K-sample problem using strong approximations of empirical copula processes

In this article we explore asymptotic properties of some statistics based on K-sample extensions of multivariate empirical copula processes. These statistics can be used to test the equality of copulas pertaining to K independent samples.     

Parallel Interactions at Large Horizontal Displacement in Pyridine–Pyridine and Benzene–Pyridine Dimers

A study of crystal structures from the Cambridge Structural Database (CSD) and DFT calculations reveals that parallel pyridine–pyridine and benzene–pyridine interactions at large horizontal displacements (offsets) can be important, similar to parallel benzene–benzene interactions. In the crystal structures from the CSD preferred parallel pyridine–pyridine interactions were observed at a large horizontal displacement (4.0–6.0 Å) and not at an offset of 1.5 Å with the lowest calculated energy. The calculated interaction energies for pyridine–pyridine and benzene–pyridine dimers at a large offset (4.5 Å) are about 2.2 and 2.1 kcal mol^?1, respectively. Substantial attraction at large offset values is a consequence of the balance between repulsion and dispersion. That is, dispersion at large offsets is reduced, however, repulsion is also reduced at large offsets, resulting in attractive interactions.     

Determination of137Cs and134Cs in air samples collected near Belgrade /Yugoslavia/ following the Chernobyl accident

This paper presents the results of measurements of¹³⁷Cs and¹³⁴Cs content in air sampled during May 1986. Maximum concentrations:¹³⁷Cs 2.94±0.01 Bq m^–3 and¹³⁴Cs 1.38±0.01 Bq m^–3 were registered on May 3. Several other long lived radionuclides having -energies in the region 33 keV to 1365 keV were registered in the same samples two years later. The results of measurements of the total -activity in air for the same period are also presented.     

Mechanistic investigation of the oxygen-atom-transfer reactivity of dioxo-molybdenum(VI) complexes

The oxygen-atom-transfer (OAT) reactivity of [LiPrMoO2(OPh)] (1, LiPr=hydrotris(3-isopropylpyrazol-1-yl)borate) with the tertiary phosphines PEt3 and PPh2Me in acetonitrile was investigated. The first step, [LiPrMoO2(OPh)]+PR3-->[LiPrMoO(OPh)(OPR3)], follows a second-order rate law with an associative transition state (PEt3, DeltaH not equal=48.4 (+/-1.9) kJ mol-1, DeltaS not equal=-149.2 (+/-6.4) J mol-1 K-1, DeltaG not equal=92.9 kJ mol-1; PPh2Me, DeltaH not equal=73.4 (+/-3.7) kJ mol-1, DeltaS not equal=-71.9 (+/-2.3) J mol-1 K-1, DeltaG not equal=94.8 kJ mol-1). With PMe3 as a model substrate, the geometry and the free energy of the transition state (TS) for the formation of the phosphine oxide-coordinated intermediate were calculated. The latter, 95 kJ mol-1, is in good agreement with the experimental values. An unexpectedly large O-P-C angle calculated for the TS suggests that there is significant O-nucleophilic attack on the P--C sigma* in addition to the expected nucleophilic attack of the P on the Mo==O pi*. The second step of the reaction, that is, the exchange of the coordinated phosphine oxide with acetonitrile, [LiPrMoO(OPh)(OPR3)]+MeCN-->[LiPrMoO(OPh)(MeCN)]+OPR3, follows a first-order rate law in MeCN. A dissociative interchange (Id) mechanism, with activation parameters of DeltaH not equal=93.5 (+/-0.9) kJ mol-1, DeltaS not equal=18.2 (+/-3.3) J mol-1 K-1, DeltaG not equal=88.1 kJ mol-1 and DeltaH not equal=97.9 (+/-3.4) kJ mol-1, DeltaS not equal=47.3 (+/-11.8) J mol-1 K-1, DeltaG not equal=83.8 kJ mol-1, for [LiPrMoO(OPh)(OPEt3)] (2 a) and [LiPrMoO(OPh)(OPPh2Me)] (2 b), respectively, is consistent with the experimental data. Although gas-phase calculations indicate that the Mo--OPMe3 bond is stronger than the Mo--NCMe bond, solvation provides the driving force for the release of the phosphine oxide and formation of [LiPrMoO(OPh)(MeCN)] (3).     

Hydrogen Bonding between Metal‐Ion Complexes and Noncoordinated Water: Electrostatic Potentials and Interaction Energies

The hydrogen bonding of noncoordinated water molecules to each other and to water molecules that are coordinated to metal‐ion complexes has been investigated by means of a search of the Cambridge Structural Database (CSD) and through quantum chemical calculations. Tetrahedral and octahedral complexes that were both charged and neutral were studied. A general conclusion is that hydrogen bonds between noncoordinated water and coordinated water are much stronger than those between noncoordinated waters, whereas hydrogen bonds of water molecule in tetrahedral complexes are stronger than in octahedral complexes. We examined the possibility of correlating the computed interaction energies with the most positive electrostatic potentials on the interacting hydrogen atoms prior to interaction and obtained very good correlation. This study illustrates the fact that electrostatic potentials computed for ground‐state molecules, prior to interaction, can provide considerable insight into the interactions.     

