A Strategy for Modeling Nonstatistical Reactivity Effects: Combining Chemical Activation Estimates with a Vibrational Relaxation Model.

The kinetics of many chemical reactions can be readily explained with a statistical approach, for example, using a form of transition state theory and comparing calculated Gibbs energies along the reaction coordinate(s). However, there are cases where this approach fails, notably when the vibrational relaxation of the molecule to its statistical equilibrium occurs on the same time scale as the reaction dynamics, whether it is caused by slow relaxation, a fast reaction, or both. These nonstatistical phenomena are then often explored computationally using (quasi)classical ab initio molecular dynamics by calculating a large number of trajectories while being prone to issues such as zero-point energy leakage. On the other side of the field, we see resource-intensive quantum dynamics simulations, which significantly limit the size of explorable systems. We find that using a Fermi's golden rule type of model for vibrational relaxation, based on anharmonic coupling constants, we can extract the same qualitative information while giving insights into how to enhance (or destroy) the bottlenecks causing the phenomena. We present this model as a middle ground for exploring complex nonstatistical behavior, capable of treating medium-sized organic molecules or biologically relevant fragments. We also cover the challenges involved, in particular quantifying the excess energy in terms of vibrational modes. Relying on readily available electronic structure methods and providing results in a simple master equation form, this model shows promise as a screening tool for opportunities in mode-selective chemistry without external control.

σ-dominated charge transport in sub-nanometer molecular junctions.

Quantum tunneling conductance of molecular junctions originates from the charge transport through the π-orbitals (π-transport) and the σ-orbitals (σ-transport) of the molecules, but the σ-transport can not be observed due to the more rapid decay of the tunneling conductance in the σ-system compared to that in the π-system. Here, we demonstrate that dominant σ-transport can be observed in π-conjugated molecular junctions at the sub-nanometer scale using the scanning tunneling microscope break junction technique (STM-BJ). We have found that the conductance of meta-connected picolinic acid, which mainly occurs by σ-transport, is ∼35 times higher than that of its para-isomer, which is entirely different from what is expected from π-transport through these systems. Flicker noise analysis reveals that the transport through the meta-connection exhibits more through-bond transport than the para-counterpart and density functional theory (DFT) shows that the σ-system provides the dominant transport path. These results reveal that the σ-electrons, rather than the π-electrons, can dominate charge transport through conjugated molecular junctions at the sub-nanometer scale, and this provides a new avenue toward the future miniaturization of molecular devices and materials.

Making the Most of Nothing: One-Class Classification for Single-Molecule Transport Studies.

Single-molecule experiments offer a unique means to probe molecular properties of individual molecules-yet they rest upon the successful control of background noise and irrelevant signals. In single-molecule transport studies, large amounts of data that probe a wide range of physical and chemical behaviors are often generated. However, due to the stochasticity of these experiments, a substantial fraction of the data may consist of blank traces where no molecular signal is evident. One-class (OC) classification is a machine learning technique to identify a specific class in a data set that potentially consists of a wide variety of classes. Here, we examine the utility of two different types of OC classification models on four diverse data sets from three different laboratories. Two of these data sets were measured at cryogenic temperatures and two at room temperature. By training the models solely on traces from a blank experiment, we demonstrate the efficacy of OC classification as a powerful and reliable method for filtering out blank traces from a molecular experiment in all four data sets. On a labeled 4,4'-bipyridine data set measured at 4.2 K, we achieve an accuracy of 96.9 ± 0.3 and an area under the receiver operating characteristic curve of 99.5 ± 0.3 as validated over a fivefold cross-validation. Given the wide range of physical and chemical properties that can be probed in single-molecule experiments, the successful application of OC classification to filter out blank traces is a major step forward in our ability to understand and manipulate molecular properties.

Electromigration Forces on Atoms on Graphene Nanoribbons: The Role of Adsorbate-Surface Bonding.

The synthesis of the two-dimensional (2D) material graphene and nanostructures derived from graphene has opened up an interdisciplinary field at the intersection of chemistry, physics, and materials science. In this field, it is an open question whether intuition derived from molecular or extended solid-state systems governs the physical properties of these materials. In this work, we study the electromigration force on atoms on 2D armchair graphene nanoribbons in an electric field using ab initio simulation techniques. Our findings show that the forces are related to the induced charges in the adsorbate-surface bonds rather than only to the induced atomic charges, and the left and right effective bond order can be used to predict the force direction. Focusing in particular on 3d transition metal atoms, we show how a simple model of a metal atom on benzene can explain the forces in an inorganic chemistry picture. This study demonstrates that atom migration on 2D surfaces in electric fields is governed by a picture that is different from the commonly used electrostatic description of a charged particle in an electric field as the underlying bonding and molecular orbital structure become relevant for the definition of electromigration forces. Accordingly extended models including the ligand field of the atoms might provide a better understanding of adsorbate diffusion on surfaces under nonequilibrium conditions.

Understanding Current Density in Molecules Using Molecular Orbitals.

