Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. II. Extended Results for Square-Lattice Chromatic Polynomial

We study the chromatic polynomials for m×n square-lattice strips, of width 9m13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.     

Unusual Corrections to Scaling in the 3-State Potts Antiferromagnet on a Square Lattice

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae ² (1+be ^– +···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.     

Calculation of quantum tunneling for a spatially extended defect: the dislocation kink in copper has a low effective mass

Several experiments indicate that there are atomic tunneling defects in plastically deformed metals. How this is possible has not been clear, given the large mass of the metal atoms. Using a classical molecular-dynamics calculation, we determine the structures, energy barriers, effective masses, and quantum tunneling rates for dislocation kinks and jogs in copper screw dislocations. We find that jogs are unlikely to tunnel, but the kinks should have large quantum fluctuations. The kink motion involves hundreds of atoms each shifting a tiny amount, leading to a small effective mass and tunneling barrier.     

STM induced light from nontrivial metal structures: Local variations in emission efficiency

Scanning tunneling microscopy is performed on a gold surface which is structured on a length scale of 10–100 nm by colloidal lithography and the light emission induced by the tunneling electrons is investigated. The lithographically defined structure is reflected in a contrast in photon emission. It turns out that a major contrast mechanism depends only on the local geometry of the tunnel contact. Remarkable variations in photon images are observed, dark flat areas and bright slopes as well as the inverted case may be obtained upon imaging with different tips. A qualitative explanation for this behavior is proposed.     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

Fe-contacts on InAs(100) and InP(100) characterised by conversion electron Mössbauer spectroscopy

We have grown 4 nm thin films of ⁵⁷Fe on InAs(100) and InP(100) surfaces by use of MBE and studied the samples by ⁵⁷Fe conversion electron Mössbauer spectroscopy. In the case of InAs, the Mössbauer spectrum showed a sextet due to α-Fe and a further magnetically split component with slightly smaller hyperfine field, which is attributed to interface components. This result indicates that there is a relatively sharp interface between Fe and InAs. On the contrary, the spectrum of the InP sample showed a sextet with very broad lines and a smaller average hyperfine field. This suggests a strong chemical reaction between iron and the substrate, which results in the formation of a poorly crystalline phase.     

Determination of ionic metabolites from ethylene glycol in human blood by isotachophoresis

Conditions for isotachophoretic determination of anionic metabolites in blood from ethylene glycol in poisoned humans were established. Leading electrolytes with 5 mM chloride and and 2.5 gave good separation. Optimal separation was found with leading electrolytes at pH 2.5, and 10 mM acetic acid as terminating electrolyte. Separation and quantification of four out of six metabolites were possible. The four were glycolic acid, glyoxylic acid, oxalic acid and formic acid. Besides these compounds, citric acid, lactic acid, and alpha- and beta-hydroxybutyric acid were separated and quantified. The formation of mixed zones did not give any serious problems, although in samples with high amounts of glycolic acid we had to reduce the maximum injected amount from 3 to 1 microliter. This method might be valuable in further studies of the mechanism of ethylene glycol toxicity and as an important supplement in the diagnosis of late stages of ethylene glycol poisoning in which the glycol has been metabolized to glycolic acid.     

Transition‐Metal‐Free Formal Sonogashira Coupling and α‐Carbonyl Arylation Reactions

Transition‐metal‐free formal Sonogashira coupling and α‐carbonyl arylation reactions have been developed. These transformations are based on the nucleophilic aromatic substitution (S_NAr) of β‐carbonyl sulfones to electron‐deficient aryl fluorides, producing a key intermediate that, depending on the reaction conditions, gives the aromatic alkynes or α‐aryl carbonyl compounds. The development of these reactions is presented and, based on investigations under basic and acidic conditions, mechanisms have been proposed. To develop the formal Sonogashira coupling further, a milder, two‐step protocol is also disclosed that expands the reaction concept. The scope of these reactions is demonstrated for the synthesis of Sonogashira and α‐carbonyl arylated products from a range of electron‐deficient aryl fluorides with a variety of functional groups and aryl‐, heteroaryl‐, alkyl‐, and alkoxy‐substituted sulfone nucleophiles. These transition‐metal‐free reactions complement the metal‐catalyzed versions in terms of substitution patterns, simplicity, and reaction conditions.