Raman spectra of complexes of HNO3 and NO3- with NO2 at surfaces and with N2O4 in solution

Raman spectra of HNO(3).NO(2) have been detected on liquid and solid surfaces in the presence of concentrated HNO(3) and NO(2) gas. The Raman spectrum of HNO(3) solutions containing N(2)O(4) has been partly reinterpreted in terms of contributions from HNO(3).N(2)O(4) and N(2)O(4).NO(3)(-) complexes.     

Complexes of HNO3 and NO3 - with NO2 and N2O4, and their potential role in atmospheric HONO formation

Calculations were performed to determine the structures, energetics, and spectroscopy of the atmospherically relevant complexes (HNO(3)).(NO(2)), (HNO(3)).(N(2)O(4)), (NO(3)(-)).(NO(2)), and (NO(3)(-)).(N(2)O(4)). The binding energies indicate that three of the four complexes are quite stable, with the most stable (NO(3)(-)).(N(2)O(4)) possessing binding energy of almost -14 kcal mol(-1). Vibrational frequencies were calculated for use in detecting the complexes by infrared and Raman spectroscopy. An ATR-FTIR experiment showed features at 1632 and 1602 cm(-1) that are attributed to NO(2) complexed to NO(3)(-) and HNO(3), respectively. The electronic states of (HNO(3)).(N(2)O(4)) and (NO(3)(-)).(N(2)O(4)) were investigated using an excited state method and it was determined that both complexes possess one low-lying excited state that is accessible through absorption of visible radiation. Evidence for the existence of (NO(3)(-)).(N(2)O(4)) was obtained from UV/vis absorption spectra of N(2)O(4) in concentrated HNO(3), which show a band at 320 nm that is blue shifted by 20 nm relative to what is observed for N(2)O(4) dissolved in organic solvents. Finally, hydrogen transfer reactions within the (HNO(3)).(NO(2)) and (HNO(3)).(N(2)O(4)) complexes leading to the formation of HONO, were investigated. In both systems the calculated potential profiles rule out a thermal mechanism, but indicate the reaction could take place following the absorption of visible radiation. We propose that these complexes are potentially important in the thermal and photochemical production of HONO observed in previous laboratory and field studies.     

On the densities of cliques and independent sets in graphs

Let r; s≥2 be integers. Suppose that the number of blue r-cliques in a red/blue coloring of the edges of the complete graph K _n is known and fixed. What is the largest possible number of red s-cliques under this assumption? The well known Kruskal-Katona theorem answers this question for r = 2 or s = 2. Using the shifting technique from extremal set theory together with some analytical arguments, we resolve this problem in general and prove that in the extremal coloring either the blue edges or the red edges form a clique.     

Judicious partitions of directed graphs

The area of judicious partitioning considers the general family of partitioning problems in which one seeks to optimize several parameters simultaneously, and these problems have been widely studied in various combinatorial contexts. In this paper, we study essentially the most fundamental judicious partitioning problem for directed graphs, which naturally extends the classical Max Cut problem to this setting: we seek bipartitions in which many edges cross in each direction. It is easy to see that a minimum outdegree condition is required in order for the problem to be nontrivial, and we prove that every directed graph with m edges and minimum outdegree at least two admits a bipartition in which at least edges cross in each direction. We also prove that if the minimum outdegree is at least three, then the constant can be increased to . If the minimum outdegree tends to infinity with n, then the constant increases to . All of these constants are best‐possible, and provide asymptotic answers to a question of Alex Scott. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 147–170, 2016     

Compatible Hamilton cycles in random graphs

A graph is Hamiltonian if it contains a cycle passing through every vertex. One of the cornerstone results in the theory of random graphs asserts that for edge probability , the random graph G(n, p) is asymptotically almost surely Hamiltonian. We obtain the following strengthening of this result. Given a graph , an incompatibility system over G is a family where for every , the set F_v is a set of unordered pairs . An incompatibility system is Δ‐bounded if for every vertex v and an edge e incident to v, there are at most Δ pairs in F_v containing e. We say that a cycle C in G is compatible with if every pair of incident edges of C satisfies . This notion is partly motivated by a concept of transition systems defined by Kotzig in 1968, and can be used as a quantitative measure of robustness of graph properties. We prove that there is a constant such that the random graph with is asymptotically almost surely such that for any μnp‐bounded incompatibility system over G, there is a Hamilton cycle in G compatible with . We also prove that for larger edge probabilities , the parameter μ can be taken to be any constant smaller than . These results imply in particular that typically in G(n, p) for , for any edge‐coloring in which each color appears at most μnp times at each vertex, there exists a properly colored Hamilton cycle. Furthermore, our proof can be easily modified to show that for any edge‐coloring of such a random graph in which each color appears on at most μnp edges, there exists a Hamilton cycle in which all edges have distinct colors (i.e., a rainbow Hamilton cycle). © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 533–557, 2016     

