Interpreting non-semielliptical complex bands.

Complex band structure (CBS) emerges when translational symmetry is broken and material states with complex wavevectors become admissible. The resulting complex bands continuously connect conventional bands and their shapes are directly related to measurable physical quantities. To date, interpretations of complex bands usually assume they are semielliptical because this is the shape produced by the Su-Schrieffer-Heeger (SSH) model.

Complex band structure and electronic transmission eigenchannels.

It is natural to characterize materials in transport junctions by their conductance length dependence, β. Theoretical estimations of β are made employing two primary theories: complex band structure and density functional theory (DFT) Landauer transport. It has previously been shown that the β value derived from total Landauer transmission can be related to the β value from the smallest |k| complex band; however, it is an open question whether there is a deeper relationship between the two.

A unified perspective of complex band structure: interpretations, formulations, and applications.

Complex band structure generalizes conventional band structure by also considering wavevectors with complex components. In this way, complex band structure describes both the bulk-propagating states from conventional band structure and the evanescent states that grow or decay from one unit cell to the next. Even though these latter states are excluded by translational symmetry, they become important when translational symmetry is broken via, for example, a surface or impurity.

Estimating the Landauer-Büttiker transmission function from single molecule break junction experiments.

When investigating the electronic response properties of molecules, experiments often measure conductance whereas computation predicts the transmission probability. Although Landauer-Büttiker theory usually relates the two, comparison between experiment and computation remains difficult because experimental data (specifically those from break junctions) are statistical and computational results are deterministic. In this work we develop tools to quantitatively estimate-with error bars-the shape of the Landauer-Büttiker transmission function directly from experimental statistics on conductance and thermopower (if the latter is also available).

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.

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.

Response to "Comment on 'Rethinking first-principles electron transport theories with projection operators: the problems caused by partitioning the basis set'" [J. Chem. Phys. 140, 177103 (2014)].

The thesis of Brandbyge's comment [J. Chem. Phys.

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.

The role of dimensionality in the decay of surface effects.

We computationally investigate the decay of surface effects in one-, two-, and three-dimensional materials using two-band tight-binding models. These general models facilitate a direct comparison between materials of differing dimensionality, which reveals that material dimensionality (not material-specific chemistry/physics) is the primary factor controlling the decay of surface effects. Our results corroborate more sophisticated, material-specific studies, finding that surface effects decay after ∼10, ∼25, and ≳ 100 layers in three-dimensional, two-dimensional, and one-dimensional materials, respectively.

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.

Model for adsorption of ligands to colloidal quantum dots with concentration-dependent surface structure.

A study of the adsorption equilibrium of solution-phase CdS quantum dots (QDs) and acid-derivatized viologen ligands (N-[1-heptyl],N'-[3-carboxypropyl]-4,4'-bipyridinium dihexafluorophosphate, V(2+)) reveals that the structure of the surfaces of the QDs depends on their concentration. This adsorption equilibrium is monitored through quenching of the photoluminescence of the QDs by V(2+) upon photoinduced electron transfer. When modeled with a simple Langmuir isotherm, the equilibrium constant for QD-V(2+) adsorption, K(a), increases from 6.

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 wire's resonance and diminish conductance near such a resonance. We also find that the interwire distance (related to the adlayer density) is a key quantity.

Guidelines for choosing molecular "alligator clip" binding motifs in electron transport devices.

We employ a one-electron, tight-binding model of an electrode-molecule-electrode junction to explore the fundamental relationship between adsorption geometry and electron transport, producing exact results (within this model). By varying the chemisorption location (e.g.

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 metal's 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.

A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated "m-mixing" problem.

An efficient split-operator technique for solving the time-dependent Schrödinger equation in an angular coordinate system is presented, where a fast spherical harmonics transform accelerates the conversions between angle and angular momentum representations. Unlike previous techniques, this method features facile inclusion of azimuthal asymmetries (solving the "m-mixing" problem), adaptive time stepping, and favorable scaling, while simultaneously avoiding the need for both kinetic and potential energy matrix elements. Several examples are presented.

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.

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.

Laser field alignment of organic molecules on semiconductor surfaces: toward ultrafast molecular switches.

An ultrafast, nanoscale molecular switch is proposed, based on extension of the concept of nonadiabatic alignment to surface-adsorbed molecules. The switch consists of a conjugated organic molecule adsorbed onto a semiconducting surface and placed near a scanning tunneling microscope tip. A low-frequency, polarized laser field is used to switch the system by orienting the molecule with the field polarization axis, enabling conductance through the junction.