responses of symmetric and asymmetric O-H stretch modes of water have opposite phase and equal magnitude and are separated in energy by intramolecular vibrational coupling and a heterogeneous environment. The sum of the symmetric and asymmetric responses implies that an O-H stretch in a heterodyne chiral SFG spectrum should appear as two peaks with opposite phase and equal amplitude. Using pairs of Lorentzian functions to fit water O-H stretch vibrational bands, we improve spectral fitting of previously acquired experimental spectra of model ß-sheet proteins and reduce the number of free parameters. The fitting allows us to estimate the vibrational frequency distribution and thus reveals the molecular interactions of water in hydration shells of biomolecules directly from chiral SFG spectra.

Probing Nonadiabaticity of Proton-Coupled Electron Transfer in Ribonucleotide Reductase.

The enzyme ribonucleotide reductase, which is essential for DNA synthesis, initiates the conversion of ribonucleotides to deoxyribonucleotides via radical transfer over a 32 Å pathway composed of proton-coupled electron transfer (PCET) reactions. Previously, the first three PCET reactions in the α subunit were investigated with hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations. Herein, the fourth PCET reaction in this subunit between C439 and guanosine diphosphate (GDP) is simulated and found to be slightly exoergic with a relatively high free energy barrier. To further elucidate the mechanisms of all four PCET reactions, we analyzed the vibronic and electron-proton nonadiabaticities. This analysis suggests that interfacial PCET between Y356 and Y731 is vibronically and electronically nonadiabatic, whereas PCET between Y731 and Y730 and between C439 and GDP is fully adiabatic and PCET between Y730 and C439 is in the intermediate regime. These insights provide guidance for selecting suitable rate constant expressions for these PCET reactions.

Direct Evidence for a Sequential Electron Transfer-Proton Transfer Mechanism in the PCET Reduction of a Metal Hydroxide Catalyst.

The proton-coupled electron transfer (PCET) mechanism for the reaction Mox-OH + e- + H+ → Mred-OH2 was determined through the kinetic resolution of the independent electron transfer (ET) and proton transfer (PT) steps. The reaction of interest was triggered by visible light excitation of [RuII(tpy)(bpy')H2O]2+, RuII-OH2, where tpy is 2,2':6',2″-terpyridine and bpy' is 4,4'-diaminopropylsilatrane-2,2'-bipyridine, anchored to In2O3:Sn (ITO) thin films in aqueous solutions. Interfacial kinetics for the PCET reduction reaction were quantified by nanosecond transient absorption spectroscopy as a function of solution pH and applied potential. Data acquired at pH = 5-10 revealed a stepwise electron transfer-proton transfer (ET-PT) mechanism, while kinetic measurements made below pKa(RuIII-OH/OH2) = 1.3 were used to study the analogous interfacial reaction, where electron transfer was the only mechanistic step. Analysis of this data with a recently reported multichannel kinetic model was used to construct a PCET zone diagram and supported the assignment of an ET-PT mechanism at pH = 5-10. Ultimately, this study represents a unique example among Mox-OH/Mred-OH2 reactivity where the protonation and oxidation states of the intermediate were kinetically and spectrally resolved to firmly establish the PCET mechanism.

Squeezed Protons and Infrared Plasmonic Resonance Energy Transfer.

Unusual nuclear quantum effects may emerge near noble metal nanostructures such as squeezed vibrational states in molecular junctions and plasmonic resonance energy transfer in the infrared domain. Herein, nuclear quantum effects near heavy metals are studied by nuclear-electronic orbital density functional theory (NEO-DFT) with an effective core potential. For a quantum proton sandwiched between a pair of gold tips modeled by two Au6 clusters, NEO-DFT calculations suggest that the quantum proton density can be squeezed as the tip distance decreases. For an HF molecule placed near a one-dimensional Au nanowire composed of up to 34 Au atoms, real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) shows that the infrared plasmonic motion within the Au nanowire may resonantly transfer electronic energy to the HF proton vibrational stretch mode. Overall, these calculations illustrate the advantages of the NEO approach for probing nuclear quantum effects, such as squeezed proton vibrational states and infrared plasmonic resonance energy transfer.

Modeling the Weak pH Dependence of Proton-Coupled Electron Transfer for Tryptophan Derivatives.

