On the nature of electron donor-acceptor interactions: 2. Mulliken's charge-transfer theory and the problem of the increase in intensity of the infrared band associated with iodine-base complexes

A relation between the enthalpy of formation and the rate of change with normal coordinate of the dipole moment contribution due to the charge-transfer phenomenon is derived for electron donor-acceptor complexes formed between halogen and organic molecules. The relation is found to hold for a number of iodine complexes.     

13C chemical shifts of phenol derivatives. A correlation with electronic structure

The ¹³C chemical shifts of twenty chloro- and nitro-substituted phenols have been measured in d-chloroform. The influence of substituents on the screening at C-1, on the total charge at this position and on the dipole moments is reported and analysed. The results of this study suggest that variations of the chemical shifts at C-1 for meta-methyl-, meta-chloro-, meta-nitro-, ortho- and para-methyl-, ortho- and para-chlorosubstituents mainly reflect charge density changes. The influence of ortho-nitro groups on the screening of C-1 is more complex.     

Linearized Boltzmann equations I: Representation of solutions

In this paper we obtain a probabilistic representation of the solutions of a linearized Boltzmann equation. By making use of dual Markov processes we extend Pinsky's results to the case where there is a gradient force field present.     

CNDO/2 molecular orbital calculations of the hemi-Dewar and valene structures of naphthalene

CNDO/2 molecular orbital calculations have been carried out on the hemi-Dewar and valene structures of naphthalene in order to determine the configuration of minimum energy.     

Strong and electromagnetic J/ψ and ψ(2S) decays into pion and kaon pairs

We discuss interference effects important for the form factors extraction in the vicinity of J/ψ andψ(2S)resonances in combination with resonance parameters determination.The implementation to the Monte Carlo event generator PHOKHARA of the J/ψ and ψ(2S)contributions to the muon,pion and kaon pairs production associated with a photon at next-to-leading order is also described.     

On the optimal convergence rate of universal and nonuniversal algorithms for multivariate integration and approximation

We study the maximal rate of convergence (mrc) of algorithms for (multivariate) integration and approximation of -variate functions from reproducing kernel Hilbert spaces . Here is an arbitrary kernel all of whose partial derivatives up to order satisfy a Hölder-type condition with exponent . Algorithms use function values and we analyze their rate of convergence as tends to infinity. We focus on universal algorithms which depend on , , and but not on the specific kernel , and nonuniversal algorithms which may depend additionally on .

For universal algorithms the mrc is for both integration and approximation, and for nonuniversal algorithms it is for integration and with for approximation. Hence, the mrc for universal algorithms suffers from the curse of dimensionality if is large relative to , whereas the mrc for nonuniversal algorithms does not since it is always at least for integration, and for approximation. This is the price we have to pay for using universal algorithms. On the other hand, if is large relative to , then the mrc for universal and nonuniversal algorithms is approximately the same.

We also consider the case when we have the additional knowledge that the kernel has product structure, . Here are some univariate kernels whose all derivatives up to order satisfy a Hölder-type condition with exponent . Then the mrc for universal algorithms is for both integration and approximation, and for nonuniversal algorithms it is for integration and with for approximation. If or for all , then the mrc is at least , and the curse of dimensionality is not present. Hence, the product form of reproducing kernels breaks the curse of dimensionality even for universal algorithms.

     

Coordination ability of trans-cyclohexane-1,2-diamine-N,N,N',N'-tetrakis(methylenephosphonic acid) towards lanthanide(III) ions

The proton and metal complex equilibria of trans-cyclohexane-1,2-diamine-N,N,N',N'-tetrakis(methylenephosphonic acid) (CDTP) with lanthanide(iii) ions, where Ln(III) = La(III), Nd(III), Sm(III), Eu(III), Gd(III), Tb(III), Ho(III) and Lu(III) were studied. The stoichiometry, protonation and complex formation constants were determined by potentiometric titration at 25.0 degrees C and ionic strength of 0.1 mol dm(-3) (KCl). All metal ions form several species: [LnH4L]-, [LnH3L](2-), [LnH2L](3-), [LnHL](4-), [LnL](5-), [LnH(-1)L](6-) and [LnH(-2)L](7-) in the pH range between 2 and 11. The stability constants log beta(LnL) were found to be between 14.7 and 16.7. The studied complexes were also characterized by spectroscopic methods (31P NMR, UV-Vis absorption and emission spectroscopy). These studies allowed to reveal a distinct structural change of the Ln(III)-CDTP complex which occurs between protonated and hydroxy species in solutions at pH around 7.5. The major change is caused by the involvement of both nitrogen donors in the metal ion coordination occurring in ML species. The data obtained from UV-Vis spectroscopy allowed to draw conclusions about complex symmetry and to estimate a number of coordinated water molecules. The hydration number or more precisely the number of two OH oscillators was found to be approximately one in all species formed over the pH range between 5 and 10. The structure of the major hydroxy complex was supported by X-ray crystallographic data. The crystal structures of the Eu(III) and Tb(III) complexes clearly show that the CDTP ligand is coordinated to the Ln(III) ion by two nitrogen and four oxygen atoms in such a way that only one oxygen atom from each phosphonic group is placed in the lanthanide inner sphere. The monomeric complex anion is connected to a symmetry related ion through short hydrogen bonds formed by two hydroxy ions and one water molecule. In this way the two neighbouring anions form a quasi-dimer in which one of the Ln(III) ion is seven-coordinate (two N atoms, four O atoms and one hydroxy ion) and the other is eight-coordinate (two N atoms, four O atoms, one hydroxy ion and one water molecule).