Interplay between adsorbates and polarons: CO on rutile TiO2_2(110)

Polaron formation plays a major role in determining the structural, electrical and chemical properties of ionic crystals. Using a combination of first principles calculations and scanning tunneling microscpoy/atomic force microscopy (STM/AFM), we analyze the interaction of polarons with CO molecules adsorbed on the rutile TiO$_2$(110) surface. Adsorbed CO shows attractive coupling with polarons in the surface layer, and repulsive interaction with polarons in the subsurface layer. As a result, CO adsorption depends on the reduction state of the sample. For slightly reduced surfaces, many adsorption configurations with comparable adsorption energies exist and polarons reside in the subsurface layer. At strongly reduced surfaces, two adsorption configurations dominante: either inside an oxygen vacancy, or at surface Ti$_{5c}$ sites, coupled with a surface polaron

Formation and dynamics of small polarons on the rutile TiO2_2(110) surface

Charge trapping and formation of polarons is a pervasive phenomenon in transition metal oxide compounds, in particular at the surface, affecting fundamental physical properties and functionalities of the hosting materials. Here we investigate via first-principle techniques the formation and dynamics of small polarons on the reduced surface of titanium dioxide, an archetypal system for polarons, for a wide range of oxygen vacancy concentrations. We report how the essential features of polarons can be adequately accounted in terms of few quantities: the local structural and chemical environment, the attractive interaction between negatively charged polarons and positively charged oxygen vacancies, and the spin-dependent polaron-polaron Coulomb repulsion. We combined molecular dynamics simulations on realistic samples derived from experimental observations with simplified static models, aiming to disentangle the various variables at play. We find that depending on the specific trapping site, different types of polarons can be formed, with distinct orbital symmetries and different degree of localization and structural distortion. The energetically most stable polaron site is the subsurface Ti atom below the undercoordinated surface Ti atom, owing to a small energy cost to distort the lattice and a suitable electrostatic potential. Polaron-polaron repulsion and polaron-vacancy attraction determine the spatial distribution of polarons as well as the energy of the polaronic in-gap state. In the range of experimentally reachable oxygen vacancy concentrations the calculated data are in excellent agreement with observations, thus validating the overall interpretation

Direct assessment of the proton affinity of individual surface hydroxyls with non-contact atomic force microscopy

The state of protonation/deprotonation of surfaces has far-ranging implications in all areas of chemistry: from acid-base catalysis$^1$ and the electro- and photocatalytic splitting of water$^2$, to the behavior of minerals$^3$ and biochemistry$^4$. The acidity of a molecule or a surface site is described by its proton affinity (PA) and pK$_\mathrm{a}$ value (the negative logarithm of the equilibrium constant of the proton transfer reaction in solution). For solids, in contrast to molecules, the acidity of individual sites is difficult to assess. For mineral surfaces such as oxides they are estimated by semi-empirical concepts such as bond-order valence sums$^5$, and also increasingly modeled with first-principles molecular dynamics simulations$^{6,7}$. Currently such predictions cannot be tested - the experimental measures used for comparison are typically average quantities integrated over the whole surface or, in some cases, individual crystal facets$^8$, such as the point of zero charge (pzc)$^9$. Here we assess individual hydroxyls on In$_2$O$_3$(111), a model oxide with four different types of surface oxygen atoms, and probe the strength of their hydrogen bond with the tip of a non-contact atomic force microscope (AFM). The force curves are in quantitative agreement with density-functional theory (DFT) calculations. By relating the results to known proton affinities and pK$_\mathrm{a}$ values of gas-phase molecules, we provide a direct measure of proton affinity distributions at the atomic scale

Course Allocation via Stable Matching

The allocation of students to courses is a wide-spread and repeated task in higher education, often accomplished by a simple first-come first-served (FCFS) procedure. FCFS is neither stable nor strategy-proof, however. The Nobel Prize in Economic Sciences was awarded to Al Roth and Lloyd Shapley for theirwork on the theory of stable allocations. This theory was influential in many areas, but found surprisingly little application in course allocation as of yet. In this paper, different approaches for course allocation with a focus on appropriate stablematchingmechanisms are surveyed. Two such mechanisms are discussed in more detail, the Gale- Shapley student optimal stable mechanism (SOSM) and the efficiency adjusted deferred acceptance mechanism (EADAM). EADAM can be seen as a fundamental recent contribution which recovers efficiency losses from SOSM at the expense of strategy-proofness. In addition to these two important mechanisms, a survey of recent extensions with respect to the assignment of schedules of courses rather than individual courses is provided. The survey of the theoretical literature is complemented with results of a field experiment, which help understand the benefits of stable matching mechanisms in course allocation applications