Understanding molecular and electrochemical charge transfer: theory and computations.

Electron, proton, and proton-coupled electron transfer (PCET) are crucial elementary processes in chemistry, electrochemistry, and biology. We provide here a gentle overview of retrospective and currently developing theoretical formalisms of chemical, electrochemical and biological molecular charge transfer processes, with examples of how to bridge electron, proton, and PCET theory with experimental data. We offer first a theoretical minimum of molecular electron, proton, and PCET processes in homogeneous solution and at electrochemical interfaces. We illustrate next the use of the theory both for simple electron transfer processes, and for processes that involve molecular reorganization beyond the simplest harmonic approximation, with dissociative electron transfer and inclusion of all charge transfer parameters. A core example is the electrochemical reduction of the S2O82- anion. This is followed by discussion of core elements of proton and PCET processes and the electrochemical dihydrogen evolution reaction on different metal, semiconductor, and semimetal (say graphene) electrode surfaces. Other further focus is on stochastic chemical rate theory, and how this concept can rationalize highly non-traditional behaviour of charge transfer processes in mixed solvents. As a second major area we address ("long-range") chemical and electrochemical electron transfer through molecular frameworks using notions of superexchange and hopping. Single-molecule and single-entity electrochemistry are based on electrochemical scanning probe microscopies. (In operando) scanning tunnelling microscopy (STM) and atomic force microscopy (AFM) are particularly emphasized, with theoretical notions and new molecular electrochemical phenomena in the confined tunnelling gap. Single-molecule surface structure and electron transfer dynamics are illustrated by self-assembled thiol molecular monolayers and by more complex redox target molecules. This discussion also extends single-molecule electrochemistry to bioelectrochemistry of complex redox metalloproteins and metalloenzymes. Our third major area involves computational overviews of molecular and electronic structure of the electrochemical interface, with new computational challenges. These relate to solvent dynamics in bulk and confined space (say carbon nanostructures), electrocatalysis, metallic and semiconductor nanoparticles, d-band metals, carbon nanostructures, spin catalysis and "spintronics", and "hot" electrons. Further perspectives relate to metal-organic frameworks, chiral surfaces, and spintronics.

Electronic Spillover from a Metallic Nanoparticle: Can Simple Electrochemical Electron Transfer Processes Be Catalyzed by Electronic Coupling of a Molecular Scale Gold Nanoparticle Simultaneously to the Redox Molecule and the Electrode?

Electrochemical electron transfer (ET) of transition metal complexes or redox metalloproteins can be catalyzed by more than an order of magnitude by molecular scale metallic nanoparticles (NPs), often rationalized by concentration enhancement of the redox molecules in the interfacial region, but collective electronic AuNP array effects have also been forwarded. Using DFT combined with molecular electrochemical ET theory we explore here whether a single molecular scale Au nanocluster (AuC) between a Au (111) surface and the molecular redox probe ferrocene/ferricinium (Fc/Fc+) can trigger an ET rate increase. Computational challenges limit us to AunCs (n up to 147), which are smaller than most electrocatalytic AuCs studied experimentally. AuC-coating thiols are addressed both as adsorption of two S atoms at the structural Au55 bridge sites and as superexchange of variable-size AuCs via a single six-carbon alkanethiyl bridge. Our results are guiding, but enable comparing many AuC surface details (apex, ridge, face, direct vs superexchange ET) with a planar Au(111) surface. The rate-determining electronic transmission coefficients for ET between Fc/Fc+ and AuC are highly sensitive to subtle AuC electronic features. The transmission coefficients mostly compete poorly with direct Fc/Fc+ ET at the Au(111) surface, but Fc/Fc+ 100 face-bound on Au79 and Au147 and ridge bound on Au19 leads to a 2- or 3-fold rate enhancement, in different distance ranges. Single AuCs can thus indeed cause rate enhancement of simple electrochemical ET, but additional, possibly collective AuNC effects, as well as larger clusters and more complete coating layers, also need to be considered.

