A Resilient Platform for the Discrete Functionalization of Gold Surfaces Based on N-Heterocyclic Carbene Self-Assembled Monolayers.

We describe the synthesis and characterization of a versatile platform for gold functionalization, based on self-assembled monolayers (SAMs) of distal-pyridine-functionalized N-heterocyclic carbenes (NHC) derived from bis(NHC) Au(I) complexes. The SAMs are characterized using polarization-modulation infrared reflectance-absorption spectroscopy, surface-enhanced Raman spectroscopy, and X-ray photoelectron spectroscopy. The binding mode is examined computationally using density functional theory, including calculations of vibrational spectra and direct comparisons to the experimental spectroscopic signatures of the monolayers. Our joint computational and experimental analyses provide structural information about the SAM binding geometries under ambient conditions. Additionally, we examine the reactivity of the pyridine-functionalized SAMs toward H2SO4 and W(CO)5(THF) and verify the preservation of the introduced functionality at the interface. Our results demonstrate the versatility of N-heterocyclic carbenes as robust platforms for on-surface acid-base and ligand exchange reactions.

Proton-Tunneling Dynamics along Low-Barrier Hydrogen Bonds: A Full-Dimensional Instanton Study of 6-Hydroxy-2-formylfulvene.

Understanding the dynamics of proton transfer along low-barrier hydrogen bonds remains an outstanding challenge of great fundamental and practical interest, reflecting the central role of quantum effects in reactions of chemical and biological importance. Here, we combine ab initio calculations with the semiclassical ring-polymer instanton method to investigate tunneling processes on the ground electronic state of 6-hydroxy-2-formylfulvene (HFF), a prototypical neutral molecule supporting low-barrier hydrogen-bonding. The results emerging from a full-dimensional ab initio instanton analysis reveal that the tunneling path does not pass through the instantaneous transition-state geometry. Instead, the tunneling process involves a multidimensional reaction coordinate with concerted reorganization of the heavy-atom skeletal framework to substantially reduce the donor-acceptor distance and drive the ensuing intramolecular proton-transfer event. The predicted tunneling-induced splittings for HFF isotopologues are in good agreement with experimental findings, leading to percentage deviations of only 20-40%. Our full-dimensional results allow us to characterize vibrational contributions along the tunneling path, highlighting the intrinsically multidimensional nature of the attendant hydron-migration dynamics.

Matsubara dynamics approximation for generalized multi-time correlation functions.

We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.

An exact imaginary-time path-integral phase-space formulation of multi-time correlation functions.

An exact representation of quantum mechanics using the language of phase-space variables provides a natural starting point to introduce and develop semiclassical approximations for the calculation of time correlation functions. Here, we introduce an exact path-integral formalism for calculations of multi-time quantum correlation functions as canonical averages over ring-polymer dynamics in imaginary time. The formulation provides a general formalism that exploits the symmetry of path integrals with respect to permutations in imaginary time, expressing correlations as products of imaginary-time-translation-invariant phase-space functions coupled through Poisson bracket operators. The method naturally recovers the classical limit of multi-time correlation functions and provides an interpretation of quantum dynamics in terms of "interfering trajectories" of the ring-polymer in phase space. The introduced phase-space formulation provides a rigorous framework for the future development of quantum dynamics methods that exploit the invariance of imaginary time path integrals to cyclic permutations.

Collective Proton Transfers in Cyclic Water-Ammonia Tetramers: A Path Integral Machine-Learning Study.

We present results from machine-learning-based path integral molecular dynamics simulations that describe isomerization paths articulated via collective proton transfers along mixed, cyclic tetramers combining water and ammonia at cryogenic conditions. The net result of such isomerizations is a reverse of the chirality of the global hydrogen-bonding architecture along the different cyclic moieties. In monocomponent tetramers, the classical free energy profiles associated with these isomerizations present the usual symmetric double-well characteristics whereas the reactive paths exhibit full concertedness among the different intermolecular transfer processes. Contrastingly, in mixed water/ammonia tetramers, the incorporation of a second component introduces imbalances in the strengths of the different hydrogen bonds leading to a partial loss of concertedness, most notably at the vicinity of the transition state. As such, the highest and lowest degrees of progression are registered along OH···N and O···HN coordinations, respectively. These characteristics lead to polarized transition state scenarios akin to solvent-separated ion-pair configurations. The explicit incorporation of nuclear quantum effects promotes drastic depletions in the activation free energies and modifications in the overall shape of the profiles which include central plateau-like stages, indicating the prevalence of deep tunneling regimes. On the other hand, the quantum treatment of the nuclei partially restores the degree of concertedness among the evolutions of the individual transfers.

