Density functional theory investigation of competitive free-radical processes during the thermal cracking of methylated polyaromatics: estimation of kinetic parameters

Density functional B3LYP and BH&HLYP calculations with the 6-31G** basis set have been performed to investigate elementary reactions playing an important role in the pyrolysis of 1-methylnaphthalene. The pathways describing the destiny of the main radicals, H, methyl, hydromethylnaphthyl and methylnaphthyl, have been studied. At low temperature, addition of H atoms on the aromatic ring is favored over hydrogen abstraction. Except at low temperature (below 400 K), the hydromethylnaphthyl radical undergoes preferentially a loss of hydrogen rather than a bimolecular hydrogen transfer with methylnaphthalene or addition reaction on methylnaphthalene forming a hydrogenated dimer. In the range 400-750 K, the formation of methane by hydrogen abstraction of methyl radical on methylnaphthalene is predominant compared to the formation of hydrodimethylnaphthalenes by addition reaction. Rate constants of reactions describing the formation of heavy products like methyldinaphthylmethanes or dimethylbinaphthalenes have been calculated and discussed. They are also compared to recombination reactions from the literature. Rate constants of these reactions have been computed using transition state theory and can be integrated in kinetic radical schemes of methylated polyaromatic compounds pyrolysis from geological to laboratory conditions.     

Communication: Bond length alternation of conjugated oligomers: Another step on the fifth rung of Perdew's ladder of functional

In this work, we present the application of the hybrid short-range density functional theory/long-range MP2 energy gradients to the bond length alternation in polymethineimine and polyacetylene conjugated oligomers. Compared to other density functional calculations, our results are quite superior, even to fourth rung functionals, usually better than MP2 and very close to the available CCSD(T) values.     

Unbounded asymmetry of stretch factors

A result of Handel–Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group F_N$F_N$ and its inverse is bounded by a constant C_N$C_N$. In this short note, we show that this constant C_N$C_N$ cannot be chosen independent of the rank N.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

A dual extremum principle for a population equation

A dual extremum principle for the Verhulst-Pearl population equation is constructed using a complementary variational technique. The dual formulation utilizes a minimum principle recently developed by Leitmann to convert the functional optimization problem into a parameter optimization problem.This research was supported in part by NASA Grant No. NGR-36-010-024. The first author would like to thank Dr. W. Stadler, Department of Mechanical Engineering, University of California, Berkeley, for his valuable suggestions.     

Two-generator subgroups of the pure braid group

We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.