Understanding local electrophilicity/nucleophilicity activation through a single reactivity difference index

A local reactivity difference index R(k) is shown to be able to predict the local electrophilic and/or nucleophilic activation within an organic molecule. Together with the electrophilic and/or nucleophilic behavior of the center k given by the sign, the magnitude of the R(k) index accounts for the extent of the electronic activation, a behavior that allows for the use of the R(k) index as a measure of the molecular reactivity especially in polar processes.     

Origin of the synchronicity in bond formation in polar Diels-Alder reactions: an ELF analysis of the reaction between cyclopentadiene and tetracyanoethylene

The origin of the synchronicity in C-C bond formation in polar Diels-Alder (P-DA) reactions involving symmetrically substituted electrophilic ethylenes has been studied by an ELF analysis of the electron reorganization along the P-DA reaction of cyclopentadiene (Cp) with tetracyanoethylene (TCE) at the B3LYP/6-31G* level. The present study makes it possible to establish that the synchronicity in C-C bond formation in P-DA reactions is controlled by the symmetric distribution of the electron-density excess reached in the electrophile through the charge transfer process, which can be anticipated by an analysis of the spin electron-density at the corresponding radical anion. The ELF comparative analysis of bonding along the DA reactions of Cp with ethylene and with TCE asserts that these DA reactions, which have a symmetric electron reorganization, do not have a cyclic electron reorganization as the pericyclic mechanism states. Due to the very limited number of cases of symmetrically substituted ethylenes, we can conclude that the synchronous mechanism is an exception of DA reactions.     

Quasi-classical trajectory calculations analyzing the reactivity and dynamics of asymmetric stretch mode excitations of methane in the H + CH4 reaction

An exhaustive dynamics study was performed at two collision energies, 1.52 and 2.20 eV, analyzing the effects of the asymmetric (nu3) stretch mode excitation in the reactivity and dynamics of the gas-phase H + CH4 reaction. Quasi-classical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories, were performed on an analytical potential energy surface previously developed by our group. First, strong coupling between different vibrational modes in the entry channel was observed, indicating that energy can flow between these modes, and therefore that they do not preserve their adiabatic character along the reaction path; i.e., the reaction is nonadiabatic. Second, we found that the reactant vibrational excitation has a significant influence on the vibrational and rotational product distributions. With respect to the vibrational distribution, our results confirm the purely qualitative experimental evidence, although the theoretical results presented here are also quantitative. The rotational distributions are predictive, because no experimental data have been reported. Third, with respect to the reactivity, we found that the nu3 mode excitation by one quantum is more reactive than the ground state by a factor of about 2, independently of the collision energy, and in agreement with the experimental measurement of 3.0 +/- 1.5. Fourth, the state-to-state angular distributions of the products reproduce the experimental behavior at 1.52 eV, where the CH3 products scatter sideways and backward. At 2.20 eV this experimental information is not available, and therefore the results reported here are again predictive. The satisfactory reproduction of a great variety of experimental data by the present QCT study lends confidence to the potential energy surface constructed by our group and to those results whose accuracy cannot be checked by comparison with experiment.     

Analytical potential energy surface describing abstraction reactions in asymmetrically substituted polyatomic systems of type CX3Y + A--> products

The gas-phase reaction between chloromethane and hydrogen proceeds by two channels, Cl- and H-abstraction, and was chosen as a model of asymmetrically substituted polyatomic reactions of type CX3Y + A --> products. The analytical potential energy surface for this reaction was constructed with suitable functional forms to represent vibrational modes, and both channels were independently fitted to reproduce experimental and theoretical information only at the stationary points. The rate constants for the Cl- and H-channels and the overall reaction were calculated using variational transition-state theory with multidimensional tunneling effect over a wide temperature range, 298-3000 K. The Cl-abstraction reaction is preferred until 2100 K, while above this temperature the H-abstraction channel is favored. The theoretical overall rate constants agree with the experimental data in the common temperature range, 500-800 K, with a small curvature of the Arrhenius plot due mainly to the role of the tunneling in the H-abstraction channel. This surface was then used to analyze dynamical features, such as reaction-path curvature, and coupling between the reaction-coordinate and vibrational modes. It was found qualitatively that excitation of the C-Cl and C-H stretching reactive modes enhances the forward rate constants for the Cl- and H-abstraction channels, respectively, and only the Cl-H and H-H stretching modes in the products of the Cl- and H-abstraction reactions, respectively, appear vibrationally excited.     

