Vibrational spectra of α-glucose, β-glucose, and sucrose: anharmonic calculations and experiment

The anharmonic vibrational spectra of α-D-glucose, β-D-glucose, and sucrose are computed by the vibrational self-consistent field (VSCF) method, using potential energy surfaces from electronic structure theory, for the lowest energy conformers that correspond to the gas phase and to the crystalline phase, respectively. The results are compared with ultraviolet-infrared (UV-IR) spectra of phenyl β-D-glucopyranoside in a molecular beam, with literature results for sugars in matrices and with new experimental data for the crystalline state. Car-Parrinello dynamics simulations are also used to study temperature effects on the spectra of α-D-glucose and β-D-glucose and to predict their vibrational spectra at 50, 150, and 300 K. The effects of temperature on the spectral features are analyzed and compared with results of the VSCF calculations conducted at 0 K. The main results include: (i) new potential surfaces, constructed from Hartree-Fock, adjusted to fit harmonic frequencies from M?ller-Plesset (MP2) calculations, that give very good agreement with gas phase, matrix, and solid state spectra; (ii) computed infrared spectra of the crystalline solid of α-glucose, which are substantially improved by including mimic groups that represent the effect of the solid environment on the sugar; and (iii) identification of a small number of combination-mode transitions, which are predicted to be strong enough for experimental observation. The results are used to assess the role of anharmonic effects in the spectra of the sugars in isolation and in the solid state and to discuss the spectroscopic accuracy of potentials from different electronic structure methods.     

Interaction and reaction of the hydroxyl ion with β-d-galactose and its hydrated complex: an ab initio molecular dynamics study

The interaction of OH(-) with the sugar β-d-galactose is studied computationally, with Ab Initio Molecular Dynamics (AIMD) as the prime tool. The main findings are: (1) the OH(-) abstracts a proton from the sugar in a barrier-less process, yielding H(2)O and a Deprotonated beta-d-Galactose anion, (Dep-beta-d-G)(-). (2) This reaction can be reversed when two additional H(2)O molecules are present in the sugar. (3) At 500 K, a ring-opening reaction occurs in (Dep-beta-d-G)(-) within a timescale of 10 ps. The (neutral) sugar itself is stable over this timescale, and well beyond. This indicates that OH(-) can catalyze the degradation of β-d-galactose. Implications of this process are briefly discussed.     

Chromatic number, clique subdivisions, and the conjectures of Hajós and Erdős-Fajtlowicz

For a graph G, let χ(G) denote its chromatic number and σ(G) denote the order of the largest clique subdivision in G. Let H(n) be the maximum of χ(G)=σ(G) over all n-vertex graphs G. A famous conjecture of Hajós from 1961 states that σ(G) ≥ χ(G) for every graph G. That is, H(n)≤1 for all positive integers n. This conjecture was disproved by Catlin in 1979. Erd?s and Fajtlowicz further showed by considering a random graph that H(n)≥cn ^1/2/logn for some absolute constant c>0. In 1981 they conjectured that this bound is tight up to a constant factor in that there is some absolute constant C such that χ(G)=σ(G) ≤ Cn ^1/2/logn for all n-vertex graphs G. In this paper we prove the Erd?s-Fajtlowicz conjecture. The main ingredient in our proof, which might be of independent interest, is an estimate on the order of the largest clique subdivision which one can find in every graph on n vertices with independence number α.     

Beyond nC60: strategies for identification of transformation products of fullerene oxidation in aquatic and biological samples

Owing to their exceptional properties and versatility, fullerenes are in widespread use for numerous applications. Increased production and use of fullerenes will inevitably result in accelerated environmental release. However, study of the occurrence, fate, and transport of fullerenes in the environment is complicated because a variety of surface modifications can occur as a result of either intentional functionalization or natural processes. To gain a better understanding of the effect and risk of fullerenes on environmental health, it is necessary to acquire reliable data on the parent compounds and their congeners. Whereas currently established quantification methods generally focus on analysis of unmodified fullerenes, we discuss in this review the occurrence and analysis of oxidized fullerene congeners (i.e., their corresponding epoxides and polyhydroxylated derivatives) in the environment and in biological specimens. We present possible strategies for detection and quantification of parent nanomaterials and their various derivatives.     

On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph K _N contains a monochromatic copy of H. A famous result of Chváatal, Rödl, Szemerédi and Trotter states that there exists a constant c(Δ) such that r(H) ≤ c(Δ)n for every graph H with n vertices and maximum degree Δ. The important open question is to determine the constant c(Δ). The best results, both due to Graham, Rödl and Ruciński, state that there are positive constants c and c′ such that $2^{c'\Delta } \leqslant c(\Delta ) \leqslant ^{c\Delta \log ^2 \Delta }$ . We improve this upper bound, showing that there is a constant c for which c(Δ) ≤ 2 ^cΔlogΔ . The induced Ramsey number r _ind (H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd?s conjectured the existence of a constant c such that, for any graph H on n vertices, r _ind (H) ≤ 2 ^cnlogn . We move a step closer to proving this conjecture, showing that r _ind (H) ≤ 2 ^cnlogn . This improves upon an earlier result of Kohayakawa, Prömel and Rödl by a factor of logn in the exponent.     

Polarization memory in single quantum dots

We measured the polarization memory of excitonic and biexcitonic optical transitions from single quantum dots at either positive, negative or neutral charge states. Positive, negative and no circular or linear polarization memory was observed for various spectral lines, under the same quasi-resonant excitation below the wetting layer bandgap. We developed a model which explains both qualitatively and quantitatively the experimentally measured polarization spectrum for all these optical transitions. We consider quite generally the loss of spin orientation of the photogenerated electron–hole pair during their relaxation towards the many-carrier ground states. Our analysis unambiguously demonstrates that while electrons maintain their initial spin polarization to a large degree, holes completely dephase.