Photoelectron diffraction: from phenomenological demonstration to practical tool

The potential of photoelectron diffraction—exploiting the coherent interference of directly-emitted and elastically scattered components of the photoelectron wavefield emitted from a core level of a surface atom to obtain structural information—was first appreciated in the 1970s. The first demonstrations of the effect were published towards the end of that decade, but the method has now entered the mainstream armoury of surface structure determination. This short review has two objectives: First, to outline the way that the idea emerged and the way this evolved in my own collaboration with Neville Smith and his colleagues at Bell Labs in the early years: Second, to provide some insight into the current state-of-the art in application of (scanned-energy mode) photoelectron diffraction to address two key issue in quantitative surface structure determination, namely, complexity and precision. In this regard a particularly powerful aspect of photoelectron diffraction is its elemental and chemical-state specificity

The adsorption structure of furan on Pd(1 1 1)

The structure of molecular furan, C4H4O, on Pd(1 1 1) has been investigated by O K-edge near-edge X-ray absorption fine structure (NEXAFS) and C 1s scanned-energy mode photoelectron diffraction (PhD). NEXAFS shows the molecule to be adsorbed with the molecular plane close to parallel to the surface, a conclusion confirmed by the PhD analysis. Chemical-state specific C 1s PhD data were obtained for the two inequivalent C atoms in the furan, the α-C atoms adjacent to the O atom, and the β-C atoms bonded only to C atoms, but only the PhD modulations for the α-C emitters were of sufficiently large amplitude for detailed evaluation using multiple scattering calculations. This analysis shows the α-C atoms to be located approximately 0.6 Å off-atop surface Pd atoms with an associated C–Pd bondlength of 2.13 ± 0.03 Å. Two alternative local geometries consistent with the data place the O atom in off-atop or near-hollow locations, and for each of these local structures there are two equally-possible registries relative to the fcc and hcp hollow sites. The results are in good agreement with earlier density functional theory calculations which indicate that the fcc and hcp registries are equally probable, but the PhD results fail to distinguish the two distinct local bonding geometries

Validation of the inverted adsorption structure for free-base tetraphenyl porphyrin on Cu(111)

Utilising normal incidence X-ray standing waves we rigourously scrutinise the “inverted model” as the adsorption structure of free-base tetraphenyl porphyrin on Cu(111). We demonstrate that the iminic N atoms are anchored at near-bridge adsorption sites on the surface displaced laterally by 1.1 ± 0.2 Å in excellent agreement with previously published calculations

A structural study of a C3H3 species coadsorbed with CO on Pd(1 1 1)

The combination of chemical-state-specific C 1s scanned-energy mode photoelectron diffraction (PhD) and O K-edge near-edge X-ray absorption fine structure (NEXAFS) has been used to determine the local adsorption geometry of the coadsorbed C3H3 and CO species formed on Pd(1 1 1) by dissociation of molecular furan. CO is found to adopt the same geometry as in the Pd(1 1 1)c(4 × 2)-CO phase, occupying the two inequivalent three-fold coordinated hollow sites with the C–O axis perpendicular to the surface. C3H3 is found to lie with its molecular plane almost parallel to the surface, most probably with the two ‘outer’ C atoms in equivalent off-atop sites, although the PhD analysis formally fails to distinguish between two distinct local adsorption sites

Identifying the Azobenzene/Aniline reaction intermediate on TiO2-(110) : a DFT Study

Density functional theory (DFT) calculations, both with and without dispersion corrections, have been performed to investigate the nature of the common surface reaction intermediate that has been shown to exist on TiO2(110) as a result of exposure to either azobenzene (C6H5N═NC6H5) or aniline (C6H5NH2). Our results confirm the results of a previous DFT study that dissociation of azobenzene into two adsorbed phenyl imide (C6H5N) fragments, as was originally proposed, is not energetically favorable. We also find that deprotonation of aniline to produce this surface species is even more strongly energetically disfavored. A range of alternative surface species has been considered, and while dissociation of azobenzene to form surface C6H4NH species is energetically favored, the same surface species cannot form from adsorbed aniline. On the contrary, adsorbed aniline is much the most stable surface species. Comparisons with experimental determinations of the local adsorption site, the Ti–N bond length, the molecular orientation, and the associated C 1s and N 1s photoelectron core level shifts are all consistent with the DFT results for adsorbed aniline and are inconsistent with other adsorbed species considered. Possible mechanisms for the hydrogenation of azobenzene required to produce this surface species are discussed

The One-Way Communication Complexity of Dynamic Time Warping Distance

We resolve the randomized one-way communication complexity of Dynamic Time Warping (DTW) distance. We show that there is an efficient one-way communication protocol using O~(n/alpha) bits for the problem of computing an alpha-approximation for DTW between strings x and y of length n, and we prove a lower bound of Omega(n / alpha) bits for the same problem. Our communication protocol works for strings over an arbitrary metric of polynomial size and aspect ratio, and we optimize the logarithmic factors depending on properties of the underlying metric, such as when the points are low-dimensional integer vectors equipped with various metrics or have bounded doubling dimension. We also consider linear sketches of DTW, showing that such sketches must have size Omega(n)