Ultrafast Charge Relocation Dynamics in Enol-Keto Tautomerization Monitored with a Local Soft-X-ray Probe.

Proton-coupled electron transfer (PCET) is the underlying mechanism governing important reactions ranging from water splitting in photosynthesis to oxygen reduction in hydrogen fuel cells. The interplay of proton and electronic charge distribution motions can vary from sequential to concerted schemes, with elementary steps occurring on ultrafast time scales. We demonstrate with a simulation study that femtosecond soft-X-ray spectroscopy provides key insights into the PCET mechanism of a photoinduced intramolecular enol* → keto* tautomerization reaction. A full quantum treatment of the electronic and nuclear dynamics of 2-(2'-hydroxyphenyl)benzothiazole upon electronic excitation reveals how spectral signatures of local excitations from core to frontier orbitals display the distinctly different stages of charge relocation for the H atom, donating, and accepting sites. Our findings indicate that ultraviolet/X-ray pump-probe spectroscopy provides a unique way to probe ultrafast electronic structure rearrangements in photoinduced chemical reactions essential to understanding the mechanism of PCET.

Sub-Nanometer Mapping of the Interfacial Electric Field Profile Using a Vibrational Stark Shift Ruler.

The characterization of electrical double layers is important since the interfacial electric field and electrolyte environment directly affect the reaction mechanisms and catalytic rates of electrochemical processes. In this work, we introduce a spectroscopic method based on a Stark shift ruler that enables mapping the electric field strength across the electric double layer of electrode/electrolyte interfaces. We use the tungsten-pentacarbonyl(1,4-phenelenediisocyanide) complex attached to the gold surface as a molecular ruler. The carbonyl (CO) and isocyanide (NC) groups of the self-assembled monolayer (SAM) provide multiple vibrational reporters situated at different distances from the electrode. Measurements of Stark shifts under operando electrochemical conditions and direct comparisons to density functional theory (DFT) simulations reveal distance-dependent electric field strength from the electrode surface. This electric field profile can be described by the Gouy-Chapman-Stern model with Stern layer thickness of ∼4.5 Å, indicating substantial solvent and electrolyte penetration within the SAM. Significant electro-induction effect is observed on the W center that is ∼1.2 nm away from the surface despite rapid decay of the electric field (∼90%) within 1 nm. The applied methodology and reported findings should be particularly valuable for the characterization of a wide range of microenvironments surrounding molecular electrocatalysts at electrode interfaces and the positioning of electrocatalysts at specific distances from the electrode surface for optimal functionality.

Equilibrium and Dynamical Characteristics of Hydrogen Bond Bifurcations in Water-Water and Water-Ammonia Dimers: A Path Integral Molecular Dynamics Study.

We present path integral molecular dynamics results that describe the effects of nuclear quantum fluctuations on equilibrium and dynamical characteristics pertaining to bifurcation pathways in hydrogen bonded dimers combining water and ammonia, at cryogenic temperatures of the order of 20 K. Along these isomerizations, the hydrogen atoms in the molecules acting as hydrogen-bond donors interchange their original dangling/connective characters. Our results reveal that the resulting quantum transition paths comprise three stages: the initial and final ones involve overall rotations during which the two protons retain their classical-like characteristics. Effects from quantum fluctuation are clearly manifested in the changes operated at the intermediate passages over transition states, as the spatial extents of the protons stretch over typical lengths comparable to the distances between connective and dangling basins of attractions. Consequently, the classical over-the-hill path is replaced by a tunneling controlled mechanism which, within the path integral perspective, can be cast in terms of concerted inter-basin migrations of polymer beads from dangling-to-connective and from connective-to-dangling, at practically no energy costs. We also estimated the characteristic timescales describing such interconversions within the approximate ring polymer rate theory. Effects derived from full and partial deuteration are also discussed.

Vibrational Stark shift spectroscopy of catalysts under the influence of electric fields at electrode-solution interfaces.

External control of chemical processes is a subject of widespread interest in chemical research, including control of electrocatalytic processes with significant promise in energy research. The electrochemical double-layer is the nanoscale region next to the electrode/electrolyte interface where chemical reactions typically occur. Understanding the effects of electric fields within the electrochemical double layer requires a combination of synthesis, electrochemistry, spectroscopy, and theory. In particular, vibrational sum frequency generation (VSFG) spectroscopy is a powerful technique to probe the response of molecular catalysts at the electrode interface under bias. Fundamental understanding can be obtained via synthetic tuning of the adsorbed molecular catalysts on the electrode surface and by combining experimental VSFG data with theoretical modelling of the Stark shift response. The resulting insights at the molecular level are particularly valuable for the development of new methodologies to control and characterize catalysts confined to electrode surfaces. This Perspective article is focused on how systematic modifications of molecules anchored to surfaces report information concerning the geometric, energetic, and electronic parameters of catalysts under bias attached to electrode surfaces.

