Normality and smoothness of simple linear group compactifications

Given a semisimple algebraic group $G$ , we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant $G\times G$ -compactifications possessing a unique closed orbit which arise in a projective space of the shape $\mathbb{P }(\mathrm{End}(V))$ , where $V$ is a finite dimensional rational $G$ -module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of $V$ . In particular, we show that ${\mathrm{Sp}}(2r)$ (with $r \geqslant 1$ ) is the unique non-adjoint simple group which admits a simple smooth compactification.     

Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation

We consider the nonlinear Klein-Gordon equation in ? ^d . We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates.     

The effect of substitution on the properties of a chemical group

The effect of the substituent R(R = F, OH, NH₂, CH₃) on the electron distribution of the C=C group of ethylene and acrylonitrile may be fairly well represented in terms of classical interactions between the and components of this group and the molecular remainder. A distinction between direct and indirect effects is made, and an estimate of the relative importance of conjugative versus inductive effects is done.This analysis has been performed on a set of 22 SCF wavefunctions calculated with the 4-31G basis set.     

Towards a comprehensive theory of lyoluminescence in alkali halide crystals: Some results and some perspectives for future research

Lyoluminescence is an interesting tool to study irradiation defects in solids and their behaviour after dissolution. A general kinetic scheme of the process valid for alkali halide crystals is presented, and some ideas about structure and properties of the interacting species, in the solid as well as in the liquid phase, are discussed.     

DFT Calculation of Deuterium Quadrupolar Tensor in Crystal Anthracene

A DFT calculation of deuterium nuclear quadrupole tensors of crystal anthracene is presented. After a careful analysis of the DFT functionals and of the basis sets, the B3LYP/6-311+G(d,3p2d) level has been identified as the best compromise between accuracy and computational cost. To account for the crystal environment, three models are proposed: one represented by a cluster of five anthracene arranged as in the crystal, the other formed by an anthracene embedded in a dielectric continuum having the dielectric permittivity of the crystal, and the last represented by an embedded dimer of anthracene. It is shown that the pure continuum model (here represented by the Integral Equation Formalism version of the Polarizable Continuum Model) already accounts for a large part of the crystal effects and that the embedded dimer almost entirely recover all the details of the explicit 5-anthracene cluster.     

The decomposition of the SCF interaction energy in hydrogen bonded dimers corrected for basis set superposition errors: An examination of the basis set dependence

A systematic examination of the components of the interaction energy, obtained with the Kitaura and Morokuma method, for nine H-bonded dimers without and with counterpoise corrections (CP ) is presented. The nine dimers H_n A …? HBH_m correspond to all the possible combinations of HF, H₂O, and NH₃ as electron donors and electron acceptors. The interaction energy and the corresponding components have been computed over a sizable interval of intermolecular distances with five basis sets (STO -3G, MINI -1, 3-21G, 4-31G, 6-31G**) selected among those most extensively used to study interactions in larger systems. The CP corrections to the ΔE components have been obtained with a method, implemented in our group, which permits assignment to the pertinent components of ΔE of a physically reasonable portion of the CP correction even though different CP corrections are adopted. We examine here three versions of the CP correction, namely, the full CP correction (i.e., the original version of Boys and Bernardi) and CP corrections limited to the virtual space of the partner or to the electron donor only. The resulting data are employed to assess the basis set dependence of several models of hydrogen bonding (the electrostatic model, the semiclassical model, etc.) both with and without CP corrections.     

Excitation energy transfer (EET) between molecules in condensed matter: a novel application of the polarizable continuum model (PCM)

We present a quantum-mechanical theory to study excitation energy transfers between molecular systems in solution. The model is developed within the time-dependent (TD) density-functional theory and the solvent effects are introduced in terms of the polarizable continuum model (PCM). Unique characteristic of this model is that both "reaction field" and screening effects are included in a coherent and self-consistent way. This is obtained by introducing proper solvent-specific operators in the Kohn-Sham equations and in the corresponding TD scheme. The solvation model exploits the integral equation formalism (IEF) version of PCM and it defines the solvent operators on a molecular cavity modeled on the real three-dimensional (3D) structure of the solute systems. Applications to EET in dimers of ethylene and naphtalene are presented and discussed.     

Light-Lithophile Element Metasomatism of Finero Peridotite (W ALPS): A Secondary-Ion Mass Spectrometry Study

The high sensitivity of Secondary-Ion Mass Spectrometry (SIMS) in determining very low trace-element concentrations (down to few ppb wt) has been used to address the important issue of the Light-Lithophile Element (LLE) signatures of mantle peridotites and their potential utility as tracers of transfer of subducted material into the overlying mantle wedge operated either by slab-related fluids or melts. The effects of such metasomatic agents have been described and interpreted on the basis of geochemical and isotopic characteristics of peridotites. However, direct observation of metasomatic processes occurring in the mantle is limited because the most highly metasomatised peridotites are usually found as xenoliths which do not allow large-scale chemical information. In this context, the Finero phlogopite-peridotite massif (Ivrea-Verbano Zone, western Italian Alps) offers a unique opportunity because it contains hydrous mineral assemblages (amphibole + phlogopite ± apatite) and trace element enrichments, supposed to be related to the pervasive migration of slab-derived melts. In this study we report the results of texture-related SIMS investigations performed on a wide range of trace elements such as Li, B, Large-Ion Lithophile Elements (LILE), Rare Earth Elements (REE), Nb, Zr, Ti on clinopyroxenes from the Finero peridotite. SIMS analyses revealed unusual LLE signatures that highlight the role of crust-derived components and open new perspectives on the timing of metasomatic processes.     

A time-dependent polarizable continuum model: theory and application

This work presents an extention of the polarizable continuum model to explicitly describe the time-dependent response of the solvent to a change in the solute charge distribution. Starting from an initial situation in which solute and solvent are in equilibrium, we are interested in modeling the time-dependent evolution of the solvent response, and consequently of the solute-solvent interaction, after a perturbation in this equilibrium situation has been switched on. The model introduces an explicit time-dependent treatment of the polarization by means of the linear-response theory. Two strategies are tested to account for this time dependence: the first one employs the Debye model for the dielectric relaxation, which assumes an exponential decay of the solvent polarization; the second one is based on a fitting of the experimental data of the solvent complex dielectric permittivity. The first approach is simpler and possibly less accurate but allows one to write an analytic expression of the equations. By contrast, the second approach is closer to the experimental evidence but it is limited to the availability of experimental data. The model is applied to the ionization process of N,N-dimethyl-aniline in both acetonitrile and water. The nonequilibrium free-energy profile is studied both as a function of the solvent relaxation coordinate and as a function of time. The solvent reorganization energy is evaluated as well.