The role of dimensionality in the decay of surface effects

A Green's Function Approach for Determining Surface Induced Broadening and Shifting of Molecular Energy Levels

Upon adsorption of a molecule onto a surface, the molecular energy levels (MELs) broaden and change their alignment. This phenomenon directly affects electron transfer across the interface and is, therefore, a fundamental observable that influences electrochemical device performance. Here, we propose a rigorous parameter-free framework, built upon the theoretical construct of Green's functions, for studying the interface between a molecule and a bulk surface and its effect on MELs. The method extends beyond the usual wide-band limit approximation, and its generality allows its use with any level of electronic structure theory. We demonstrate its ability to predict the broadening and shifting of MELs as a function of intramolecular coupling, molecule/surface coupling, and the surface density of states for a molecule with two MELs adsorbed on a one-dimensional model metal surface. The new approach could help provide guidelines for the design and experimental characterization of electrochemical devices with optimal electron transport.

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. However, numerous studies have reported CBSs with distinctly non-semielliptical shapes, including loops (essentially deformed, asymmetric semiellipses), spikes, and vertical lines. The primary goal of this work is to explore the phenomenology of these shapes such that deeper physical insight can be obtained from a qualitative inspection of a material's CBS. By using several variations on the SSH model, we find that (i) vertical lines are unphysical numerical artifacts, (ii) spikes indicate perfectly evanescent states in the material that couple adjacent layers but do not transfer amplitude, and (iii) asymmetric loops result from hybridization. Secondarily, we also develop a strategy for eliminating any unphysical vertical lines from calculations, thereby improving computational techniques for CBS.

Resonance State Method for Electron Injection in Dye Sensitized Solar Cells

Herein, the ab initio method is applied to examine metastable molecular excited states on a solid surface using resonance state theory and Green's function. A formula for the complex energy correction that determines the decay rate is presented; the configuration interaction effect together with major molecule-surface interactions are considered in more detail as compared to previous studies. Furthermore, the lifetimes of the excited states of Ru-terpyridine dyes adsorbed on an anatase surface are calculated, and the effects of the molecular structure and adsorption mode on the electron injection rate are studied. Also, the adsorption structures and relative stabilities of a series of Ru-terpyridine dyes-including the black dye-are reported. An implicit solvation model is necessary to reliably calculate the alignment between the photoabsorption spectrum and the conduction band density of states, governing the injection rate. Finally, some of the factors that limit the injection ability of dyes are discussed.

Probing charge transfer dynamics in a single iron tetraphenylporphyrin dyad adsorbed on an insulating surface

Although the dynamics of charge transfer (CT) processes can be probed with ultimate lifetime resolution, the inability to control CT at the nanoscale is one of the most important roadblocks to revealing some of its deep fundamental aspects. In this work, we present an investigation of CT dynamics in a single iron tetraphenylporphyrin (Fe-TPP) donor/acceptor dyad adsorbed on a CaF2/Si(100) insulating surface. The tip of a scanning tunneling microscope (STM) is used to create local ionic states in one fragment of the dyad. The CT process is monitored by imaging subsequent changes in the neighbor acceptor molecule and its efficiency is mapped, revealing the influence of the initial excited state in the donor molecule. In the validation of the experiments, simulations based on density functional theory show that holes have a higher donor-acceptor CT rate compared to electrons and highlight a noticeable initial state dependence on the CT process. We leverage the unprecedented spatial resolution achieved in our experiments to show that the CT process in the dyad is governed via molecule-molecule coherent tunneling with negligible surface-mediated character.

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. Many studies over the last 80 years have directly or indirectly developed complex band structure for an impressive range of applications, but very few discuss its fundamentals or compare its various results. In this work we build upon these previous efforts to expose the physical foundation of complex band structure, which mathematically implies its existence. We find that a material's static and dynamic electronic structure are both completely described by complex band structure. Furthermore, we show that complex band structure reflects the minimal, intrinsic information contained in the material's Hamiltonian. These realizations then provide a context for comparing and unifying the different formulations and applications of complex band structure that have been reported over the years. Ultimately, this discussion introduces the idea of examining the amount of information contained in a material's Hamiltonian so that we can find and exploit the minimal information necessary for understanding a material's properties.

Molecule-lead coupling at molecular junctions: relation between the real- and state-space perspectives

We present insights into the lead-molecule coupling scheme in molecular electronics junctions. Using a "site-to-state" transformation that provides direct access to the coupling matrix elements between the molecular states and the eigenstate manifold of each lead, we find coupling bands whose character depends on the geometry and dimensionality of the lead. We use a standard tight-binding model to elucidate the origin of the coupling bands and explain their nature via simple "particle-in-a-box" type considerations. We further show that these coupling bands can shed light on the charge transport behavior of the junction. The picture presented in this study is not limited to the case of molecular electronics junctions and is relevant to any scenario where a finite molecular entity is coupled to a (semi)infinite system.