Ring-polymer, centroid, and mean-field approximations to multi-time Matsubara dynamics.

Based on a recently developed generalization of Matsubara dynamics to the multi-time realm, we present a formal derivation of multi-time generalizations of ring-polymer molecular dynamics, thermostatted ring-polymer molecular dynamics (TRPMD), centroid molecular dynamics (CMD), and mean-field Matsubara dynamics. Additionally, we analyze the short-time accuracy of each methodology. We find that for multi-time correlation functions of linear operators, (T)RPMD is accurate up to order t3, while CMD is only correct up to t, indicating a degradation in the accuracy of these methodologies with respect to the single-time counterparts. The present work provides a firm justification for the use of path-integral-based approximations for the calculation of multi-time correlation functions.

Vibronic Dynamics of Photodissociating ICN from Simulations of Ultrafast X-Ray Absorption Spectroscopy.

Ultrafast UV-pump/soft-X-ray-probe spectroscopy is a subject of great interest since it can provide detailed information about dynamical photochemical processes with ultrafast resolution and atomic specificity. Here, we focus on the photodissociation of ICN in the 1 Π1 excited state, with emphasis on the transient response in the soft-X-ray spectral region as described by the ab initio spectral lineshape averaged over the nuclear wavepacket probability density. We find that the carbon K-edge spectral region reveals a rich transient response that provides direct insights into the dynamics of frontier orbitals during the I-CN bond cleavage process. The simulated UV-pump/soft-X-ray-probe spectra exhibit detailed dynamical information, including a time-domain signature for coherent vibration associated with the photogenerated CN fragment.

Two-dimensional Raman spectroscopy of Lennard-Jones liquids via ring-polymer molecular dynamics.

The simulation of multidimensional vibrational spectroscopy of condensed-phase systems including nuclear quantum effects is challenging since full quantum-mechanical calculations are still intractable for large systems comprising many degrees of freedom. Here, we apply the recently developed double Kubo transform (DKT) methodology in combination with ring-polymer molecular dynamics (RPMD) for evaluating multi-time correlation functions [K. A. Jung et al., J. Chem. Phys. 148, 244105 (2018)], providing a practical method for incorporating nuclear quantum effects in nonlinear spectroscopy of condensed-phase systems. We showcase the DKT approach in the simulation of the fifth-order two-dimensional (2D) Raman spectroscopy of Lennard-Jones liquids as a prototypical example, which involves nontrivial nonlinear spectroscopic observables of systems described by anharmonic potentials. Our results show that the DKT can faithfully reproduce the 2D Raman response of liquid xenon at high temperatures, where the system behaves classically. In contrast, liquid neon at low temperatures exhibits moderate but discernible nuclear quantum effects in the 2D Raman response compared to the responses obtained with classical molecular dynamics approaches. Thus, the DKT formalism in combination with RPMD simulations enables simulations of multidimensional optical spectroscopy of condensed-phase systems that partially account for nuclear quantum effects.

Robust Binding of Disulfide-Substituted Rhenium Bipyridyl Complexes for CO2 Reduction on Gold Electrodes.

Heterogenization of homogenous catalysts on electrode surfaces provides a valuable approach for characterization of catalytic processes in operando conditions using surface selective spectroelectrochemistry methods. Ligand design plays a central role in the attachment mode and the resulting functionality of the heterogenized catalyst as determined by the orientation of the catalyst relative to the surface and the nature of specific interactions that modulate the redox properties under the heterogeneous electrode conditions. Here, we introduce new [Re(L)(CO)3Cl] catalysts for CO2 reduction with sulfur-based anchoring groups on a bipyridyl ligand, where L = 3,3'-disulfide-2,2'-bipyridine (SSbpy) and 3,3'-thio-2,2'-bipyridine (Sbpy). Spectroscopic and electrochemical analysis complemented by computational modeling at the density functional theory level identify the complex [Re(SSbpy)(CO)3Cl] as a multi-electron acceptor that combines the redox properties of both the rhenium tricarbonyl core and the disulfide functional group on the bipyridyl ligand. The first reduction at -0.85 V (vs. SCE) involves a two-electron process that breaks the disulfide bond, activating it for surface attachment. The heterogenized complex exhibits robust anchoring on gold surfaces, as probed by vibrational sum-frequency generation (SFG) spectroscopy. The binding configuration is normal to the surface, exposing the active site to the CO2 substrate in solution. The attachment mode is thus particularly suitable for electrocatalytic CO2 reduction.

