Electron transfer from the perspective of electron transmission: Biased non-adiabatic intermolecular reactions in the single-particle picture

On the application of Marcus-Hush theory to small polaron chemical dynamics in oxides: its relationship to the Holstein model and the importance of lattice-orbital symmetries

The chemical dynamics of small polaron hopping within oxides is often interpreted through two-site variations on Marcus-Hush theory, while from a physics perspective small polaron hopping is more often approached from Holstein's solid-state formalism. Here we seek to provide a chemically oriented viewpoint, focusing on small polaron hopping in oxides, concerning these two phenomenological frameworks by employing both tight-binding modelling and first-principles calculations. First, within a semiclassical approach the Marcus-Hush relations are overviewed as a two-site reduction of Holstein's model. Within the single-band regime, similarities and differences between Holstein derived small polaron hopping and the Marcus-Hush model are also discussed. In this context the emergence of adiabaticity (or, conversely, diabaticity) is also explored within each framework both analytically and by directly evolving the system wavefunction. Then, through first-principles calculations of select oxides we explore how coupled lattice and orbital symmetries can impact on hopping properties - in a manner that is quite distinct typical chemical applications of Marcus-Hush theory. These results are then related back to the Holstein model to explore the relative applicability of the two frameworks towards interpreting small polaron hopping properties, where it is emphasized that the Holstein model offers an increasingly more appealing physicochemical interpretation of hopping processes as band and/or coupling interactions increase. Overall, this work aims to strengthen the physically oriented exploration of small polarons and their physicochemical properties in the growing oxide chemistry community.

Single-Electron Currents in Designer Single-Cluster Devices

Atomically precise clusters can be used to create single-electron devices wherein a single redox-active cluster is connected to two macroscopic electrodes via anchoring ligands. Unlike single-electron devices comprising nanocrystals, these cluster-based devices can be fabricated with atomic precision. This affords an unprecedented level of control over the device properties. Herein, we design a series of cobalt chalcogenide clusters with varying ligand geometries and core nuclearities to control their current-voltage (I-V) characteristics in a scanning tunneling microscope-based break junction (STM-BJ) device. First, the device geometry is modified by precisely positioning junction-anchoring ligands on the surface of the cluster. We show that the I-V characteristics are independent of ligand placement, confirming a sequential, single-electron tunneling mechanism. Next, we chemically fuse two clusters to realize a larger cluster dimer that behaves as a single electronic unit, possessing a smaller reorganization energy and more accessible redox states than the monomeric analogues. As a result, dimer-based devices exhibit significantly higher currents and can even be pushed to current saturation at high bias. Owing to these controllable properties, single-cluster junctions serve as an excellent platform for exploring incoherent charge transport processes at the nanoscale. With this understanding, as well as properties such as nonlinear I-V characteristics and rectification, these molecular clusters may function as conductive inorganic nodes in new devices and materials.

Fully Quantized Electron Transfer Observed in a Single Redox Molecule at a Metal Interface

Long-range electron transfer is a ubiquitous process that plays an important role in electrochemistry, biochemistry, organic electronics, and single molecule electronics. Fundamentally, quantum mechanical processes, at their core, manifest through both electron tunneling and the associated transition between quantized nuclear vibronic states (intramolecular vibrational relaxation) mediated by electron-nuclear coupling. Here, we report on measurements of long-range electron transfer at the interface between a single ferrocene molecule and a gold substrate separated by a hexadecanethiol quantum tunneling barrier. These redox measurements exhibit quantized nuclear transitions mediated by electron-nuclear coupling at 4.7 K in vacuum. By detecting the electric force associated with redox events by atomic force microscopy (AFM), with increasing AFM oscillation amplitude, the intensity of the observed  cantilever resonance frequency shift peak increases and then exhibits a series of discrete steps that are indicative of quantized nuclear transitions. The observed peak shapes agree well with a single-electron tunneling model with quantized nuclear state transitions associated with the conversion of the molecule between oxidized and reduced electronic states. This technique opens the door to simultaneously investigating quantized electron and nuclear dynamics in a diverse range of systems.

Reorganization energy upon charging a single molecule on an insulator measured by atomic force microscopy

Intermolecular single-electron transfer on electrically insulating films is a key process in molecular electronics^1-4 and an important example of a redox reaction^5,6. Electron-transfer rates in molecular systems depend on a few fundamental parameters, such as interadsorbate distance, temperature and, in particular, the Marcus reorganization energy ⁷ . This crucial parameter is the energy gain that results from the distortion of the equilibrium nuclear geometry in the molecule and its environment on charging^8,9. The substrate, especially ionic films ¹⁰ , can have an important influence on the reorganization energy^11,12. Reorganization energies are measured in electrochemistry ¹³ as well as with optical^14,15 and photoemission spectroscopies^16,17, but not at the single-molecule limit and nor on insulating surfaces. Atomic force microscopy (AFM), with single-charge sensitivity^18-22, atomic-scale spatial resolution ²⁰ and operable on insulating films, overcomes these challenges. Here, we investigate redox reactions of single naphthalocyanine (NPc) molecules on multilayered NaCl films. Employing the atomic force microscope as an ultralow current meter allows us to measure the differential conductance related to transitions between two charge states in both directions. Thereby, the reorganization energy of NPc on NaCl is determined as (0.8 ± 0.2) eV, and density functional theory (DFT) calculations provide the atomistic picture of the nuclear relaxations on charging. Our approach presents a route to perform tunnelling spectroscopy of single adsorbates on insulating substrates and provides insight into single-electron intermolecular transport.