While the use of molecular orbitals (MOs) and their isosurfaces to explain physical phenomena in chemical systems is a time-honored tool, we show that the nodes are an equally important component for understanding the current density through single-molecule junctions. We investigate three different model systems consisting of an alkane, alkene, and even [n]cumulene and show that we can explain the form of the current density using the MOs of the molecule. Essentially, the MOs define the region in which current can flow and their gradients define the direction in which current flows within that region. We also show that it is possible to simplify the current density for improved understanding by either partitioning the current density into more chemically intuitive parts, such as σ- and π-systems, or by filtering out MOs with negligible contributions to the overall current density. Our work highlights that it is possible to infer a non-equilibrium property (current density) given only equilibrium properties (MOs and their gradients), and this, in turn, grants deeper insight into coherent electron transport.

Visualizing and comparing quantum interference in the π-system and σ-system of organic molecules.

Quantum interference effects in conjugated molecules have been well-explored, with benzene frequently invoked as a pedagogical example. These interference effects have been understood through a quantum interference map in which the electronic transmission is separated into interfering and non-interfering terms, with a focus on the π-orbitals for conjugated molecules. Recently, saturated molecules have also been reported to exhibit destructive quantum interference effects; however, the very different σ-orbital character in these molecules means that it is not clear how orbital contributions manifest. Herein, we demonstrate that the quantum interference effects in conjugated molecules are quite different from those observed in saturated molecules, as demonstrated by the quantum interference map. While destructive interference at the Fermi energy in the π-system of benzene arises from interference terms between paired occupied and virtual orbitals, this is not the case at the Fermi energy in saturated systems. Instead, destructive interference is evident when contributions from a larger number of non-paired orbitals cancel, leading to more subtle and varied manifestations of destructive interference in saturated systems.

Trusting our machines: validating machine learning models for single-molecule transport experiments.

In this tutorial review, we will describe crucial aspects related to the application of machine learning to help users avoid the most common pitfalls. The examples we present will be based on data from the field of molecular electronics, specifically single-molecule electron transport experiments, but the concepts and problems we explore will be sufficiently general for application in other fields with similar data. In the first part of the tutorial review, we will introduce the field of single-molecule transport, and provide an overview of the most common machine learning algorithms employed. In the second part of the tutorial review, we will show, through examples grounded in single-molecule transport, that the promises of machine learning can only be fulfilled by careful application. We will end the tutorial review with a discussion of where we, as a field, could go from here.

Substituent Control of σ-Interference Effects in the Transmission of Saturated Molecules.

The single-molecule conductance of saturated molecules can potentially be fully suppressed by destructive quantum interference in their σ-system. However, only few molecules with σ-interference have been identified, and the structure-property relationship remains to be elucidated. Here, we explore the role of substituents in modulating the electronic transmission of saturated molecules. In functionalized bicyclo[2.2.2]octanes, the transmission is suppressed by σ-interference when fluorine substituents are applied. For bicyclo[2.2.2]octasilane and -octagermanes, the transmission is suppressed when carbon-based substituents are used, and such molecules are likely to be highly insulating. For the carbon-based substituents, we find a strong correlation between the appropriate Hammett constants and the transmission. The substituent effect enables systematic optimization of the insulating properties of saturated molecular cores.

Destructive quantum interference in heterocyclic alkanes: the search for ultra-short molecular insulators.

Designing highly insulating sub-nanometer molecules is difficult because tunneling conductance increases exponentially with decreasing molecular length. This challenge is further enhanced by the fact that most molecules cannot achieve full conductance suppression with destructive quantum interference. Here, we present results for a series of small saturated heterocyclic alkanes where we show that conductance is suppressed due to destructive interference. Using the STM-BJ technique and density functional theory calculations, we confirm that their single-molecule junction conductance is lower than analogous alkanes of similar length. We rationalize the suppression of conductance in the junctions through analysis of the computed ballistic current density. We find there are highly symmetric ring currents, which reverse direction at the antiresonance in the Landauer transmission near the Fermi energy. This pattern has not been seen in earlier studies of larger bicyclic systems exhibiting interference effects and constitutes clear-cut evidence of destructive σ-interference. The finding of heterocyclic alkanes with destructive quantum interference charts a pathway for chemical design of short molecular insulators using organic molecules.

Quantification of the Helicality of Helical Molecular Orbitals.

The frontier molecular orbital (MO) topology of linear carbon molecules, such as polyynes, can be visually identified as helices. However, there is no clear way to quantify the helical curvature of these π-MOs, and it is thus challenging to quantify correlations between the helical curvature and molecular properties. In this paper, we develop a method that enables us to compute the helical curvature of MOs based on their nodal planes. Using this method, we define a robust way of quantifying the helical nature of MOs (helicality) by their deviation from a perfect helix. We explore several limiting cases, including polyynes, metallacumulenes, cyclic allenes, and spiroconjugated systems, where the change in helical curvature is subtle yet clearly highlighted with this method. For example, we show that strain only has a minor effect on the helicality of the frontier orbitals of cycloallenes and that the MOs of spiroconjugated systems are close to perfect helices around the spiro-carbon. Our work provides a well-defined method for assessing orbital helicality beyond visual inspection of MO isosurfaces, thus paving the way for future studies of how the helicality of π-MOs affects molecular properties.