Multi-time formulation of Matsubara dynamics.

Matsubara dynamics has recently emerged as the most general form of a quantum-Boltzmann-conserving classical dynamics theory for the calculation of single-time correlation functions. Here, we present a generalization of Matsubara dynamics for the evaluation of multitime correlation functions. We first show that the Matsubara approximation can also be used to approximate the two-time symmetrized double Kubo transformed correlation function. By a straightforward extension of these ideas to the multitime realm, a multitime Matsubara dynamics approximation can be obtained for the multitime fully symmetrized Kubo transformed correlation function. Although not a practical method, due to the presence of a phase-term, this multitime formulation of Matsubara dynamics represents a benchmark theory for future development of Boltzmann preserving semiclassical approximations to general higher order multitime correlation functions. It also reveals a connection between imaginary time-ordering in the path integral and the classical dynamics of multitime correlation functions.

Chiral Inversion of Amino Acids in Antiparallel ß-Sheets at Interfaces Probed by Vibrational Sum Frequency Generation Spectroscopy.

A parallel study of protein variants with all (l-), all (d-), or mixed (l-)/(d-) amino acids can be used to assess how backbone architecture versus side chain identity determines protein structure. Here, we investigate the secondary structure and side chain orientation dynamics of the antiparallel ß-sheet peptide LK7ß (Ac-Leu-Lys-Leu-Lys-Leu-Lys-Leu-NH2) composed of all (l-), all (d-), or alternating (l-Leu)/(d-Lys) amino acids. Using interface-selective vibrational sum frequency generation spectroscopy (VSFG), we observe that the alternating (l-)/(d-) peptide lacks a resonant C-H stretching mode compared to the (l-) and (d-) variants and does not form antiparallel ß-sheets. We rationalize our observations on the basis of density functional theory calculations and molecular dynamics (MD) simulations of LK7ß at the air-water interface. Irrespective of the handedness of the amino acids, leucine side chains prefer to orient toward the hydrophobic air phase while lysine side chains prefer the hydrophilic water phase. These preferences dictate the backbone configuration of LK7ß and thereby the folding of the peptide. Our MD simulations show that the preferred side chain orientations can force the backbone of a single strand of (l-) LK7ß at the air-water interface to adopt ß-sheet Ramachandran angles. However, denaturation of the ß-sheets at pH = 2 results in a negligible chiral VSFG amide I response. The combined computational and experimental results lend critical support to the theory that a chiral VSFG response requires macroscopic chirality, such as in ß-sheets. Our results can guide expectations about the VSFG optical responses of proteins and should improve understanding of how amino acid chirality modulates the structure and function of natural and de novo proteins at biological interfaces.

Heterogenized Molecular Catalysts: Vibrational Sum-Frequency Spectroscopic, Electrochemical, and Theoretical Investigations.

Rhenium and manganese bipyridyl tricarbonyl complexes have attracted intense interest for their promising applications in photocatalytic and electrocatalytic CO2 reduction in both homogeneous and heterogenized systems. To date, there have been extensive studies on immobilizing Re catalysts on solid surfaces for higher catalytic efficiency, reduced catalyst loading, and convenient product separation. However, in order for the heterogenized molecular catalysts to achieve the combination of the best aspects of homogeneous and heterogeneous catalysts, it is essential to understand the fundamental physicochemical properties of such heterogeneous systems, such as surface-bound structures of Re/Mn catalysts, substrate-adsorbate interactions, and photoinduced or electric-field-induced effects on Re/Mn catalysts. For example, the surface may act to (un)block substrates, (un)trap charges, (de)stabilize particular intermediates (and thus affect scaling relations), and shift potentials in different directions, just as protein environments do. The close collaboration between the Lian, Batista, and Kubiak groups has resulted in an integrated approach to investigate how the semiconductor or metal surface affects the properties of the attached catalyst. Synthetic strategies to achieve stable and controlled attachment of Re/Mn molecular catalysts have been developed. Steady-state, time-resolved, and electrochemical vibrational sum-frequency generation (SFG) spectroscopic studies have provided insight into the effects of interfacial structures, ultrafast vibrational energy relaxation, and electric field on the Re/Mn catalysts, respectively. Various computational methods utilizing density functional theory (DFT) have been developed and applied to determine the molecular orientation by direct comparison to spectroscopy, unravel vibrational energy relaxation mechanisms, and quantify the interfacial electric field strength of the Re/Mn catalyst systems. This Account starts with a discussion of the recent progress in determining the surface-bound structures of Re catalysts on semiconductor and Au surfaces by a combined vibrational SFG and DFT study. The effects of crystal facet, length of anchoring ligands, and doping of the semiconductor on the bound structures of Re catalysts and of the substrate itself are discussed. This is followed by a summary of the progress in understanding the vibrational relaxation (VR) dynamics of Re catalysts covalently adsorbed on semiconductor and metal surfaces. The VR processes of Re catalysts on TiO2 films and TiO2 single crystals and a Re catalyst tethered on Au, particularly the role of electron-hole pair (EHP)-induced coupling on the VR of the Re catalyst bound on Au, are discussed. The Account also summarizes recent studies in quantifying the electric field strength experienced by the catalytically active site of the Re/Mn catalyst bound on a Au electrode based on a combined electrochemical SFG and DFT study of the Stark tuning of the CO stretching modes of these catalysts. Finally, future research directions on surface-immobilized molecular catalyst systems are discussed.

