Orbital Overlap Effects in Electron Transfer Reactions across a Metal Nanowire/Electrolyte Solution Interface

Abstract

In this communication we report on calculations of the orbital overlap between Fe(III) and Cr(III) aquacomplexes and different electrode surfaces: Cu(111), Ag (111), Au(111), Pt(111), and corresponding monoatomic wires. The electronic structure of the monocrystalline surfaces and nanowires are described in terms of the electronic spillover and density of electronic states at the Fermi level obtained from periodic Density Functional Theory (DFT) calculations. The transmission coefficients (κ ) characterizing the first stage of outer-sphere electron transfer for the reduction of aquacomplexes are calculated on the basis of Landau-Zener theory as a function of electrodereactant separation; the electronic transmission coefficients for the [Cr(H 2 O) 6 ] 3+/2+ redox couple were found to be smaller than those for [Fe(H 2 O) 6 ] 3+/2+ . Two different intervals can be clearly distinguished for Cu, Au and Pt: "a catalytic region", where κ (wire) > κ (Me slab) and "an inhibition region", where κ (wire) < κ (Me slab). A similar behaviour exhibits the coupling constant estimated for a hydrogen atom adsorbed at the Au(111) surface and the Au monoatomic wire. These effects originate from some specific features of electronic density profile for metal nanowires: at short distances the electronic density of nanowires is higher compared with the (111) metal surfaces, while at larger separations it decreases more sharply.

Modeling of electron transfer across electrochemical interfaces: State‐of‐the art and challenges for quantum and computational chemistry

“…That is why the slopes the vs. distance dependencies obtained in Refs. differ from typical experimental values …”

“…It was shown in Refs. that in contrast to homogeneous electron transfer for a heterogeneous case, the term in Eq. can be neglected.…”

“…Then Eq. takes the form: where and .…”

“…and (i.e., the factor ) may be used for various kinetic regimes (weak and strong coupling, see also Supporting Information in Ref. ) as a good approximation. The same conclusion was made by Feldberg and Sutin who employed the “multi‐path” LZ model.…”

“…In a series of studies, another approach has been developed to calculate for heterogeneous ET processes (the reduction of [Fe(CN) 6 ] 3− , aqua‐, and amino‐complexes of transition metal ions was modeled as examples). The authors considered a mercury electrode as a solid with smooth surface or monoatomic metal wires (Cu, Ag, Au, Pt) and constructed the effective wave function of a metal, using the distance‐dependent total electronic density obtained either on the basis of the jellium model, or from periodical DFT computations, where x is a coordinate normal to the electrode surface, is the decay coefficient of electronic density, and V is the crystal volume.…”