Mechanisms for the reaction of thiophene and methylthiophene with singlet and triplet molecular oxygen

Mechanisms for the reaction of thiophene and 2-methylthiophene with molecular oxygen on both the triplet and singlet potential energy surfaces (PESs) have been investigated using ab initio methods. Geometries of various stationary points involved in the complex reaction routes are optimized at the MP2/6-311++G(d, p) level. The barriers and energies of reaction for all product channels were refined using single-point calculations at the G4MP2 level of theory. For thiophene, CCSD(T) single point energies were also determined for comparison with the G4MP2 energies. Thiophene and 2-methylthiophene were shown to react with O(2) via two types of mechanisms, namely, direct hydrogen abstraction and addition/elimination. The barriers for reaction with triplet oxygen are all significantly large (i.e., >30 kcal mol(-1)), indicating that the direct oxidation of thiophene by ground state oxygen might be important only in high temperature processes. Reaction of thiophene with singlet oxygen via a 2 + 4 cycloaddition leading to endoperoxides is the most favorable channel. Moreover, it was found that alkylation of the thiophene ring (i.e., methyl-substituted thiophene) is capable of lowering the barrier height for the addition pathway. The implication of the current theoretical results may shed new light on the initiation mechanisms for combustion of asphaltenes.     

Activity and Osmotic Coefficients from the Emf of Liquid Membrane Cells. VIII. K.3[Co(CN)6], Mg3[Co(CN)6]2, and Ca3[Co(CN)6]2

The activity coefficients of K₃[Co(CN)₆], Mg₃[Co(CN)₆]₂, and Ca₃[Co(CN)₆]₂,are examined. The results highlight close similarity with the correspondinghexacyanoferrate (III) salts. On dilution, K₃[Co(CN)₆], like K₃[Fe(CN)₆], approachesthe limiting law from the upper side, while Mg₃[Co(CN)₆]₂ and Ca₃[Co(CN)₆]₂tend to the limiting law from the opposite side, like Mg₃[Fe(CN)₆]₂,Ca₃[Fe(CN)₆]₂, Sr₃[Fe(CN)₆]₂, and Ba₃[Fe(CN)₆]₂. Both kinds of behavior agreewith theory for a model of hard spheres bearing electric charges +1 and –3 or+2 and –3, respectively. The paramater values of the Pitzer equation for activityand osmotic coefficients are reported.     

Smoothing estimates for the Schrödinger equation with unbounded potentials

We prove a local in time smoothing estimate for a magnetic Schrödinger equation with coefficients growing polynomially at spatial infinity. The assumptions on the magnetic field are gauge invariant and involve only the first two derivatives. The proof is based on the multiplier method and no pseudodifferential techniques are required.     

Nonlocal magnetic field-tuned quantum criticality in cubic CeIn(3-x)Sn(x) (x = 0.25)

We show that antiferromagnetism in lightly (approximately 8%) Sn-doped CeIn3 terminates at a critical field mu0H(c) = 42 +/- 2 T. Electrical transport and thermodynamic measurements reveal the effective mass m* not to diverge, suggesting that cubic CeIn3 is representative of a critical spin-density wave (SDW) scenario, unlike the local quantum critical points reported in anisotropic systems such as CeCu(6-x)Au(x) and YbRh2Si(2-x)Ge(x). The existence of a maximum in m* at a lower field mu0H(x) = 30 +/- 1 T may be interpreted as a field-induced crossover from local moment to SDW behavior as the Néel temperature falls below the Fermi temperature.     

Existence of maximizers for Sobolev–Strichartz inequalities

We prove the existence of maximizers of Sobolev–Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrödinger flows.     

Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators

Letters in Mathematical Physics - We prove the absence of eigenvalues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under smallness...     

Matrix algebras in Quasi-Newton methods for unconstrained minimization

Summary.  In this paper a new class of quasi-Newton methods, named ℒQN, is introduced in order to solve unconstrained minimization problems. The novel approach, which generalizes classical BFGS methods, is based on a Hessian updating formula involving an algebra ℒ of matrices simultaneously diagonalized by a fast unitary transform. The complexity per step of ℒQN methods is O(n log n), thereby improving considerably BFGS computational efficiency. Moreover, since ℒQN's iterative scheme utilizes single-indexed arrays, only O(n) memory allocations are required. Global convergence properties are investigated. In particular a global convergence result is obtained under suitable assumptions on f. Numerical experiences [7] confirm that ℒQN methods are particularly recommended for large scale problems. Received December 30, 2001 / Revised version received December 20, 2001 / Published online November 27, 2002 Mathematics Subject Classification (1991): 65K10 Correspondence to: P. Zellini