When can time-dependent currents be reproduced by the Landauer steady-state approximation?

Electrochemistry in sensing of molecular interactions of proteins and their behavior in an electric field

Electrochemical methods can be used not only for the sensitive analysis of proteins but also for deeper research into their structure, transport functions (transfer of electrons and protons), and sensing their interactions with soft and solid surfaces. Last but not least, electrochemical tools are useful for investigating the effect of an electric field on protein structure, the direct application of electrochemical methods for controlling protein function, or the micromanipulation of supramolecular protein structures. There are many experimental arrangements (modalities), from the classic configuration that works with an electrochemical cell to miniaturized electrochemical sensors and microchip platforms. The support of computational chemistry methods which appropriately complement the interpretation framework of experimental results is also important. This text describes recent directions in electrochemical methods for the determination of proteins and briefly summarizes available methodologies for the selective labeling of proteins using redox-active probes. Attention is also paid to the theoretical aspects of electron transport and the effect of an external electric field on the structure of selected proteins. Instead of providing a comprehensive overview, we aim to highlight areas of interest that have not been summarized recently, but, at the same time, represent current trends in the field.

Coherent and incoherent contributions to molecular electron transport

We numerically isolate the limits of validity of the Landauer approximation to describe charge transport along molecular junctions in condensed phase environments. To do so, we contrast Landauer with exact time-dependent non-equilibrium Green’s function quantum transport computations in a two-site molecular junction subject to exponentially correlated noise. Under resonant transport conditions, we find Landauer accuracy to critically depend on intramolecular interactions. By contrast, under nonresonant conditions, the emergence of incoherent transport routes that go beyond Landauer depends on charging and discharging processes at the electrode–molecule interface. In both cases, decreasing the rate of charge exchange between the electrodes and molecule and increasing the interaction strength with the thermal environment cause Landauer to become less accurate. The results are interpreted from a time-dependent perspective where the noise prevents the junction from achieving steady-state and from a fully quantum perspective where the environment introduces dephasing in the dynamics. Using these results, we analyze why the Landauer approach is so useful to understand experiments, isolate regimes where it fails, and propose schemes to chemically manipulate the degree of transport coherence.

Delocalization-Assisted Transport through Nucleic Acids in Molecular Junctions

The flow of charge through molecules is central to the function of supramolecular machines, and charge transport in nucleic acids is implicated in molecular signaling and DNA repair. We examine the transport of electrons through nucleic acids to understand the interplay of resonant and nonresonant charge carrier transport mechanisms. This study reports STM break junction measurements of peptide nucleic acids (PNAs) with a G-block structure and contrasts the findings with previous results for DNA duplexes. The conductance of G-block PNA duplexes is much higher than that of the corresponding DNA duplexes of the same sequence; however, they do not display the strong even-odd dependence conductance oscillations found in G-block DNA. Theoretical analysis finds that the conductance oscillation magnitude in PNA is suppressed because of the increased level of electronic coupling interaction between G-blocks in PNA and the stronger PNA-electrode interaction compared to that in DNA duplexes. The strong interactions in the G-block PNA duplexes produce molecular conductances as high as 3% G₀, where G₀ is the quantum of conductance, for 5 nm duplexes.

Coherent Electron Transport across a 3 nm Bioelectronic Junction Made of Multi-Heme Proteins

Multi-heme cytochromes (MHCs) are fascinating proteins used by bacterial organisms to shuttle electrons within, between, and out of their cells. When placed in solid-state electronic junctions, MHCs support temperature-independent currents over several nanometers that are 3 orders of magnitude higher compared to other redox proteins of similar size. To gain molecular-level insight into their astonishingly high conductivities, we combine experimental photoemission spectroscopy with DFT+Σ current-voltage calculations on a representative Gold-MHC-Gold junction. We find that conduction across the dry, 3 nm long protein occurs via off-resonant coherent tunneling, mediated by a large number of protein valence-band orbitals that are strongly delocalized over heme and protein residues. This picture is profoundly different from the electron hopping mechanism induced electrochemically or photochemically under aqueous conditions. Our results imply that the current output in solid-state junctions can be even further increased in resonance, for example, by applying a gate voltage, thus allowing a quantum jump for next-generation bionanoelectronic devices.

