Can BB double bond be as potential proton acceptor: A UB3LYP and UMP2 theoretical study on unusual intermolecular T-shaped XH…π interactions between the triplet state HBBH and HF, HCl, HCN or H2C2

The unusual weak T-shaped XH…π hydrogen bonds are found between the BB double bond of the triplet state HBBH and the acid hydrogen of HF, HCl, HCN and H₂C₂ using UMP2 and UB3LYP methods at 6-311++G(2df,2p) and aug-cc-pVTZ levels. The binding energies follow the order of HBBH…HF > HBBH…HCl > HBBH…HCN > HBBH…H₂C₂, and the hydrogen-bonded interactions in the triplet state complexes HBBH…HX (³B₁) are found to be weaker than those in HCCH…HX and OCBBCO…HX. The analyses of natural bond orbital (NBO) and the electron density shifts reveal that the nature of the T-shaped XH…π hydrogen-bonded interaction is that the lost density from the π-orbital of BB bond is shifted toward the hydrogen atom of HX, leading to the electron density accumulation and the formation of the hydrogen bond. The atoms in molecules (AIM) theory has been also applied to characterize bond critical points and confirm that it is difficult for the ground electronic state of HBBH to be as the hydrogen-bond proton acceptor, perhaps due to the nature of electron-deficient BB double bond.     

The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators

In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracial state on this algebra which proves the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of finitely many time-frequency shifts of one function. We also estimate the coefficient decay of the inverse of finite linear combinations of time-frequency shifts.

     

Excited state polarizabilities from solvatochromic shifts

A new method is proposed to estimate the polarizability (α_e) of a molecule in an excited state using solvatochromic shift measurements and McRae's equation. In the earlier methods the contribution due to polarizability was not considered. In view of this, the proposed method is also expected to give a better estimation of excited state electric dipole moment (μ_e) and the (θ) angle between excited and ground state electric dipole moments, μ_e and μ_g apart from giving values of polarizability of the molecules in the excited state. This method has been applied in the case of the La band of p-nitro aniline and the results for all the parameters are found to be satisfactory and of right order in comparison with that reported in literature.     

Competition between the Hydrated Fluoride Anion and Hexanoic Acid for Inclusion in β-Cyclodextrin: An 1H-NMR Study in Aqueous Solution

β-cyclodextrin (βCD) and two guests (hexanoic acid and the hydrated fluoride ion) are considered as a system in the NMR chemical shift fast exchange regime. The measured chemical shift variations for the βCD H5 protons are expressed as functions of the mole fractions for the free and complexed states, and their slopes, , are evaluated. When the NaF concentration is varied ([NaF]₀/mM = {50,100, 150, 200, 250}) for a defined value of the hexanoic acid concentration ([Hex]₀/mM = {5, 7.5, 10, 12.5, 15}), the chemical shift variations of the βCD H5 protons for 2.5 mM βCD solutions in D₂O present a second order polynomial variation with a minimum, suggesting two opposing trends. The first trend corresponding to the decrease of Δδ values (relative shielding) is traced to increasingly negative values of . Corresponding to the increase of Δδ values (relative deshielding), the second trend is mainly associated with the increase of the mole fraction for the inclusion complex βCD·F(H₂O)₆⁻, as the concentration of NaF increases. The kosmotropic, stabilizing features of the fluoride ion are consistent with the results of HF/6–31G* single point energy calculations showing that βCD·F(H₂O)₆⁻ is energetically favourable, in contrast with βCD·Cl(H₂O)₆⁻ and βCD·Br(H₂O)₈⁻. Due to its smaller size, F(H₂O)₆⁻ is not appreciably distorted inside the βCD cavity as compared with Cl(H₂O)₆⁻ and Br(H₂O)₈⁻.     

On k-hyperexpansive operators

This paper considers the k-hyperexpansive Hilbert space operators T (those satisfying , 1?n?k) and the k-expansive operators (those satisfying the above inequality merely for n=k). It is known that if T is k-hyperexpansive then so is any power of T; we prove the analogous result for T assumed merely k-expansive. Turning to weighted shift operators, we give a characterization of k-expansive weighted shifts, and produce examples showing the k-expansive classes are distinct. For a weighted shift W that is k-expansive for all k (that is, completely hyperexpansive) we obtain results for k-hyperexpansivity of back step extensions of W. In addition, we discuss the completely hyperexpansive completion problem which is parallel to Stampfli's subnormal completion problem.     

Experimental and theoretical study of N2-broadened acetylene line parameters in the ν1 + ν3 band over a range of temperatures

N₂-broadened line widths and N₂-pressure induced line shifts have been measured for transitions in the ν₁?+?ν₃ band of acetylene at seven temperatures in the range 213–333?K to obtain the temperature dependences of broadening and shift coefficients. For the room-temperature spectra the line mixing effects have been also investigated. The Voigt and hard-collision line profile models were used to retrieve the line parameters. All spectra were recorded using a 3-channel tuneable diode laser spectrometer. The line-broadening and line-shifting coefficients as well as their temperature-dependence parameters have been also evaluated theoretically, in the frame of a semi-classical approach based on an exponential representation of the scattering operator, an intermolecular potential composed of electrostatic quadrupole–quadrupole and pairwise atom–atom interactions as well as on exact trajectories driven by an effective isotropic potential.     

1H NMR study of the hetero‐association of unsaturated alcohols with pyridine

The ¹H NMR titration method is used to investigate the association of some unsaturated alcohols with pyridine in benzene. The association constant for allyl alcohol (2‐propen‐1‐ol) is slightly higher than for alkanols, but putting one methylene group between the OH and vinyl group completely eliminates this enhancement. In alkynols both the OH and ≡CH protons associate with pyridine. Here, the effects of chain‐lengthening on the association constant are irregular. Values for alkynols and some alcohols with hetero‐atom substituents are lower than expected on the basis of a Taft polar constant (σ*) correlation of alkanol association constants and of a correlation with the pK_a’s of the corresponding carboxylic acids. It is suggested that stabilization of the ground state by OH/π interactions is responsible for these low association constants. Small increases in the NMR shifts of the OH protons in the 3‐carbon and 4‐carbon alkenols and alkynols can also be attributed to OH/π interactions, but the 5‐carbon analogues have shifts as low as alkanols. Copyright © 2011 John Wiley & Sons, Ltd.