On the Barzilai and Borwein choice of steplength for the gradient method

In a recent paper, Barzilai and Borwein presented a new choiceof steplength for the gradient method. Their choice does notguarantee descent in the objective function and greatly speedsup the convergence of the method. They presented a convergenceanalysis of their method only in the two-dimensional quadraticcase. We establish the convergence of the Barzilai and Borweingradient method when applied to the minimization of a strictlyconvex quadratic function of any number of variables.     

Maximum Principle for Nonlinear Cooperative Elliptic Systems on R^N

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation method for the considered system.     

A theoretical analysis of the excited states in 2-benzoylthiophene

The lower excited states of 2-benzoylthiophene have been studied using ab initio quantum chemical methods based on multiconfigurational wave functions. Six singlet and six triplet excited states have been characterized. The geometry has been optimized for the two lowest triplet states, which are responsible for the photoreactivity of the chromophore in the photosensitizing drug tiaprofenic acid. The T¹(π → π?) and T₂(n → π?) states have been found to be close in energy with the π → π? state slightly lower. The excited states have been characterized using density difference and spin density plots. The different photochemical behaviour of the two triplet states can be rationalized from the theoretical data.     

Calculations of the static polarizability and hyperpolarizability of the LiF molecule including vibrational contributions

The static dipole moment, polarizability and first hyperpolarizability of the LiF molecule have been calculated, including vibrational corrections, using Möller—Plesset perturbation theory and coupled cluster methods. The results show that the vibrational corrections, dominated by the nuclear relaxation term, are as important for the calculations of the polarizability and hyperpolarizability as the electronic contribution, and that the electron correlation effects play an important role in the calculations of both electronic and vibrational contributions for these static properties.     

The reactions of Cl+ (3P) and Cl+ (1D) with hydrogen sulphide. A G2 molecular orbital study

G2 ab initio molecular orbital calculations have been performed to study the potential energy surfaces (PESs) associated with the reactions of Cl⁺ in its ³P ground state and in its ¹D first excited state with hydrogen sulphide. [H₂, Cl, S]⁺ singlet and triplet state cations present very different bonding characteristics. The latter are systematically ion-dipole or hydrogen-bonded weakly bound species, while the former are covalent molecular ions. As a consequence, although the Cl⁺(³P) is 34.5 kcal mol^?1 more stable than Cl⁺(¹D), the global minimum of the singlet PES lies 37.3 kcal mol^?1 below the global minimum of the triplet PES. Both singlet and triplet potential energy surfaces show significant differences with respect to those associated with Cl⁺ + H₂O reactions as well as with SH₂ reactions with F⁺. In both cases, the major product should be SH⁺ ₂; SH⁺ and HCl⁺ being the minor products, in agreement with the experimental evidence. The estimated heat of formation for the most stable H₂SCl⁺ singlet state species is 198 ± 1 kcal mol^?1.     

Bis(salicylaldiminate) copper(II) and palladium(II) complexes: towards columnar mesophases

Copper and palladium complexes of new salicylaldimines derived from 3,4,5-tridecyloxyaniline, 2,3,4-tridecyloxyaniline and 4-decyloxyaniline have been synthesized and characterized. All the ligands bear four or more aliphatic chains with the aim of inducing columnar mesophases at low temperatures. In particular, metal complexes derived from 4-(3,4,5-tridecyloxybenzoyloxy)-salicyliden-3,4,5-tridecyloxyaninile display rectangular columnar mesophases at (or near) room temperature. These mesophase assignments have been confirmed by X-ray diffraction. A significant decrease of the melting points of the compounds is observed in the tridecyloxyaniline derivatives compared with those of similar complexes derived from mono- or di-decyloxyaniline.