Chiral Selectivity in Inter-reactant Recognition and Electron Transfer of the Oxidation of Horse Heart Cytochrome c by Trioxalatocobaltate(III).

Outer-sphere electron transfer (ET) between optically active transition-metal complexes and either other transition-metal complexes or metalloproteins is a prototype reaction for kinetic chirality. Chirality as the ratio between bimolecular rate constants of two enantiomers mostly amounts to 1.05-1.2 with either the Λ or Δ form the more reactive, but the origin of chirality in ET parameters such as work terms, electronic transmission coefficient, and nuclear reorganization free energy has not been addressed. We report a study of ET between the Λ-/Δ-[Co(Ox)3](3-) pair (Ox = oxalate) and horse heart cytochrome c (cyt c). This choice is prompted by strong ion-pair formation that enables separation into inter-reactant interaction (chiral "recognition") and ET within the ion pair ("stereoselectivity"). Chiral selectivity was first addressed experimentally. Λ-[Co(Ox)3](3-) was found to be both the more strongly bound and faster reacting enantiomer expressed respectively by the ion-pair formation constant KX and ET rate constant kET(X) (X = Λ and Δ), with KΛ/KΔ and kET(Λ)/kET(Δ) both ≈1.1-1.2. rac-[Co(Ox)3](3-) behavior is intermediate between those of Λ- and Δ-[Co(Ox)3](3-). Chirality was next analyzed by quantum-mechanical ET theory combined with density functional theory and statistical mechanical computations. We also modeled the ion pair K(+)·[Co(Ox)3](3-) in order to address the influence of the solution ionic strength. The complex structure of cyt c meant that this reactant was represented solely by the heme group including the chiral axial ligands L-His and L-Met. Both singlet and triplet hemes as well as hemes with partially deprotonated propionic acid side groups were addressed. The computations showed that the most favorable inter-reactant configuration involved a narrow distance and orientation space very close to the contact distance, substantiating the notion of a reaction complex and the equivalence of the binding constant to a bimolecular reaction volume. The reaction is significantly diabatic even at these short inter-reactant distances, with electronic transmission coefficients κel(X) = 10(-3)-10(-2). The computations demonstrated chirality in both KX and κel(X) but no chirality in the reorganization and reaction free energy (driving force). As a result of subtle features in both KX and κel(X) chirality, the "operational" chirality κET(Λ)KΛ/κET(Δ)KΔ emerges larger than unity (1.1-1.2) from the molecular modeling as in the experimental data.

A spectroscopic and computational study of Al(III) complexes in cryolite melts: Effect of cation nature.

Lithium, sodium and potassium cryolite melts are probed by Raman spectroscopy in a wide range of the melt composition. The experimental data demonstrate a slight red shift of main peaks and a decrease of their half-widths in the row Li(+), Na(+), K(+). Quantum chemical modelling of the systems is performed at the density functional theory level. The ionic environment is found to play a crucial role in the energy of fluoroaluminates. Potential energy surfaces describing the formation/dissociation of certain complex species, as well as model Raman spectra are constructed and compared with those obtained recently for sodium containing cryolite melts (R.R. Nazmutdinov, et al., Spectrochim, Acta A 75 (2010) 1244.). The calculations show that the cation nature affects the geometry of the ionic associates as well as the equilibrium and kinetics of the complexation processes. This enables to interpret both original experimental data and those reported in literature.

Modeling and computations of the intramolecular electron transfer process in the two-heme protein cytochrome c(4).