The oxidation of tryptophan (Trp) is an important step in many biological processes and often occurs by sequential or concerted proton-coupled electron transfer (PCET). The apparent rate constants for the photochemical oxidation of two Trp derivatives in water have been shown to be pH-independent at low pH and to exhibit weak pH dependence at higher pH. Herein, these systems are investigated with a general, multi-channel model that includes sequential and concerted mechanisms as well as various proton donors and acceptors. This model can reproduce the kinetic data for both Trp derivatives with physically meaningful parameters and suggests that the weak pH dependence may arise from the competition between OH- and H2O as proton acceptors in concerted PCET. Deprotonation of an ammonium group for one of the systems leads to a more complex pH dependence at higher pH. This work demonstrates the importance of considering multiple competing channels for the analysis of the pH dependence of apparent PCET rate constants.

First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems.

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Nuclear-Electronic Orbital Quantum Mechanical/Molecular Mechanical Real-Time Dynamics.

Simulating the nuclear-electronic quantum dynamics of large-scale molecular systems in the condensed phase is key for studying biologically and chemically important processes such as proton transfer and proton-coupled electron transfer reactions. Herein, the real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) approach is combined with a hybrid quantum mechanical/molecular mechanical (QM/MM) strategy to enable the accurate description of coupled nuclear-electronic quantum dynamics in the presence of heterogeneous environments such as solvent or proteins. The densities of the electrons and quantum protons are propagated in real time, while the other nuclei are propagated classically on the instantaneous electron-proton vibronic surface. This approach is applied to phenol bound to lysozyme, intramolecular proton transfer in malonaldehyde, and nonequilibrium excited-state intramolecular proton transfer in o-hydroxybenzaldehyde. These examples illustrate that the RT-NEO-TDDFT framework, coupled with an atomistic representation of the environment, allows the simulation of condensed-phase systems that exhibit significant nuclear quantum effects.

Assessing Implicit and Explicit Polarizable Solvation Models for Nuclear-Electronic Orbital Systems: Quantum Proton Polarization and Solvation Energetics.

Accurate simulations of many chemical processes require the inclusion of both nuclear quantum effects and a solvent environment. The nuclear-electronic orbital (NEO) approach, which treats electrons and select nuclei quantum mechanically on the same level, combined with a polarizable continuum model (PCM) for the solvent environment, addresses this challenge in a computationally practical manner. In this work, the NEO-PCM approach is extended beyond the IEF-PCM (integral equation formalism PCM) and C-PCM (conductor PCM) approaches to the SS(V)PE (surface and simulation of volume polarization for electrostatics) and ddCOSMO (domain decomposed conductor-like screening model) approaches. IEF-PCM, SS(V)PE, C-PCM, and ddCOSMO all exhibit similar solvation energies as well as comparable nuclear polarization within the NEO framework. The calculations show that the nuclear density does not leak out of the molecular cavity because it is much more localized than the electronic density. Finally, the polarization of quantized protons is analyzed in both continuum solvent and explicit solvent environments described by the polarizable MB-pol model, illustrating the impact of specific hydrogen-bonding interactions captured only by explicit solvation. These calculations highlight the relationship among solvation formalism, nuclear polarization, and energetics.

Electro-inductive Effect Dominates Vibrational Frequency Shifts of Conjugated Probes on Gold Electrodes.

Interfacial electric fields play a critical role in electrocatalysis and are often characterized by using vibrational probes attached to an electrode surface. Understanding the physical principles dictating the impact of the applied electrode potential on the vibrational probe frequency is important. Herein, a comparative study is performed for two molecular probes attached to a gold electrode. Both probes contain a nitrile (CN) group, but 4-mercaptobenzonitrile (4-MBN) exhibits continuous conjugation from the electrode through the nitrile group, whereas this conjugation is interrupted for 2-(4-mercaptophenyl)acetonitrile (4-MPCN). Periodic density functional theory calculations predict that the CN vibrational frequency shift of the 4-MBN system is dominated by induction, which is a through-bond polarization effect, leading to a strong potential dependence that does not depend significantly on the orientation of the CN bond relative to the surface. In contrast, the CN vibrational frequency shift of the 4-MPCN system is influenced less by induction and more by through-space electric field effects, leading to a weaker potential dependence and a greater orientation dependence. These theoretical predictions were confirmed by surface-enhanced Raman spectroscopy experiments. Balancing through-bond and through-space electrostatic effects may assist in the fundamental understanding and design of electrocatalytic systems.

Multicomponent Cholesky Decomposition: Application to Nuclear-Electronic Orbital Theory.

