Acyclic edge colorings of graphs

A proper coloring of the edges of a graph G is called acyclic if there is no 2‐colored cycle in G. The acyclic edge chromatic number of G, denoted by a′(G), is the least number of colors in an acyclic edge coloring of G. For certain graphs G, a′(G) ≥ Δ(G) + 2 where Δ(G) is the maximum degree in G. It is known that a′(G) ≤ 16 Δ(G) for any graph G. We prove that there exists a constant c such that a′(G) ≤ Δ(G) + 2 for any graph G whose girth is at least cΔ(G) log Δ(G), and conjecture that this upper bound for a′(G) holds for all graphs G. We also show that a′(G) ≤ Δ + 2 for almost all Δ‐regular graphs. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 157–167, 2001     

List Coloring of Random and Pseudo-Random Graphs

choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). It is shown that the choice number of the random graph G(n, p(n)) is almost surely whenever . A related result for pseudo-random graphs is proved as well. By a special case of this result, the choice number (as well as the chromatic number) of any graph on n vertices with minimum degree at least in which no two distinct vertices have more than common neighbors is at most . Received: October 13, 1997     

Determination of Deuterated Phenylalanine and Tyrosine in Egg Protein by GCQ

In order to study protein digestibility by means of noninvasive tracer techniques (stable isotopes), a representative oral tracer, i.e. a stable isotope labeled protein, is needed. Therefore, egg white containing L-[ring-²H₅]phenylalanine and L-[ring-²H₄]tyrosine was prepared. The aim of this study was to measure the isotopic enrichment of the labeled amino acids in the egg white. The use of a standard GC-MS, based on ion trap technology was found to be a reliable technique. The enrichment of L-[ring-²H₅]phenylalanine and L-[ring-²H₄]tyrosine, expressed in Molar Percent (MP) amounted to 23.2 MP and 2.8 MP respectively.     

Mutually exclusive hole and electron transfer coupling in cross stacked acenes

The topology of frontier molecular orbitals (FMOs) induces highly sensitive charge transfer coupling with variation in the intermolecular arrangement. A consistent optoelectronic property correlated to a specific aggregate architecture independent of the nature of the monomer is a rare phenomenon. Our theoretical investigation on stacked dimeric systems of linear [n]acenes (n = 2–5) and selected non-linear acenes with a D_2h point group reveals that the Greek cross (+) stacked orientation, irrespective of the molecular candidate, exhibits mutually exclusive hole and electron transfer couplings. The deactivation of either hole or electron transfer coupling is a consequence of the zero inter-orbital overlap between the highest occupied molecular orbitals (HOMOs) or lowest unoccupied molecular orbitals (LUMOs) of the monomers possessing gerade symmetry. In the Greek cross (+) stacked alignment, the (4n + 2) π-electronic acene systems with an odd number of benzenoids exhibit exclusive electron transfer coupling, while the even numbered acenes exhibit selective hole transfer coupling. The trend is reversed for representative 4n π-electronic acene systems. The effect of mutually exclusive charge transfer coupling in the hopping regime of charge transport was evaluated using semiclassical Marcus theory, and selective charge carrier mobility was exhibited by the Greek cross (+) stacks of the considered acene candidates. Additionally, the characteristic charge transfer coupling of the orthogonal acene stacks resulted in negligible short-range exciton coupling, inciting null exciton splitting at short interplanar distances. Engineering chromophores in precise angular orientations ensuring characteristic emergent properties can have tremendous potential in the rational design of advanced optoelectronic materials.

Acenes in the Greek cross (+) stack orientation exhibit selective hole and electron transfer coupling based on gerade symmetry in frontier molecular orbitals.     

Cover Feature: Effects of Microhydration on the Mechanisms of Hydrolysis and Cl− Substitution in Reactions of N2O5 and Seawater (ChemPhysChem 5/2023)

The reaction of N₂O₅ at atmospheric interfaces has recently received considerable attention due to its importance in atmospheric chemistry. N₂O₅ reacts preferentially with Cl⁻ to form ClNO₂/NO₃⁻ (Cl⁻ substitution), but can also react with H₂O to form 2HNO₃ (hydrolysis). In this paper, we explore these competing reactions in a theoretical study of the clusters N₂O₅/Cl⁻/nH₂O (n=2–5), resulting in the identification of three reaction motifs. First, we uncovered an S_N2-type Cl⁻ substitution reaction of N₂O₅ that occurs very quickly due to low barriers to reaction. Second, we found a low-lying pathway to hydrolysis via a ClNO₂ intermediate (two-step hydrolysis). Finally, we found a direct hydrolysis pathway where H₂O attacks N₂O₅ (one-step hydrolysis). We find that Cl⁻ substitution is the fastest reaction in every cluster. Between one-step and two-step hydrolysis, we find that one-step hydrolysis barriers are lower, making two-step hydrolysis (via ClNO₂ intermediate) likely only when concentrations of Cl⁻ are high.