The di-heme protein Pseudomonas stutzeri cytochrome c(4) (cyt c(4)) has emerged as a useful model for studying long-range protein electron transfer (ET). Recent experimental observations have shown a dramatically different pattern of intramolecular ET between the two heme groups in different local environments. Intramolecular ET in homogeneous solution is too slow (>10 s) to be detected but fast (ms-µs) intramolecular ET in an electrochemical environment has recently been achieved by controlling the molecular orientation of the protein assembled on a gold electrode surface. In this work we have performed computational modeling of the intramolecular ET process by a combination of density functional theory (DFT) and quantum mechanical charge transfer theory to disclose reasons for this difference. We first address the electronic structures of the model heme core with histidine and methionine axial ligands in both low- and high-spin states by structure-optimized DFT. The computations enable estimating the intramolecular reorganization energy of the ET process for different combinations of low- and high-spin heme couples. Environmental reorganization free energies, work terms ("gating") and driving force were determined using dielectric continuum models. We then calculated the electronic transmission coefficient of the intramolecular ET rate using perturbation theory combined with the electronic wave functions determined by the DFT calculations for different heme group orientations and Fe-Fe separations. The reactivity of low- and high-spin heme groups was notably different. The ET rate is exceedingly low for the crystallographic equilibrium orientation but increases by several orders of magnitude for thermally accessible non-equilibrium configurations. Deprotonation of the propionate carboxyl group was also found to enhance the ET rate significantly. The results are discussed in relation to the observed surface immobilization effect and support the notion of conformationally gated ET.

Chemistry of cysteine assembly on Au(100): electrochemistry, in situ STM and molecular modeling.

Cysteine (Cys) is an essential amino acid with a carboxylic acid, an amine and a thiol group. We have studied the surface structure and adsorption dynamics of l-cysteine adlayers on Au(100) from aqueous solution using electrochemistry, high-resolution electrochemical scanning tunnelling microscopy (in situ STM), and molecular modelling. Cys adsorption on this low-index Au-surface has been much less studied than Cys adsorption on Au(111)- and Au(110)-electrode surfaces. Chronopotentiometry was employed to monitor the adsorption dynamics at sub-second resolution and showed that adsorption is completed in 30 minutes at Cys concentrations above 100 µM. Two consecutive steps could be fitted to these data. Two separate reductive desorption peaks of Cys adlayers on Au(100) with a total coverage of 2.52 (±0.15) × 10-10 mol cm-2 were observed. In situ STM showed that the adsorbed Cys is organized in stripes with "fork-like" features which co-exist in (11 × 2)-2Cys and (7 × 2)-2Cys lattices, quite differently from Cys adsorption on Au(111)-electrode surfaces. Stripe structures with bright STM contrast in the center suggest that a second Cys adlayer on top of a first adlayer is formed, supporting the dual-peak reductive desorption of Cys adlayers. In addition, monolayers of both pure l-Cys and pure d-Cys and a 1 : 1 racemic mixture of l- and d-Cys on Au(100) were studied. Virtually identical macroscopic electrochemical features were found, but in situ STM discloses many more defects for the racemic mixture than for the pure enantiomers due to structural mismatch of l- and d-Cys. Density functional theory (DFT) calculations combined with a cluster model for the Au(100) surface were carried out to investigate the adsorption energy and geometry of the adsorbed monomer and dimer Cys species in different orientations, with detailed attention to the chirality effects. Optimized DFT geometries were used to construct model STM images, and kinetic Monte Carlo simulations undertaken to illuminate the growth of adsorbate rows and the mechanism of the adlayer formation as well as the Cys adsorption patterns specific to the Au(100)-electrode surface.

A spectroscopic and computational study of Al(III) complexes in sodium cryolite melts: ionic composition in a wide range of cryolite ratios.

The structure of sodium cryolite melts was studied using Raman spectroscopy and quantum chemical calculations performed at the density functional theory level. The existence of bridged forms in the melts was argued first from the analysis of experimental Raman spectra. In the quantum chemical modelling emphasis was put on the construction of potential energy surfaces describing the formation/dissociation of certain complex species. Effects of the ionic environment were found to play a crucial role in the energetics of model processes. The structure of the simplest possible polymeric forms involving two Al centres linked through F atoms ("dimers") was thoroughly investigated. The calculated equilibrium constants and model Raman spectra yield additional evidence in favour of the dimers. This agrees with a self-consistent analysis of a series of Raman spectra for a wide range of the melt composition.

