Microscopic theory, analysis, and interpretation of conductance histograms in molecular junctions.

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here we develop a microscopic theory for the conductance histogram by merging the theory of force-spectroscopy with molecular conductance. The procedure yields analytical equations that accurately fit the conductance histogram of a wide range of molecular junctions and augments the information content that can be extracted from them. Our formulation captures contributions to the conductance dispersion due to conductance changes during the mechanical elongation inherent to the experiments. In turn, the histogram shape is determined by the non-equilibrium stochastic features of junction rupture and formation. The microscopic parameters in the theory capture the junction's electromechanical properties and can be isolated from separate conductance and rupture force (or junction-lifetime) measurements. The predicted behavior can be used to test the range of validity of the theory, understand the conductance histograms, design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures.

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Time-Dependent Second-Order Green's Function Theory for Neutral Excitations.

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

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.

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.

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.