Triterpenoids from Eugenia grandis: structure elucidation by NMR spectroscopy

A new pentacyclic triterpenoid, 2alpha,3beta-dihydroxylup-12-en-28-oic acid (1) and a rarely encountered pentacyclic triterpenoid, 3beta-hydroxylup-12-en-28-oic acid (2), together with five known compounds, friedelin (3), 3beta-friedelinol (4), betulinic acid (5), oleanolic acid (6) and beta-sitosterol (7) were isolated from the chloroform extract of stem bark of Eugenia grandis (Syn: Syzygium grande). The structure and stereochemistry of the new compound (1) and the rarely encountered compound (2) were established by 1D and 2D NMR spectroscopic techniques. All the above isolated compounds from this plant are reported for the first time.     

The dynamics of water evaporation from partially solvated cytochrome c in the gas phase

The study of evaporation of water from biological macromolecules is important for the understanding of electrospray mass spectrometry experiments. In electrospray ionization (ESI), electrically charged nanoscale droplets are formed from solutions of, for example, proteins. Then evaporation of the solvent leads to dry protein ions that can be analyzed in the mass spectrometer. In this work the dynamics of water evaporation from native cytochrome c covered by a monolayer of water is studied by molecular dynamics (MD) simulations at constant energy. A model of the initial conditions of the process is introduced. The temperature of the protein drops by about 100 K during the 400 picoseconds of the simulations. This sharp drop in temperature causes the water evaporation rate to decrease by about an order of magnitude, leaving the protein with 50% to 90% of the original water molecules, depending on the initial temperature of the simulation. The structural changes of the protein upon desolvation were considered through calculations of the radius of gyration and the root mean square (RMS) of the protein. A variation of 0.4 A in the radius of gyration, together with an RMS value of less than 3 A, indicates only minor changes in the overall shape of the protein structure. The water coordination number of the solvation shell is much smaller than that for bulk water. The mobility of water is high at the beginning of the simulations and drops as the simulation progresses and the temperature decreases. Incomplete desolvation of protein ions was also observed in recent experiments.     

Metal Coordination Sphere Deformation Induced Highly Stokes-Shifted,Ultra Broadband Emission in 2D Hybrid Lead-Bromide Perovskites and Investigation of Its Origin

Published studies of layered (2D) (100)-oriented hybrid lead-bromide perovskites evidence a correlation between increased inter-octahedral (Pb-Br-Pb) distortions and the appearance of broadband white light emission. However, the impact of distortions within their constituent [PbBr₆]⁴⁻ octahedra has yet to be assessed. Herein, we report two new (100)-oriented 2D Pb-Br perovskites, whose structures display unusually high intra-octahedral distortions, whilst retaining minimal inter-octahedral distortions. Using a combination of temperature-dependent, power-dependent and time-resolved photoluminescence spectroscopic measurements, we show that increased intra-octahedral distortion induces exciton localization processes and leads to formation of multiple photoinduced emissive colour centres. Ultimately, this leads to highly Stokes-shifted, ultrabroad white light emission at room temperature.     

Large almost monochromatic subsets in hypergraphs

We show that for all ℓ and ε > 0 there is a constant c = c(ℓ, ε) > 0 such that every ℓ-coloring of the triples of an N-element set contains a subset S of size $ c\sqrt {\log N} $ c\sqrt {\log N} such that at least 1 − ε fraction of the triples of S have the same color. This result is tight up to the constant c and answers an open question of Erdős and Hajnal from 1989 on discrepancy in hypergraphs. For ℓ ≥ 4 colors, it is known that there is an ℓ-coloring of the triples of an N-element set whose largest monochromatic subset has cardinality only Θ(log log N). Thus, our result demonstrates that the maximum almost monochromatic subset that an ℓ-coloring of the triples must contain is much larger than the corresponding monochromatic subset. This is in striking contrast with graphs, where these two quantities have the same order of magnitude. To prove our result, we obtain a new upper bound on the ℓ-color Ramsey numbers of complete multipartite 3-uniform hypergraphs, which answers another open question of Erdős and Hajnal.     

Mechanical model for staggered bio-structure

A generic mechanical model for bio-composites, including stiff platelets arranged in a staggered order inside a homogeneous soft matrix, is proposed. Equations are formulated in terms of displacements and are characterized by a set of non-dimensional parameters. The displacements, stress fields and effective modulus of the composite are formulated. Two analytical models are proposed, one which includes the shear deformations along the entire medium and another simplified model, which is applicable to a slender geometry and yields a compact expression for the effective modulus. The results from the models are validated by numerical finite element simulations and found to be compatible with each other for a wide range of geometrical and material properties. Finally, the models are solved for two bio-structures, nacre and a collagen fibril, and their solutions are discussed.