Molecular Electronics: Toward the Atomistic Modeling of Conductance Histograms

Abstract

Reliability in molecular electronics break-junction experiments has come from statistically sampling thousands of repeat measurements. Here we discuss the computational challenges in reproducing the experimental conductance histograms and introduce a computational strategy to model molecular electronics experiments with statistics. The strategy combines classical molecular dynamics (MD) of junction formation and evolution, using a reactive force field that allows for bond-breaking and -making processes, with steady-state electronic transport computations using Green’s function methods in the zero-bias limit. The strategy is illustrated using a molecular junction setup where an octanedimethylsulfide (C8SMe) connects to two gold electrodes. To attempt to reproduce the statistics encountered in experiments, we performed simulations using (1) a single MD trajectory of junction formation and evolution; (2) several MD trajectories with identical initial geometry for the electrodes; and (3) several MD trajectories each with a different geometry for the electrodes (obtained by separately crushing the electrodes and breaking the gold–gold contact). We find that these three classes of simulations can exhibit an apparent agreement with the experimental conductance histograms. Nevertheless, these simulations miss the time-averaging of the current that is inherent to the experiment. We further examined the simulated time-averaged currents for an ensemble of trajectories with crushed electrodes and found that such simulations recover the width of the experimental conductance histograms despite the additional averaging. These results highlight the challenges in connecting theory with experiment in molecular electronics and establish a hierarchy of methods that can be used to understand the factors that influence the experimental conductance histogram.

Learning Conductance: Gaussian Process Regression for Molecular Electronics

“…The resulting conductance traces and histograms are shown in Figure 1. They show a most probable conductance of around 10 −5 G 0 , which is in line with previous calculations and experiments 47,98 .…”

“…Ten octanedimethylsulfide (C 8 H 16 (SMe) 2 ) molecules are added randomly close to the wire. This system is well characterized by previous experimental and theoretical studies 47,98 and poses a challenge for machine learning approaches, since a huge variety of conformations or electrode-molecule binding configuration can be encountered. Since we try to capture the full evolution of the junction from the initial forming to rupture, we can sample situations where, e.g., multiple molecules form a junction, which is not included in MD simulations based on already-formed molecular junctions.…”

“…The shape of the conductance histograms cannot be obtained from calculations of a static junction in a minimum energy conformation, as these calculations do not take into account the conformational variability encountered in experiments. To capture the histograms, it is necessary to perform molecular dynamics (MD) simulations of junction formation and evolution using techniques such as classical force fields [42][43][44][45][46] , reactive force fields 47,48 , or ab-initio MD techniques [49][50][51][52][53][54] . Even for such simulations, complete sampling of the experimental situation remains challenging 55 .…”

“…While we chose reactive force fields 94,95 and density functional tight-binding (DFTB) 96 calculations for our simulations, any method which performs the structural sampling of a molecular junction and provides transport properties for selected snapshots may provide the basis for our machine learning approach. MD simulations employing reactive force fields have been successfully used in the past to compute trajectories of MCBJ experiments for the same molecule used here or similar systems 47,48,97 . Since electronic structure calculations are the most expensive component in the construction of the conductance histograms, we aim to predict conductance solely on structural information.…”

Long-Range Charge Transport in Homogeneous and Alternating-Rigidity Chains

“…[12][13][14][15] , in long junctions such methods reach a) Electronic mail: francisco.lai@mail.utoronto.ca b) Electronic mail: dvira.segal@utoronto.ca their computational limit. Alternatively, a common approximate approach to deal with the impact of nuclear effects on electronic conduction is to employ classical molecular dynamics simulations for sampling molecular configurations, in conjunction with the Green's function formalism for transport [16][17][18][19][20][21][22] . Yet, even this approximate method becomes computationally impractical for large systems and it requires an additional level of coarsegraining 17 .…”