Molecular structure and benzene ring deformation of three ethynylbenzenes from gas-phase electron diffraction and quantum chemical calculations

The molecular structures of ethynylbenzene and s-triethynylbenzene have been accurately determined by gas-phase electron diffraction and ab initio/DFT MO calculations and are compared to that of p-diethynylbenzene from a previous study [Domenicano, A.; Arcadi, A.; Ramondo, F.; Campanelli, A. R.; Portalone, G.; Schultz, G.; Hargittai, I. J. Phys. Chem. 1996, 100, 14625]. Although the equilibrium structures of the three molecules have C2v, D3h, and D2h symmetry, respectively, the corresponding average structures in the gaseous phase are best described by nonplanar models of Cs, C3v, and C2v symmetry, respectively. The lowering of symmetry is due to the large-amplitude motions of the substituents out of the plane of the benzene ring. The use of nonplanar models in the electron diffraction analysis yields ring angles consistent with those from MO calculations. The molecular structure of ethynylbenzene reported from microwave spectroscopy studies is shown to be inaccurate in the ipso region of the benzene ring. The variations of the ring C-C bonds and C-C-C angles in p-diethynylbenzene and s-triethynylbenzene are well interpreted as arising from the superposition of independent effects from each substituent. In particular, experiments and calculations consistently show that the mean length of the ring C-C bonds increases by about 0.002 A per ethynyl group. MO calculations at different levels of theory indicate that though the length of the C[triple bond]C bond of the ethynyl group is unaffected by the pattern of substitution, the C(ipso)-C(ethynyl) bonds in p-diethynylbenzene are 0.001-0.002 A shorter than the corresponding bonds in ethynylbenzene and s-triethynylbenzene. This small effect is attributed to conjugation of the two substituents through the benzene ring. Comparison of experimental and MO results shows that the differences between the lengths of the C(ipso)-C(ethynyl) and C(ipso)-C(ortho) bonds in the three molecules, 0.023-0.027 A, are correctly computed at the MP2 and B3LYP levels of theory but are overestimated by a factor of 2 when calculated at the HF level.     

Some polynomials associated with the $${\vavec{}}$$-Whitney numbes

In the present article, we study three families of polynomials associated with the r-Whitney numbers of the second kind. They are the r-Dowling polynomials, r-Whitney–Fubini polynomials and the r-Eulerian–Fubini polynomials. Then we derive several combinatorial results by using algebraic arguments (Rota’s method), combinatorial arguments (set partitions) and asymptotic methods.     

A family of polylog-trigonometric integrals

In this paper, we study the sequences

$$\begin{aligned} I_n=\int _0^1\mathrm {Li}_n(\sin \pi x)\mathrm {d}x\quad \text{ and }\quad J_n=\int _0^1\mathrm {Li}_n(\cos \pi x)\mathrm {d}x, \end{aligned}$$

where \(\mathrm {Li}_n\) is the nth polylogarithm function. Among others, we determine their generating functions, asymptotic behaviour and their connection to the well-known log-sine integrals

$$\begin{aligned} S_n=(-1)^n\int _0^1\log ^n(\sin \pi x)\mathrm {d}x. \end{aligned}$$

With the help of the explicit forms of \(I_n\) and \(J_n\), we deduce closed-form evaluations for a number of polylog-trigonometric definite integrals.

     

Unexpected formation of higher polythionates in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium

It has been clearly shown that not only tetrathionate but also pentathionate or even higher polythionates is formed in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium. In thiosulfate excess, the absorbance-time curves registered at 250 nm may go through a maximum followed by a minimum, suggesting the presence of a short-lived absorbing intermediate proposed to be S(2)O(3)OCl(3-). Matrix rank analysis (MRA) studies have revealed that altogether five independent absorbing species are present in the wavelength range 240-400 nm. A kinetic model is suggested to take all of the experimental observations into account.     

Non-central limit theorems for random selections

Selection from finite sets is a basic procedure of statistics and the partial sum behavior of selected elements is completely known under the “uniform asymptotic negligibility” condition of central limit theory. The purpose of the present paper is to determine the asymptotic behavior of partial sums when the central limit theorem fails. As an application, we describe the limiting properties of permutation and bootstrap statistics in case of infinite variance.     

Electric field dependence of phase equilibria of binary Stockmayer fluid mixtures

A perturbation theory based study of the effect of an external electric field on the phase equilibrium properties of binary Stockmayer fluids is presented. The dipole–dipole interaction and the applied field are treated as independent perturbations to a Lennard–Jones mixture, and the reference fluid is treated by the van der Waals one-fluid approximation. A third-order free energy expression in the electric field strength is established, and the dielectric constant is calculated for a needle-shaped sample parallel to the field direction. We present and discuss vapour–liquid and liquid–liquid equilibrium curves at a given temperature for some dipolar mixtures exposed to an electric field, including chlorodifluoromethane +?difluoromethane and acetonitrile +?methanol. A sufficiently high electric field may result in massive shifts of vapour pressures and critical or azeotropic points, and can considerably alter the properties of coexisting phases. The vapour pressure decreases with increasing field strength.     

On admissibility of the resolvent of discrete Volterra equations

Suppose that a pair of sequence spaces is admissible with respect to a discrete linear Volterra operator. This paper gives sufficient conditions for the same pair of spaces to be admissible with respect to the associated resolvent operator. The spaces considered include spaces of weighted bounded and weighted convergent sequences. Classes of discrete kernels are discussed for which the appropriate weight sequences are not purely exponential, but the product of an exponential and a slowly decaying sequence.     

On G-arc-regular dihedrants and regular dihedral maps

A graph Γ is said to be G-arc-regular if a subgroup $G \le\operatorname{\mathsf{Aut}}(\varGamma)$ acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D _2n of order 2n whose cyclic subgroup C _n ≤D _2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D _2n , n odd, are classified.     

Synchronization engineering: theoretical framework and application to dynamical clustering

A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.