Simultaneous Suppression of π- and σ-Transmission in π-Conjugated Molecules.

Molecular dielectric materials require ostensibly conflicting requirements of high polarizability and low conductivity. As previous efforts toward molecular insulators focused on saturated molecules, it remains an open question whether π- and σ-transport can be simultaneously suppressed in conjugated systems. Here, we demonstrate that there are conjugated molecules where the σ-transmission is suppressed by destructive σ-interference, while the π-transmission can be suppressed by a localized disruption of conjugation. Using density functional theory, we study the Landauer transmission and ballistic current density, which allow us to determine how the transmission is affected by various structural changes in the molecule. We find that in para-linked oligophenyl rings the σ-transmission can be suppressed by changing the remaining hydrogens to methyl groups due to the inherent gauche-like structure of the carbon backbone within a benzene ring, similar to what was previously seen in saturated systems. At the same time, the methyl groups fulfill a dual purpose as they modulate the twist angle between neighboring phenyl rings. When neighboring rings are orthogonal to each other, the transmission through both π- and σ-systems is effectively suppressed. Alternatively, breaking conjugation in a single phenyl ring by saturating two carbons atoms with two methyl substituents on each carbon, results in suppressed π- and σ-transport independent of dihedral angle. These two strategies demonstrate that methyl-substituted oligophenyls are promising candidates for the development of molecular dielectric materials.

Permethylation Introduces Destructive Quantum Interference in Saturated Silanes.

The single-molecule conductance of silanes is suppressed due to destructive quantum interference in conformations with cisoid dihedral angles along the molecular backbone. Yet, despite the structural similarity, σ-interference effects have not been observed in alkanes. Here we report that the methyl substituents used in silanes are a prerequisite for σ-interference in these systems. Through density functional theory calculations, we find that the destructive interference is not evident to the same extent in nonmethylated silanes. We find the same is true in alkanes as the transmission is significantly suppressed in permethylated cyclic and bicyclic alkanes. Using scanning tunneling microscope break-junction method we determine the single-molecule conductance of functionalized cyclohexane and bicyclo[2.2.2]octane that are found to be higher than that of equivalent permethylated silanes. Rather than the difference between carbon and silicon atoms in the molecular backbones, our calculations reveal that it is primarily the difference between hydrogen and methyl substituents that result in the different electron transport properties of nonmethylated alkanes and permethylated silanes. Chemical substituents play an important role in determining the single-molecule conductance of saturated molecules, and this must be considered when we improve and expand the chemical design of insulating organic molecules.

Helical orbitals and circular currents in linear carbon wires.

Disubstituted odd-carbon cumulenes are linear carbon wires with near-degenerate helical π-orbitals. Such cumulenes are chiral molecules but their electronic structure consists of helical orbitals of both chiralities. For these helical molecular orbitals to give rise to experimentally observable effects, the near-degenerate orbitals of opposite helicities must be split. Here we show how pyramidalized single-faced π-donors, such as the amine substituent, provide a strategy for splitting the helical molecular orbitals. The chirality induced by the amine substituents allow for systematic control of the helicity of the frontier orbitals. We examine how the helical orbitals in odd-carbon cumulenes control the coherent electron transport properties, and we explicitly predict two modes in the experimental single-molecule conductance for these molecules. We also show that the current density through these linear wires exhibits strong circular currents. The direction of the circular currents is systematically controlled by the helicity of the frontier molecular orbitals, and is therefore altered by changing between the conformations of the molecule. Furthermore, the circular currents are subject to a full ring-reversal around antiresonances in the Landauer transmission, emphasizing the relation to destructive quantum interference. With circular currents present around truly linear carbon wires, cumulenes are promising candidates for novel applications in molecular electronics.

The Bicyclo[2.2.2]octane Motif: A Class of Saturated Group 14 Quantum Interference Based Single-Molecule Insulators.

The electronic transmission through σ-conjugated molecules can be fully suppressed by destructive quantum interference, which makes them potential candidates for single-molecule insulators. The first molecule with clear suppression of the single-molecule conductance due to σ-interference was recently found in the form of a functionalized bicyclo[2.2.2]octasilane. Here we continue the search for potential single-molecule insulators based on saturated group 14 molecules. Using a high-throughput screening approach, we assess the electron transport properties of the bicyclo[2.2.2]octane class by systematically varying the constituent atoms between carbon, silicon, and germanium, thus exploring the full chemical space of 771 different molecules. The majority of the molecules in the bicyclo[2.2.2]octane class are found to be highly insulating molecules. Though the all-silicon molecule is a clear-cut case of σ-interference, it is not unique within its class and there are many potential molecules that we predict to be more insulating. The finding of this class of quantum interference based single-molecule insulators indicates that a broad range of highly insulating saturated group 14 molecules are likely to exist.