CO2 Reduction Catalysts on Gold Electrode Surfaces Influenced by Large Electric Fields.

Attaching molecular catalysts to metal and semiconductor electrodes is a promising approach to developing new catalytic electrodes with combined advantages of molecular and heterogeneous catalysts. However, the effect of the interfacial electric field on the stability, activity, and selectivity of the catalysts is often poorly understood due to the complexity of interfaces. In this work, we examine the strength of the interfacial field at the binding site of CO2 reduction catalysts including Re(S-2,2'-bipyridine)(CO)3Cl and Mn(S-2,2'-bipyridine)(CO)3Br immobilized on Au electrodes. The vibrational spectra are probed by sum frequency generation spectroscopy (SFG), showing pronounced potential-dependent frequency shifts of the carbonyl stretching modes. Calculations of SFG spectra and Stark tuning rates based on density functional theory allow for direct interpretation of the configurations of the catalysts bound to the surfaces and the influence of the interfacial electric field. We find that electrocatalysts supported on Au electrodes have tilt angles of about 65-75° relative to the surface normal with one of the carbonyl ligands in direct contact with the surface. Large interfacial electric fields of 108-109 V/m are determined through the analysis of experimental frequency shifts and theoretical Stark tuning rates of the symmetric CO stretching mode. These large electric fields thus significantly influence the CO2 binding site.

Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy.

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.

Isotope effects in aqueous solvation of simple halides.

We present a path-integral-molecular-dynamics study of the thermodynamic stabilities of DOH⋯ X- and HOD⋯ X- (X = F, Cl, Br, I) coordination in aqueous solutions at ambient conditions. In agreement with experimental evidence, our results for the F- case reveal a clear stabilization of the latter motif, whereas, in the rest of the halogen series, the former articulation prevails. The DOH⋯ X- preference becomes more marked the larger the size of the ionic solute. A physical interpretation of these tendencies is provided in terms of an analysis of the global quantum kinetic energies of the light atoms and their geometrical decomposition. The stabilization of the alternative ionic coordination geometries is the result of a delicate balance arising from quantum spatial dispersions along parallel and perpendicular directions with respect to the relevant O-H⋯X- axis, as the strength of the water-halide H-bond varies. This interpretation is corroborated by a complementary analysis performed on the different spectroscopic signals of the corresponding IR spectra.

Isotopic equilibria in aqueous clusters at low temperatures: Insights from the MB-pol many-body potential.

By combining path-integrals molecular dynamics simulations with the accurate MB-pol potential energy surface, we investigate the role of alternative potential models on isotopic fractionation ratios between H and D atoms at dangling positions in water clusters at low temperatures. Our results show clear stabilizations of the lighter isotope at dangling sites, characterized by free energy differences ΔG that become comparable to or larger than kBT for temperatures below ∼75 K. The comparison between these results to those previously reported using the empirical q-TIP4P/F water model [P. E. Videla et al., J. Phys. Chem. Lett. 5, 2375 (2014)] reveals that the latter Hamiltonian overestimates the H stabilization by ∼25%. Moreover, predictions from the MB-pol model are in much better agreement with measured results reported for similar isotope equilibria at ice surfaces. The dissection of the quantum kinetic energies into orthogonal directions shows that the dominant differences between the two models are to be found in the anharmonic characteristics of the potential energy surfaces along OH bond directions involved in hydrogen bonds.