Submolecular electronic mapping of single cysteine molecules by in situ scanning tunneling imaging.

We have used L-cysteine (Cys) as a model system to study the surface electronic structures of single molecules at the submolecular level in aqueous buffer solution by a combination of electrochemical scanning tunneling microscopy (in situ STM), electrochemistry including voltammetry and chronocoulometry, and density functional theory (DFT) computations. Cys molecules were assembled on single-crystal Au(110) surfaces to form a highly ordered monolayer with a periodic lattice structure of c(2x2) in which each unit contains two molecules; this conclusion is confirmed by the results of calculations based on a slab model for the metal surface. The ordered monolayer offers a platform for submolecular scale electronic mapping that is an issue of fundamental interest but remains a challenge in STM imaging science and surface chemistry. Single Cys molecules were mapped as three electronic subunits contributed mainly from three chemical moieties: thiol (-SH), carboxylic (-COOH), and amine (-NH2) groups. The contrasts of the three subunits depend on the environment (e.g., pH), which affects the electronic structure of adsorbed species. From the DFT computations focused on single molecules, rational analysis of the electronic structures is achieved to delineate the main factors that determine electronic contrasts in the STM images. These factors include the molecular orientation, the chemical nature of the elements or groups in the molecule, and the interaction of the elements with the substrate and tip. The computational images recast as constant-current-height profiles show that the most favorable molecular orientation is the adsorption of cysteine as a radical in zwitterionic form located on the bridge between the Au(110) atomic rows and with the amine and carboxyl group toward the solution bulk. The correlation between physical location and electronic contrast of the adsorbed molecules was also revealed by the computational data. The present study shows that cysteine packing in the adlayer on Au(110) from the liquid environment is in contrast to that from the ultrahigh-vacuum environment, suggesting solvent plays a role during molecular assembly.

Adsorption and in situ scanning tunneling microscopy of cysteine on Au(111): Structure, energy, and tunneling contrasts.

The amino acid L-cysteine (Cys) adsorbs in highly ordered (3 square root of 3 x 6) R30 degrees lattices on Au(111) electrodes from 50 mM ammonium acetate, pH 4.6. We provide new high-resolution in situ scanning tunneling microscopy (STM) data for the L-Cys adlayer. The data substantiate previous data with higher resolution, now at the submolecular level, where each L-Cys molecule shows a bilobed feature. The high image resolution has warranted a quantum chemical computational effort. The present work offers a density functional study of the geometry optimized adsorption of four L-Cys forms-the molecule, the anion, the neutral radical, and its zwitterion adsorbed a-top-at the bridge and at the threefold hollow site of a planar Au(111) Au12 cluster. This model is crude but enables the inclusion of other effects, particularly the tungsten tip represented as a single or small cluster of W-atoms, and the solvation of the L-Cys surface cluster. The computational data are recast as constant current-height profiles as the most common in situ STM mode. The computations show that the approximately neutral radical, with the carboxyl group pointing toward and the amino group pointing away from the surface, gives the most stable adsorption, with little difference between the a-top and threefold sites. Attractive dipolar interactions screened by a dielectric medium stabilize around a cluster size of six L-Cys entities, as observed experimentally. The computed STM images are different for the different L-Cys forms. Both lateral and vertical dimensions of the radical accord with the observed dimensions, while those of the molecule and anion are significantly more extended. A-top L-Cys radical adsorption further gives a bilobed height profile resembling the observed images, with comparable contributions from sulfur and the amino group. L-Cys radical a-top adsorption therefore emerges as the best representation of L-Cys adsorption on Au(111).