Hydrophilic alginate based multidentate biopolymers for surface modification of CdS quantum dots

We report that sodium alginate and its graft-copolymers with (2-dimethylaminoethyl) methacrylate may attach to the surface of colloidal CdS-thioglycerol quantum dots (QDs) via a ligand exchange process and result in water-soluble and highly stable QD supramolecules. Optical properties of modified QDs in water showed that the emission intensity of QDs was still high after surface passivation.     

Energetics of radical transfer in DNA photolyase

Charge separation and radical transfer in DNA photolyase from Escherichia coli is investigated by computing electrostatic free energies from a solution of the Poisson-Boltzmann equation. For the initial charge separation 450 meV are available. According to recent experiments [Aubert et al. Nature 2000, 405, 586-590] the flavin receives an electron from the proximal tryptophan W382, which consequently forms a cationic radical WH(*)(+)382. The radical state is subsequently transferred along the triad W382-W359-W306 of conserved tryptophans. The radical transfer to the intermediate tryptophan W359 is nearly isoenergetic (58 meV uphill); the radical transfer from the intermediate W359 to the distal W306 is 200 meV downhill in energy, funneling and stabilizing the radical state at W306. The resulting cationic radical WH(*)(+)306 is further stabilized by deprotonation, yielding the neutral radical W(*)306, which is 214 meV below WH(*)(+)306. The time scale of the charge recombination process yielding back the resting enzyme with FADH(*) is governed by reprotonation of W306, with a calculated lifetime of 1.2 ms that correlates well with the measured lifetime of 17 ms. In photolyase from Anacystis nidulans the radical state is partially transferred to a tyrosine [Aubert et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 5423-5427]. In photolyase from Escherichia coli, there is a tyrosine (Y464) close to the distal tryptophan W306 that could play this role. We show that this tyrosine cannot be involved in radical transfer, because the electron transfer from tyrosine to W306 is much too endergonic (750 meV) and a direct hydrogen transfer is likely too slow. Coupling of specific charge states of the tryptophan triad with protonation patterns of titratable residues of photolyase is small.     

Nature of the water/aromatic parallel alignment interactions

The water/aromatic parallel alignment interactions are interactions where the water molecule or one of its O? H bonds is parallel to the aromatic ring plane. The calculated energies of the interactions are significant, up to ΔE_{CCSD(T)(limit)} = ?2.45 kcal mol^?1 at large horizontal displacement, out of benzene ring and CH bond region. These interactions are stronger than CH···O water/benzene interactions, but weaker than OH···π interactions. To investigate the nature of water/aromatic parallel alignment interactions, energy decomposition methods, symmetry‐adapted perturbation theory, and extended transition state‐natural orbitals for chemical valence (NOCV), were used. The calculations have shown that, for the complexes at large horizontal displacements, major contribution to interaction energy comes from electrostatic interactions between monomers, and for the complexes at small horizontal displacements, dispersion interactions are dominant binding force. The NOCV‐based analysis has shown that in structures with strong interaction energies charge transfer of the type π → σ*(O? H) between the monomers also exists. © 2014 Wiley Periodicals, Inc.     

Asymptotic behavior of weighted multivariate Cramér-von Mises-type statistics under contiguous alternatives

In this paper, we study the behavior of the weighted quadratic functionals of the multivariate empirical copula processes under sequences of contiguous alternatives. The Karhunen-Loève expansions of the corresponding limiting Gaussian processes are derived by using the results, in a series of papers, by Deheuvels, which are used to obtain the asymptotic distribution of the weighted multivariate Cramér-von Mises-type statistics. These results are applied to compute the relative local asymptotic efficiency of the considered statistics, in the spirit of Genest et al. (2006, 2007), and discuss briefly some aspects regarding the power of these statistical tests. Finally, we give some additional results concerning the integrated copula processes.     

Interactions of Molecules with cis and trans Double Bonds: A Theoretical Study of cis‐ and trans‐2‐Butene

Noncovalent interactions of cis‐ and trans‐2‐butene, as the smallest model systems of molecules with cis and trans double bonds, were studied to find potential differences in interactions of these molecules. The study was performed using quantum chemical methods including very accurate CCSD(T)/CBS method. We studied parallel and displaced parallel interactions in 2‐butene dimers, in butane dimers, and between 2‐butene and saturated butane. The results show the trend that interactions of 2‐butene with butane are the strongest, followed by interactions in butane dimers, whereas the interaction in 2‐butene dimers are the weakest. The strongest calculated interaction energy is between trans‐2‐butene and butane, with a CCSD(T)/CBS energy of ?2.80 kcal mol^?1. Interactions in cis‐2‐butene dimers are stronger than interactions in trans‐2‐butene dimers. Interestingly, some of the interactions involving 2‐butene are as strong as interactions in a benzene dimer. These insights into interactions of cis‐ and trans‐2‐butene can improve understanding of the properties and processes that involve molecules with cis and trans double bonds, such as fatty acids and polymers.