Tele-substitution reactions in the naphthalene series : The behaviour of 1,4 - dimethyl - 2 - nitro - 3 - phenylsulphonyl - and 2,3 - bisphenylsulphonyl - 1,4 - dimethyl - naphthalene towards sodium arenethiolates and secondary aliphatic amines

1,4 - Dimethyl - 2 - nitro - 3 - phenylsulphonylnaphthalene (2) reacts with sodium benzenethiolate in DMSO at 120° to give 1 - methyl - 2 - nitro - 4 - phenylthiomethylnaphthalene (4) [tele-substitution product (TSP) of the phenylsulphonyl group] and 1,4 - dimethyl - 3 - phenylsulphonyl - 2 - phenylthionaphthalene (5) [normal substitution product (NSP) of the nitro group]. The analogous reactions of 2 with sodium 2,4,6- trimethylbenzenethiolate and of 2,3 - bisphenylsulphonyl -1,4 - dimethylnaphthalene (3) with sodium benzenethiolate or aliphatic amines give only TSPs of the phenylsulphonyl group. In the case of the reaction of 2 with aliphatic amines both the possible TSPs (tele-substitution of the phenylsulphonyl or of the nitro group) were isolated in 9:1 relative yield. All the data show that the phenylsulphonyl is a leaving group far better than the nitro in such tele-substitution processes. The mechanism previously proposed to account for the formation of TSPs from 1,4-dimethyl - 2,3 - dinitronaphthalene is strongly supported by the obtained results.     

α Emission in proton induced reactions

The continuous spectra of theα particles emitted in reactions induced by protons on⁹³Nb,¹⁰⁷Ag,¹¹⁸Sn,¹⁶⁵Ho,¹⁶⁹Tm have been measured at several energies ranging from 20 to 45 MeV. The spectra have been analysed in the framework of the Exciton model assuming that the emittedα's pre-existed in the target nucleus and evaluating their energy distribution on the basis of nucleon-α scattering dynamics in nuclear matter. Nuclear Reactions⁹³Nb,¹⁰⁷Ag,¹¹⁸Sn,¹⁶⁵Ho,¹⁶⁹Tm(p,α...).E=20–45MeV; Measured \(\frac{{d\sigma (E_\alpha )}}{{dE_\alpha }}\) ; calculated \(\frac{{d\sigma (E_\alpha )}}{{dE_\alpha }}\) .     

Statistical Mechanics of a Simplified Bipartite Matching Problem: An Analytical Treatment

We perform an analytical study of a simplified bipartite matching problem in which there exists a constant matching energy, and both heterosexual and homosexual pairings are allowed. We obtain the partition function in a closed analytical form and we calculate the corresponding thermodynamic functions of this model. We conclude that the model is favored at high temperatures, for which the probabilities of heterosexual and homosexual pairs tend to become equal. In the limits of low and high temperatures, the system is extensive, however this property is lost in the general case. There exists a relation between the matching energies for which the system becomes more stable under external (thermal) perturbations. As the difference of energies between the two possible matches increases the system becomes more ordered, while the maximum of entropy is achieved when these energies are equal. In this limit, there is a first order phase transition between two phases with constant entropy.     

Nucleon mean free path in nuclear matter

In calculations of nuclear reaction yields at incident energies of some tens of MeV consistently better agreement with experiments is obtained by assuming a nucleon mean free path in nuclear matter longer than that deduced from the Fermi gas model and free nucleon-nucleon cross sections.     

Viscous compressible hydrodynamics at planes,spheres and cylinders with finite surface slip

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency w \omega ∼ c ² r₀ \rho_{0}^{}/h \eta , with c the speed of sound, r₀ \rho_{0}^{} the fluid density and h \eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.     

On a 3D moving load problem for an elastic half space

The paper deals with 3D dynamic response of an elastic half-space loaded by a point force moving at a constant speed along a straight line on the surface. The problem is formulated within the framework of the asymptotic hyperbolic–elliptic model developed earlier by two of the authors. The validity of the model is restricted to the range of speeds close to the Rayleigh wave speed. Steady-state near-field solutions are derived in terms of elementary functions. Transient analysis of surface motion illustrates peculiarities of the resonance associated with the Rayleigh wave.     

Raman spectrum of NaAlSi2O6 jadeite. A quantum mechanical simulation

The Raman spectrum of NaAlSi₂O₆ jadeite is simulated and compared with two recent experimental data sets. In one experiment, only 17 (out of 30 symmetry allowed) peaks and a qualitative estimate of the intensities are provided. In the second case, the digitalized spectrum is available, from which we have been able to extract 20 evident peaks and an estimate of the relative intensities. The present calculation is based on an ab initio quantum mechanical treatment. Using an all‐electron Gaussian‐type basis set, together with the hybrid B3LYP density functional, the full set of 30 active modes and their (polycrystalline and polarized) intensities are obtained. The simulated intensities (not available in a previous study of the same system) permit the two experimental spectra to be reconciled and explain why the missing peaks were not seen. This ultimately leads to excellent agreement between experiment and theory. By artificially varying the mass of the Na ⁺ and Al^{3 +} cations in the simulations, which can be performed automatically and at essentially no computational cost, the vibrational modes to which these ions contribute are identified. We conclude that quantum mechanical simulation can be a very useful complementary tool for the interpretation of experimental Raman spectra. Copyright © 2014 John Wiley & Sons, Ltd.     

CRYSCOR: a program for the post-Hartree-Fock treatment of periodic systems

Cryscor is a periodic post-Hartree-Fock program based on local functions in direct space, i.e., Wannier functions and projected atomic orbitals. It uses atom centered Gaussians as basis functions. The Hartree-Fock reference, as well as symmetry information, is provided by the Crystal program. Cryscor presently features an efficient and parallel implementation of periodic local second order M?ller-Plesset perturbation theory (MP2), which allows us to study 1D-, 2D- and 3D-periodic systems beyond 1000 basis functions per unit cell. Apart from the correlation energy also the MP2 density matrix, and from that the Compton profile, are available. Very recently, a new module for calculating excitonic band gaps at the uncorrelated Configuration-Interaction-Singles (CIS) level has been added. Other advancements include new extrapolation techniques for calculating surface adsorption on semi-infinite solids. In this paper the diverse features and recent advances of the present Cryscor version are illustrated by exemplary applications to various systems: the adsorption of an argon monolayer on the MgO (100) surface, the rolling energy of a boron nitride nanoscroll, the relative stability of different aluminosilicates, the inclusion energy of methane in methane-ice-clathrates, and the effect of electron correlation on charge and momentum density of α-quartz. Furthermore, we present some first tentative CIS results for excitonic band gaps of simple 3D-crystals, and their dependence on the diffuseness of the basis set.     

Nuclear motion effects on the density matrix of crystals: An ab initio Monte Carlo harmonic approach

In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.