π-dimerization of pleiadiene radical cations at low temperatures revealed by UV–vis spectroelectrochemistry and quantum theory

One-electron oxidation of the non-alternant polycyclic aromatic hydrocarbon pleiadiene and related cyclohepta[ c,d]pyrene and cyclohepta[c,d]fluoranthene in THF produces corresponding radical cations detectable in the temperature range of 293–263 K only on the subsecond time scale of cyclic voltammetry. Although the EPR-active red-coloured pleiadiene radical cation is stable according to the literature in concentrated sulfuric acid, spectroelectrochemical measurements reported in this study provide convincing evidence for its facile conversion into the green-coloured, formally closed shell and, hence, EPRsilent π-bound dimer dication stable in THF at 253 K. The unexpected formation of the thermally unstable dimeric product featuring a characteristic intense low-energy absorption band at 673 nm (1.84 eV; logεmax=4.0) is substantiated by ab initio calculations on the parent pleiadiene molecule and the PF6 − salts of the corresponding radical cation and dimer dication. The latter is stabilized with respect to the radical cation by 14.40 kcal mol−1 (DFT B3LYP) [37.64 kcal mol−1 (CASPT2/DFT B3LYP)]. An excellent match has been obtained between the experimental and TDDFT- calculated UV–vis spectra of the PF6 − salt of the pleiadiene dimer dication, considering solvent (THF) effects.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

On the quantum mechanical scattering statistics of many particles

The probability of a quantum particle being detected in a given solid angle is determined by the S-matrix. The explanation of this fact in time-dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the S-matrix probability emerges in the limit of large distances.

Unusual isotope effect in the reaction of chlorosilylene with trimethylsilane-1-d: Absolute rate studies and quantum chemical and Rice–Ramsperger–Kassel–Marcus calculations provide strong evidence for the involvement of an intermediate complex

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1- silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane-1-d, Me3SiD, in the gas phase. The reaction was studied at total pressures up to 100 Torr (with and without added SF6) over the temperature range of 295−407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log[(k/(cm3 molecule−1 s−1)] = (−13.22 ± 0.15) + [(13.20 ± 1.00) kJ mol−1]/(RT ln 10). When compared with previously published kinetic data for the reaction of ClSiH with Me3SiH, kinetic isotope effects, kD/kH, in the range from 7.4 (297 K) to 6.4 (407 K) were obtained. These far exceed values of 0.4−0.5 estimated for a single-step insertion process. Quantum chemical calculations (G3MP2B3 level) confirm not only the involvement of an intermediate complex, but also the existence of a low-energy internal isomerization pathway which can scramble the D and H atom labels. By means of Rice−Ramsperger−Kassel−Marcus modeling and a necessary (but small) refinement of the energy surface, we have shown that this mechanism can reproduce closely the experimental isotope effects. These findings provide the first experimental evidence for the isomerization pathway and thereby offer the most concrete evidence to date for the existence of intermediate complexes in the insertion reactions of silylenes.