Complete family of mono-, bi-, and trinuclear Re(I)(CO)3Cl complexes of the bridging polypyridyl ligand 2,3,8,9,14,15-hexamethyl-5,6,11,12,17,18-hexaazatrinapthalene: syn/anti isomer separation, characterization, and photophysics

The syn and anti isomers of the bi- and trinuclear Re(CO)(3)Cl complexes of 2,3,8,9,14,15-hexamethyl-5,6,11,12,17,18-hexaazatrinapthalene (HATN-Me(6)) are reported. The isomers are characterized by (1)H NMR spectroscopy and X-ray crystallography. The formation of the binuclear complex from the reaction of HATN-Me(6) with 2 equiv of Re(CO)(5)Cl in chloroform results in a 1:1 ratio of the syn and anti isomers. However, synthesis of the trinuclear complex from the reaction of HATN-Me(6) with 3 equiv of Re(CO)(5)Cl in chloroform produces only the anti isomer. syn-{(Re(CO)(3)Cl)(3)(μ-HATN-Me(6))} can be synthesized by reacting 1 equiv of Re(CO)(5)Cl with syn-{(Re(CO)(3)Cl)(2)(μ-HATN-Me(6))} in refluxing toluene. The product is isolated by subsequent chromatography. The X-ray crystal structures of syn-{(Re(CO)(3)Cl)(2)(μ-HATN-Me(6))} and anti-{(Re(CO)(3)Cl)(3)(μ-HATN-Me(6))} are presented both showing severe distortions of the HATN ligand unit and intermolecular π stacking. The complexes show intense absorptions in the visible region, comprising strong π → π* and metal-to-ligand charge-transfer (MLCT) transitions, which are modeled using time-dependent density functional theory (TD-DFT). The energy of the MLCT absorption decreases from mono- to bi- to trinuclear complexes. The first reduction potentials of the complexes become more positive upon binding of subsequent Re(CO)(3)Cl fragments, consistent with changes in the energy of the MLCT bands and lowering of the energy of relevant lowest unoccupied molecular orbitals, and this is supported by TD-DFT. The nature of the excited states of all of the complexes is also studied using both resonance Raman and picosecond time-resolved IR spectroscopy, where it is shown that MLCT excitation results in the oxidation of one rhenium center. The patterns of the shifts in the carbonyl bands upon excitation reveal that the MLCT state is localized on one rhenium center on the IR time scale.     

Quantitative simulation of photoacoustic signals using finite element modelling software

This paper aims to demonstrate the quantitative simulation of photoacoustic signals using finite element modelling software. The software Comsol Multiphysics is used to calculate the response of a differential Helmholtz resonator cell previously modeled using an electrical analogy. Quality factors and resonance frequencies are compared with experimental ones. Moreover, for the first time, the absorption coefficient of the gas sample and the laser intensity are also used to quantitatively predict photoacoustic signal that can be obtained in such a configuration.     

On the parallel dynamics of theQ-state Potts andQ-Ising neural networks

Using a probabilistic approach, the parallel dynamics of theQ-state Potts andQ-Ising neural networks are studied at zero and at nonzero temperatures. Evolution equations are derived for the first time step and arbitraryQ. These formulas constitute recursion relations for the exact parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis, including dynamical capacity-temperature diagrams and the temperature dependence of the overlap, is carried out forQ=3. Both types of models are compared.On leave of absence from the Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia.     

Panel The integration of voice science, voice pathology, medicine, public speaking, acting, and singing

The integration of voice science, voice pathology, medicine, public speaking, acting, and singing has been central to evolution in all fields. The Voice Foundation Symposia have played a seminal and central role in fostering integration among disciplines. The result has been an improvement in the knowledge and practice in each field. And the future promises to be even more informative and exciting.     

Perturbation of resonances in quantum mechanics

Schrödinger operators on L²($\text{R}$³) of the form ?Δ + V_λ with potentials V_λ real-analytic in λ are discussed. The analytic structure in V_λ and k (with k² the energy variable) of the resolvent kernel, the eigenvalues and resonances is exhibited and we obtain in particular convergent perturbation expansions for the resonances and the corresponding resonance functions. The lower order expansion coefficients are computed explicitly. The resonances and the corresponding functions are also computed for a particle moving under the action of n point interactions. This gives asymptotic low energy information about Schrödinger Hamiltonians with short range potentials. The perturbation theory of resonances, eigenvalues and of the corresponding functions for Hamiltonians describing n point interactions perturbed by a potential is also given.     

Parallel Dynamics of Fully Connected Q-Ising Neural Networks

Using a probabilistic approach, the parallel dynamics of fully connected Q-Ising neural networks is studied for arbitrary Q. A novel recursive scheme is set up to determine the time evolution of the order parameters through the evolution of the distribution of the local field, taking into account all feedback correlations. In contrast to extremely diluted and layered network architectures, the local field is no longer normally distributed but contains a discrete part. As an illustrative example, an explicit analysis is carried out for the first four time steps. For the case of the Q = 2 and Q = 3 model the results are compared with extensive numerical simulations and excellent agreement is found. Finally, equilibrium fixed-point equations are derived and compared with the thermodynamic approach based upon the replica-symmetric mean-field approximation.     

The short range expansion

Let V_i be short range potential and λ_i(ε) analytic functions. We show that the Hamiltonians H_ε = −Δ + ε⁻²∑_{i = l}ⁿλ_i(ε)V_i((· − x_i)/ε converge in the strong resolvent sense to the point interactions as ε → 0, and if V_i have compact support then the eigenvalues and resonances of H_ε, which remains bounded as ε → 0, are analytic in ε in a complex neighborhood of zero. We compute in closed form the eigenvalues and resonances of H_ε to the first order in ε.