A Note on Veraverbeke's Theorem

We give an elementary probabilistic proof of Veraverbeke's theorem for the asymptotic distribution of the maximum of a random walk with negative drift and heavy-tailed increments. The proof gives insight into the principle that the maximum is in general attained through a single large jump.     

Organometallic reactivity: the role of metal-ligand bond energies from a computational perspective

The association and dissociation of ligands plays a vital role in determining the reactivity of organometallic catalysts. Computational studies with density functional theory often fail to reproduce experimental metal-ligand bond energies, but recently functionals which better capture dispersion effects have been developed. Here we explore their application and discuss future challenges for computational studies of organometallic catalysis.     

Mechanically induced scission and subsequent thermal remending of perfluorocyclobutane polymers

Perfluorocyclobutane (PFCB) polymer solutions were subjected to pulsed ultrasound, leading to mechanically induced chain scission and molecular weight degradation. (19)F NMR revealed that the new, mechanically generated end groups are trifluorovinyl ethers formed by cycloreversion of the PFCB groups, a process that differs from thermal degradation pathways. One consequence of the mechanochemical process is that the trifluorovinyl ether end groups can be remended simply by subjecting the polymer solution to the original polymerization conditions, that is, heating to >150 °C. Stereochemical changes in the PFCBs, in combination with radical trapping experiments, indicate that PFCB scission proceeds via a stepwise mechanism with a 1,4-diradical intermediate, offering a potential mechanism for localized functionalization and cross-linking in regions of high stress.     

Hybrid density functional theory band structure engineering in hematite

We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.     

A new boundary integral equation for molecular electrostatics with charges over whole space

In this paper, a new integral equation of electrostatics is proposed as an integral form of a basic dielectric continuum model, which is traditionally represented in a form of Poisson differential equation. As an application in protein simulations, the new integral equation is reduced to a second kind Fredholm boundary integral equation on the interface between the solute and solvent regions for a piecewise constant permittivity function, together with two new integral expressions for the electrostatics within the solute and solvent regions. The new integral equation and expressions work for any charge problem over the whole space (including the one with charges on the interface). This valuable feature is verified numerically for a dielectric sphere model with a point charge inside, outside, or on the sphere in this paper.     

A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on R^n.We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation,including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions.     

Lift‐off protocols for thin films for use in EXAFS experiments

Lift‐off protocols for thin films for improved extended X‐ray absorption fine structure (EXAFS) measurements are presented. Using wet chemical etching of the substrate or the interlayer between the thin film and the substrate, stand‐alone high‐quality micrometer‐thin films are obtained. Protocols for the single‐crystalline semiconductors GeSi, InGaAs, InGaP, InP and GaAs, the amorphous semiconductors GaAs, GeSi and InP and the dielectric materials SiO₂ and Si₃N₄ are presented. The removal of the substrate and the ability to stack the thin films yield benefits for EXAFS experiments in transmission as well as in fluorescence mode. Several cases are presented where this improved sample preparation procedure results in higher‐quality EXAFS data compared with conventional sample preparation methods. This lift‐off procedure can also be advantageous for other experimental techniques (e.g. small‐angle X‐ray scattering) that benefit from removing undesired contributions from the substrate.     

Reversible Postsynthetic Modification in a Metal–Organic Framework

Postsynthetic modification (PSM) of metal–organic frameworks (MOFs) provides access to functional materials and advanced porous solid engineering. Herein, we report the reversible PSM of a multivariate isoreticular MOF by applying dynamic furan-maleimide Diels–Alder (DA) chemistry. The key step involves incorporating a furan group into the MOF via “click” PSM, which can then undergo repeated cycles of modification and de-modification with maleimides. The structural integrity, crystallinity, and porosity of the furan-appended MOF remained intact even after three consecutive PSM/de-modification cycles using three different functionalized maleimides.     

Thermodynamics and Spectroscopy of Halogen- and Hydrogen-Bonded Complexes of Haloforms with Aromatic and Aliphatic Amines

Similarities and differences of halogen and hydrogen bonding were explored via UV–Vis and ¹H NMR measurements, X-ray crystallography and computational analysis of the associations of CHX₃ (X=I, Br, Cl) with aromatic (tetramethyl-p-phenylenediamine) and aliphatic (4-diazabicyclo[2,2,2]octane) amines. When the polarization of haloforms was taken into account, the strengths of these complexes followed the same correlation with the electrostatic potentials on the surfaces of the interacting atoms. However, their spectral properties were quite distinct. While the halogen-bonded complexes showed new intense absorption bands in the UV–Vis spectra, the absorptions of their hydrogen-bonded analogues were close to the superposition of the absorption of reactants. Additionally, halogen bonding led to a shift in the NMR signal of haloform protons to lower ppm values compared with the individual haloforms, whereas hydrogen bonding of CHX₃ with aliphatic amines resulted in a shift in the opposite direction. The effects of hydrogen bonding with aromatic amines on the NMR spectra of haloforms were ambivalent. Titration of all CHX₃ with these nucleophiles produced consistent shifts in their protons’ signals to lower ppm values, whereas calculations of these pairs produced multiple hydrogen-bonded minima with similar structures and energies, but opposite directions of the NMR signals’ shifts. Experimental and computational data were used for the evaluation of formation constants of some halogen- and hydrogen-bonded complexes between haloforms and amines co-existing in solutions.     

Single-molecule transistors: Electron transfer in the solid state

Single-molecule transistors (SMTs) incorporating individual small molecules are unique tools for examining the fundamental physics and chemistry of electronic transport in molecular systems at the single nanometer scale. We describe the fabrication and characterization of such devices, and the synthesis and surface attachment chemistry of novel transition metal complexes that have been incorporated into such SMTs. We present gate-modulated inelastic electron tunneling vibrational spectroscopy of single molecules, strong Kondo physics (T_K ∼ 75 K) as evidence of excellent molecule/electrode electronic coupling, and a demonstration that covalent attachment chemistry can produce SMTs that survive repeated thermal cycling to room temperature. We conclude with a look ahead at the prospects for these nanoscale systems.