M. Reuter

Carborane-Based Pincers: Synthesis and Structure of SeBSe and SBS Pd(II) Complexes

We report the synthesis of several unique, boron-rich pincer complexes derived from m-carborane. The SeBSe and SBS pincer ligands can be synthesized via two independent synthetic routes and are metalated with Pd(II). These structures represent unique coordinating motifs, each with a Pd-B(2) bond chelated by two thio- or selenoether ligands. This class of structures serves as the first example of boron-metal pincer complexes and possesses several interesting electronic properties imposed by the m-carborane cage.

Signatures of Cooperative Effects and Transport Mechanisms in Conductance Histograms

We present a computational investigation into the line shapes of peaks in conductance histograms, finding that they possess high information content. In particular, the histogram peak associated with conduction through a single molecule elucidates the electron transport mechanism and is generally well-described by beta distributions. A statistical analysis of the peak corresponding to conduction through two molecules reveals the presence of cooperative effects between the molecules and also provides insight into the underlying conduction channels. This work describes tools for extracting additional interpretations from experimental statistical data, helping us better understand electron transport processes.

Molecular Conduction through Adlayers: Cooperative Effects Can Help or Hamper Electron Transport

We use a one-electron, tight-binding model of a molecular adlayer sandwiched between two metal electrodes to explore how cooperative effects between molecular wires influence electron transport through the adlayer. When compared to an isolated molecular wire, an adlayer exhibits cooperative effects that generally enhance conduction away from an isolated wires resonance and diminish conductance near such a resonance. We also find that the interwire distance (related to the adlayer density) is a key quantity. Substrate-mediated coupling induces most of the cooperative effects in dense adlayers, whereas direct, interwire coupling (if present) dominates in sparser adlayers. In this manner, cooperative effects through dense adlayers cannot be removed, suggesting an optimal adlayer density for maximizing conduction.

Molecular Transport Junctions with Semiconductor Electrodes: Analytical Forms for One-Dimensional Self-Energies †

Analytical self-energies for molecular interfaces with one-dimensional, tight-binding semiconductors are derived, along with analytical solutions to the electrode eigensystems. These models capture the fundamental differences between the transport properties of metals and semiconductors and also account for the appearance of surface states. When the models are applied to zero-temperature electrode-molecule-electrode conductance, junctions with two semiconductor electrodes exhibit a minimum bias threshold for generating current due to the absence of electrode states near the Fermi level. Molecular interactions with semiconductor electrodes additionally produce (i) non-negligible molecular-level shifting by mechanisms absent in metals and (ii) sensitivity of the transport to the semiconductor-molecule bonding configuration. Finally, the general effects of surface states on molecular transport are discussed.

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

Communication: Finding destructive interference features in molecular transport junctions

Associating molecular structure with quantum interference features in electrode-molecule-electrode transport junctions has been difficult because existing guidelines for understanding interferences only apply to conjugated hydrocarbons. Herein we use linear algebra and the Landauer-Büttiker theory for electron transport to derive a general rule for predicting the existence and locations of interference features. Our analysis illustrates that interferences can be directly determined from the molecular Hamiltonian and the molecule-electrode couplings, and we demonstrate its utility with several examples.

Closed-form Green Functions, Surface Effects, and the Importance of Dimensionality in Tight-Binding Metals

Closed-form expressions for all elements of a d-dimensional tight-binding metals Green function matrix are presented and used to explore edge effects of a surface. We find that, when moving from the surface into the bulk, the number of layers passed before the surfaced substrate behaves like the bulk decreases with dimensionality. In particular, the surface of a one-dimensional substrate becomes indistinguishable from the bulk after O(10(1)-10(2)) layers, a two-dimensional substrate after O(10(1)) layers, and a three-dimensional substrate after O(10(0)) layers. Finally, the effects of substrate dimensionality on molecule-substrate interactions are discussed.

Quantitative Interpretations of Break Junction Conductance Histograms in Molecular Electron Transport

We develop theoretical and computational tools for extracting quantitative molecular information from experimental conductance histograms for electron transport through single-molecule break junctions. These experimental setups always measure a combination of molecular conductance and direct electrode-electrode tunneling; our derivations explicitly incorporate the effects of such background tunneling. Validation of our models to simulated data shows that background tunneling is crucial for quantitative analyses (even in cases where it appears to be qualitatively negligible), and comparison to experimental data is favorable. Finally, we generalize these ideas to the case of molecules with a destructive interference feature and discuss potential signatures for interference in a conductance histogram.

Solving PDEs in irregular geometries with multiresolution methods I: Embedded Dirichlet boundary conditions ☆

In this work, we develop and analyze a formalism for solving boundary value problems in arbitrarily-shaped domains using the MADNESS (multiresolution adaptive numerical environment for scientific simulation) package for adaptive computation with multiresolution algorithms. We begin by implementing a previously-reported diffuse domain approximation for embedding the domain of interest into a larger domain (Li et al., 2009 [1]). Numerical and analytical tests both demonstrate that this approximation yields non-physical solutions with zero first and second derivatives at the boundary. This excessive smoothness leads to large numerical cancellation and confounds the dynamically-adaptive, multiresolution algorithms inside MADNESS. We thus generalize the diffuse domain approximation, producing a formalism that demonstrates first-order convergence in both near- and far-field errors. We finally apply our formalism to an electrostatics problem from nanoscience with characteristic length scales ranging from 0.0001 to 300 nm.

Rethinking first-principles electron transport theories with projection operators: The problems caused by partitioning the basis set

We revisit the derivation of electron transport theories with a focus on the projection operators chosen to partition the system. The prevailing choice of assigning each computational basis function to a region causes two problems. First, this choice generally results in oblique projection operators, which are non-Hermitian and violate implicit assumptions in the derivation. Second, these operators are defined with the physically insignificant basis set and, as such, preclude a well-defined basis set limit. We thus advocate for the selection of physically motivated, orthogonal projection operators (which are Hermitian) and present an operator-based derivation of electron transport theories. Unlike the conventional, matrix-based approaches, this derivation requires no knowledge of the computational basis set. In this process, we also find that common transport formalisms for nonorthogonal basis sets improperly decouple the exterior regions, leading to a short circuit through the system. We finally discuss the implications of these results for first-principles calculations of electron transport.