Formation of long-lived fluorofullerene trianions in collisions with Na

The first experimental observation of long-lived triply charged fluorofullerene anions in the gas phase obtained from C60F48 is reported. The existence of a Coloumb barrier trapping the third electron in the trianion is supposed to be responsible for detection of the species which is estimated to have negative third electron affinity.     

Preparation, crystallographic characterization and theoretical study of two isomers of C70(CF3)12

Two isomers of C70(CF3)12 have been isolated from a mixture obtained by trifluoromethylation of C70 with CF3I; their molecular structures determined by X-ray crystallography are in good agreement with the results of theoretical DFT calculations for the most stable C70(CF3)12 isomers.     

Metal-organic frameworks exhibiting strong anion-pi interactions

Coordination polymers offer a significant potential for applications in adsorption, guest and anion recognition and sensing. Their structure commonly provides binding sites for such specific interactions as pi-pi stacking and XH...pi hydrogen bonding. The latter reflects the ability of the pi-cloud to interact with positively polarized atoms. An electrostatic interaction between anionic species and electron deficient heterocycles, which parallels the above binding scheme, is also possible and very recently the existence of anion-pi interactions was proved in the solid state and in solution. This effect may be significant also for biomolecule/solution interfaces, as it occurs in protein structures. In fact, such interactions could be especially relevant for host-guest chemistry of coordination polymers, particularly for functionalization of hydrophobic crystal cavities and for the design of geometrically rigid anion receptors. However, typical electron deficient heterocycles such as 1,3,5-triazines and 1,2,4,5-tetrazines are very weak donors and they are hardly suitable for bridging metal ions and the generation of coordination frameworks. As a system that combines efficient donor properties towards transition metal ions and a pronounced ability for anion-pi interactions we have developed unsubstituted pyridazino[4,5-d]pyridazine, which was readily accessible by a novel one-pot synthesis involving inverse electron demand Diels-Alder cycloaddition (Scheme 1). Unusual anion binding properties of the ligand may be clearly related to its electron-deficiency (LUMO energy -1.591 vs. -0.288 eV for the parent pyridazine), influenced also by N-coordination to such Lewis acids as metal ions.     

Effective Hamiltonian models and unimolecular decomposition

Partitioning Hilbert space into two subspaces by using orthogonal projection operators yields compact forms for effective Hamiltonians for each of the subspaces. When one (the Q space) contains molecular bound states and the other (the P space) contains dissociative continua, a simple form for the non-Hermitian Q-space effective Hamiltonian, H(eff), can be obtained, subject to reasonable approximations. Namely, H(eff) = H0 - ivariant Planck's/2pi Gamma/2, where H0 is Hermitian, and the width operator variant Planck's/2pi Gamma accounts for couplings of the Q-space levels to the P-space continua. The P/Q partitioning procedure has been applied in many areas of atomic, molecular, and nuclear physics with widespread success. Inputting into this formalism ideas from random matrix theory in order to model independent open channels yields the random matrix H(eff) model. Despite numerous efforts, this model has failed to model satisfactorily the statistical transition-state theory of unimolecular decomposition (hereafter referred to as TST) in the regime of overlapping resonances, where nearly all such reactions occur. All statistical models of unimolecular decomposition are premised on rapid intramolecular vibrational redistribution (IVR) for a given set of good quantum numbers. The phase space thus accessed results in a threshold reaction rate of 1/h rho, and for K independent open channels, the rate is K/h rho. This reaction rate corresponds to a resonance width of K/2pi rho, and when K increases, the resonances (which are rho(-1) apart) overlap. In this regime, the random matrix H(eff) model fails because it does not introduce independent open channels. To illustrate the source of the problem, an analysis is carried out of a simple model that is obviously and manifestly inconsistent with TST. This model is solved exactly, and it is then put in the form of the random matrix H(eff) model, illustrating the one-to-one correspondence. This reveals the deficiencies of the latter. In manipulating this model into the form H0 - ivariant Planck's/2pi Gamma/2, it becomes clear that the independent open channels in the random matrix H(eff) model are inconsistent with TST. Rather, this model is one of gateway states (i.e., bound states that are coupled to their respective continua as well as to a manifold of zero-order bound states, none of which are coupled directly to the continua). Despite the fact that the effective Hamiltonian method is, by itself, beyond reproach, the random matrix H(eff) model is flawed as a model of unimolecular decomposition in several respects, most notably, bifurcations of the distributions of resonance widths in the regime of overlapping resonances.     

On Schurity of Finite Abelian Groups

A finite group G is called a Schur group, if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this article, it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any noncyclic abelian Schur group of odd order is isomorphic to ?₃ × ?_{3 ^k} or ?₃ × ?₃ × ? _p where k ≥ 1 and p is a prime. In addition, we prove that ?₂ × ?₂ × ? _p is a Schur group for every prime p.     

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.