The Cholesky decomposition technique is commonly used to reduce the memory requirement for storing two-particle repulsion integrals in quantum chemistry calculations that use atomic orbital bases. However, when quantum methods use multicomponent bases, such as nuclear-electronic orbitals, additional challenges are introduced due to asymmetric two-particle integrals. This work proposes several multicomponent Cholesky decomposition methods for calculations using nuclear-electronic orbital density functional theory. To analyze the errors in different Cholesky decomposition components, benchmark calculations using water clusters are carried out. The largest benchmark calculation is a water cluster (H2O)27 where all 54 protons are treated quantum mechanically. This study provides energetic and complexity analyses to demonstrate the accuracy and performance of the proposed multicomponent Cholesky decomposition method.

Exploring Proton-Coupled Electron Transfer at Multiple Scales.

The coupling of electron and proton transfer is critical for chemical and biological processes spanning a wide range of length and time scales and often occurring in complex environments. Thus, diverse modeling strategies, including analytical theories, quantum chemistry, molecular dynamics, and kinetic modeling, are essential for a comprehensive understanding of such proton-coupled electron transfer reactions. Each of these computational methods provides one piece of the puzzle, and all these pieces must be viewed together to produce the full picture.

General Kinetic Model for pH Dependence of Proton-Coupled Electron Transfer: Application to an Electrochemical Water Oxidation System.

The pH dependence of proton-coupled electron transfer (PCET) reactions, which are critical to many chemical and biological processes, is a powerful probe for elucidating their fundamental mechanisms. Herein, a general, multichannel kinetic model is introduced to describe the pH dependence of both homogeneous and electrochemical PCET reactions. According to this model, a weak pH dependence can arise from the competition among multiple sequential and concerted PCET channels involving different forms of the redox species, such as protonated and deprotonated forms, as well as different proton donors and acceptors. The contribution of each channel is influenced by the relative populations of the reactant species, which often depend strongly on pH, leading to complex pH dependence of PCET apparent rate constants. This model is used to explain the origins of the experimentally observed weak pH dependence of the electrochemical PCET apparent rate constant for a ruthenium-based water oxidation catalyst attached to a tin-doped In2O3 (ITO) surface. The weak pH dependence is found to arise from the intrinsic differences in the rate constants of participating channels and the dependence of their relative contributions on pH. This model predicts that the apparent maximum rate constant will become pH-independent at higher pH, which is confirmed by experimental measurements. Our analysis also suggests that the dominant channels are electron transfer at lower pH and sequential PCET via electron transfer followed by fast proton transfer at higher pH. This work highlights the importance of considering multiple competing channels simultaneously for PCET processes.

Nuclear-Electronic Orbital Quantum Dynamics of Plasmon-Driven H2 Photodissociation.

Leveraging localized surface plasmon resonances of metal nanoparticles to trigger chemical reactions is a promising approach for heterogeneous catalysis. First-principles modeling of such processes is challenging due to the large number of electrons and electronic excited states as well as the significance of nuclear quantum effects when hydrogen is involved. Herein, the nonadiabatic nuclear-electronic quantum dynamics of plasmon-induced H2 photodissociation near an Al13- cluster is simulated with real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT). This approach propagates the nonequilibrium quantum dynamics of both electrons and protons. The plasmonic oscillations are shown to inject hot electrons into the antibonding orbital of H2, thereby inducing H2 dissociation. The quantum mechanical treatment of the hydrogen nuclei leads to faster H2 photodissociation and slightly larger isotope effects. Analysis of the nonequilibrium electronic density suggests that these findings stem from enhanced excited-state electronic coupling between the plasmonic mode and the H2 antibonding orbital due to proton delocalization or zero-point energy effects. Given the low computational overhead for including nuclear quantum effects with the RT-NEO-TDDFT approach, this work paves the way for simulating nonadiabatic nuclear-electronic quantum dynamics in other plasmonic systems.

Characterizing Interfaces by Voronoi Tessellation.

The chemistry of interfaces differs markedly from that of the bulk. Calculation of interfacial properties depends strongly on the definition of the interface, which can lead to ambiguous results that vary between studies. There is a need for a method that can explicitly define the interfaces and boundaries in molecular systems. Voronoi tessellation offers an attractive solution to this problem through its ability to determine neighbors among specified groups of atoms. Here we discuss three cases where Voronoi tessellation combined with modeling of vibrational sum frequency generation (SFG) spectroscopy yields relevant insights: the breakdown of the air-water interface into clear and intuitive molecular layers, the study of the hydration shell in biological systems, and the acceleration of difficult spectral calculations where intermolecular vibrational couplings dominate. The utility of Voronoi tessellation has broad applications that extend beyond any single type of spectroscopy or system.