Photogeneration and reactivity of 1,n-diphenyl-1,n-azabiradicals

The 1,5-diphenyl-1,5-azapentanediyl biradical Ia was generated by photolysis of 1,2-diphenylazacyclopentane (pyrrolidine 1a). Among the reaction pathways followed by Ia, C-N bond reformation with ring closure was found to be the predominating process, as determined by separate irradiation of either of the pure enantiomers of 1a. Disproportionation was a minor process and took place only via H abstraction by the C5 benzylic radical. Another minor pathway was C5-aryl coupling, with formation of 5-phenyl-2,3,4,5-tetrahydro-1H-benzo[b]azepine (4a), which is equivalent to photo-Claisen rearrangement of 1a. Likewise, the 1,4-diphenyl-1,4-azabutanediyl biradical Ib was generated by photolysis of 1,2-diphenylazacyclobutane (azetidine 1b). This species underwent predominating C2-C3 cleavage, as indicated by the extensive styrene formation. Although N1-C4 bond reformation also took place, this is not the major pathway occurring from Ib. Besides, C4-aryl coupling to give 4-phenyl-1,2,3,4-tetrahydroquinoline (4b) was also observed. All the possible reaction pathways were theoretically studied at the UB3LYP/6-31G computational level; the results were found to be in good agreement with the experimental observations.     

Synthesis and receptor binding evaluation of clavizepine analogues with no ring D substituents

Assembly of the azepine ring of xantheno[9,1-cd]azepines by electrophilic cyclization of sulfonamide acetals provides access to clavizepine analogues in the form of 2,12b-dihydro- or 4-hydroxy-2,3,4,12b-tetrahydro-1H-xantheno[9,1-cd]azepines, in the latter case producing the trans derivative stereoselectively. Binding assays for clavizepine and analogues at adrenergic, dopaminergic, and serotonergic receptors are reported.     

Potential energy surface, kinetics, and dynamics study of the Cl+CH4-->HCl+CH3 reaction

A modified and recalibrated potential energy surface for the gas-phase Cl+CH4-->HCl+CH3 reaction is reported and tested. It is completely symmetric with respect to the permutation of the four methane hydrogen atoms and is calibrated with respect to updated experimental and theoretical stationary point properties and experimental forward thermal rate constants. From the kinetics point of view, the forward and reverse thermal rate constants and the activation energies were calculated using the variational transition-state theory with semiclassical transmission coefficients over a wide temperature range of 150-2500 K. The theoretical results reproduce the available experimental data, with a small curvature of the Arrhenius plot which indicates the role of tunneling in this hydrogen abstraction reaction. A dynamics study was also performed on this PES using quasiclassical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories. First, we found a noticeable internal energy in the coproduct methyl radical, both in the ground-state [CH4 (v=0)] and vibrationally excited [CH4 (v=1)] reactions. This CH3 internal energy was directly precluded in some experiments or oversimplified in previous theoretical studies using pseudotriatomic models. Second, our QCT calculations give HCl rotational distributions slightly hotter than those in experiment, but correctly describing the experimental trend of decreasing the HCl product rotation excitation in going from HCl (v'=0) to HCl (v'=1) for the CH4 (v=1) reaction. Third, the state specific scattering distributions present a reasonable agreement with experiment, although they tend to make the reaction more forward and backward scattered than found experimentally probably because of the hotter rotational distribution and the deficiencies of the QCT methods.     

Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space

Let M be a closed Riemann surface, N a Riemannian manifold of Hermitian non-positive curvature, f : M → N a continuous map, and E the function on the Teichmüller space of M that assigns to a complex structure on M the energy of the harmonic map homotopic to f. We show that E is a plurisubharmonic function on the Teichmüller space of M. If N has strictly negative Hermitian curvature, we characterize the directions in which the complex Hessian of E vanishes.     

Convergence of distributed optimal control problems governed by elliptic variational inequalities

First, let u _g be the unique solution of an elliptic variational inequality with source term g. We establish, in the general case, the error estimate between $u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$ and $u_{4}(\mu)=u_{\mu g_{1}+ (1-\mu) g_{2}}$ for ????[0,1]. Secondly, we consider a family of distributed optimal control problems governed by elliptic variational inequalities over the internal energy g for each positive heat transfer coefficient h given on a part of the boundary of the domain. For a given cost functional and using some monotony property between u ₃(??) and u ₄(??) given in Mignot (J.?Funct. Anal. 22:130?C185, 1976), we prove the strong convergence of the optimal controls and states associated to this family of distributed optimal control problems governed by elliptic variational inequalities to a limit Dirichlet distributed optimal control problem, governed also by an elliptic variational inequality, when the parameter h goes to infinity. We obtain this convergence without using the adjoint state problem (or the Mignot??s conical differentiability) which is a great advantage with respect to the proof given in Gariboldi and Tarzia (Appl. Math. Optim. 47:213?C230, 2003), for optimal control problems governed by elliptic variational equalities.