Toward a First-Principles Evaluation of Transport Mechanisms in Molecular Wires

Understanding charge transport through molecular wires is important for nanoscale electronics and biochemistry. Our goal is to establish a simple first-principles protocol for predicting the charge transport mechanism in such wires, in particular the crossover from coherent tunneling for short wires to incoherent hopping for longer wires. This protocol is based on a combination of density functional theory with a polarizable continuum model introduced by Kaupp et al. for mixed-valence molecules, which we had previously found to work well for length-dependent charge delocalization in such systems. We combine this protocol with a new charge delocalization measure tailored for molecular wires, and we show that it can predict the tunneling-to-hopping transition length with a maximum error of one subunit in five sets of molecular wires studied experimentally in molecular junctions at room temperature. This suggests that the protocol is also well suited for estimating the extent of hopping sites as relevant, for example, for the intermediate tunneling-hopping regime in DNA.

Force-conductance spectroscopy of a single-molecule reaction

We demonstrate how simultaneous measurements of conductance and force can be used to monitor the step-by-step progress of a mechanically-activated cis-to-trans isomerization single-molecule reaction, including events that cannot be distinguished using force or conductance alone. To do so, we simulated the force-conductance profile of cyclopropane oligomers connected to graphene nanoribbon electrodes that undergo a cis-to-trans isomerization during mechanical elongation. This was done using a combination of classical molecular dynamics simulation of the pulling using a reactive force field, and Landauer transport computations of the conductance with nonequilibrium Green's function methods. The isomerization events can be distinguished in both force and conductance profiles. However, the conductance profile during the mechanical elongation distinguishes between reaction intermediates that cannot be resolved using force. In turn, the force signals non-reactive deformations in the molecular backbone which are not visible in the conductance profile. These observations are shown to be robust to the choice of electrode and Hamiltonian model. The computations exemplify the potential of the integration of covalent mechanochemistry with molecular conductance to investigate chemical reactivity at the single-entity limit.

How Structural Defects Affect the Mechanical and Electrical Properties of Single Molecular Wires

We report how individual defects affect single graphene nanoribbons by scanning tunneling and atomic force microscopy pulling experiments simultaneously accessing their electrical and mechanical properties. The on-surface polymerization of the graphene nanoribbons is controlled by cooperative effects as theoretically suggested. Further, we find, with the help of atomistic simulations, that defects substantially vary the molecule-substrate coupling and drastically increase the flexibility of the graphene nanoribbons while keeping their desirable electronic properties intact.

Emergence of Landauer transport from quantum dynamics: A model Hamiltonian approach

The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.

Modeling Nonreactive Molecule-Surface Systems on Experimentally Relevant Time and Length Scales: Dynamics and Conductance of Polyfluorene on Au(111)

We propose a computationally efficient strategy to accurately model nonreactive molecule-surface interactions that adapts density functional theory calculations with the Tkatchenko-Scheffler scheme for van der Waals interactions into a simple classical force field. The resulting force field requires just two adjustable parameters per atom type that are needed to capture short-range and polarization interactions. The developed strategy allows for classical molecular dynamics simulation of molecules on surfaces with the accuracy of high-level electronic structure methods but for system sizes (10³ to 10⁷ atoms) and timescales (picoseconds to microseconds) that go well beyond what can be achieved with first-principles methods. Parameters for H, sp² C, and O on Au(111) are developed and employed to atomistically model experiments that measure the conductance of a single polyfluorene on Au(111) as a continuous function of its length. The simulations qualitatively capture both the gross and fine features of the observed conductance decay during initial junction elongation and lead to a revised atomistic understanding of the experiment.

Signatures of Conformational Dynamics and Electrode-Molecule Interactions in the Conductance Profile During Pulling of Single-Molecule Junctions

We demonstrate that conductance can act as a sensitive probe of conformational dynamics and electrode-molecule interactions during the equilibrium and nonequilibrium pulling of molecular junctions. To do so, we use a combination of classical molecular dynamics simulations and Landauer electron transport computations to investigate the conductance of a family of Au-alkanedithiol-Au junctions as they are mechanically elongated. The simulations show an overall decay of the conductance during pulling that is due to a decrease in the through-space electrode-molecule interactions, and that sensitivity depends on the electrode geometry. In addition, characteristic kinks induced by level alignment shifts (and to a lesser extent by quantum destructive interference) were also observed superimposed to the overall decay during pulling simulations. The latter effect depends on the variation of the molecular dihedral angles during pulling and therefore offers an efficient solution to experimentally monitor conformational dynamics at the single-molecule limit.