Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) in the Kohn–Sham (KS) complete basis set (CBS) limit. Correlation‐consistent cc‐pVxZ and cc‐pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ‐pVxZ, unc‐ccJ‐pVxZ, and aug‐cc‐pVTZ‐J) and polarization‐consistent pc‐n and pcJ‐n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT‐predicted isotropic shieldings, spin–spin values, and the experimental values was good and similar for the modified correlation‐consistent and polarization‐consistent basis sets. The BHandH method predicted the most accurate ¹H, ¹⁷O isotropic shieldings and ¹J(OH) coupling constant (deviations from experiment of about ? 0.2 and ? 1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and ¹J(OH) is similar to the more advanced methods, second‐order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit. Copyright © 2008 John Wiley & Sons, Ltd.     

Intensity distribution in the vibronic side bands of the Γ7(2 T 2g ) → Γ8(4 A 2g ) origin of ReX 6 2- doped K2PtCl6-type crystals

Intensities of vibronic transitions are calculated using an electronic vibrational coupling scheme of symmetrized and localized interactions. The model consists of an active central ion subject to a valence force field originating from nearest-neighbor displacements. The intensities of vibronic fundamentals are obtained from a generalized Lorentzian line shape function which is applied to the ₇(² T _2g ) ₈(⁴ A _2g ) transition of ReCl ₆ ^2- and ReBr ₆ ^2- in various cubic host crystals A₂MX₆ (A = Rb, Cs; M = Te, Sn, Pb; X = Cl, Br). Relative intensities of the odd vibronic side bands are calculated without knowing actual values for ligand field and spin-orbit coupling parameters, and considering only octahedral vibrational frequencies. The sidebands acquire intensity by a coupling which is cubic in the electron coordinates and linear in the nuclear normal coordinates. With some necessary approximations the present model is able to reproduce the experimental intensity distribution satisfactorily.Dedicated to Professor Dr. H. Hartmann on the occasion of his 65th birthday     

On a group of two-parameter intramolecular distributions and their properties

A group of two-parameter intramolecular distributions for degenerate vibrations has been investigated. The distributions are of physical significance in calculating electronic transitions and have certain important properties which are formulated in terms of addition theorems.     

Concentration of the first eigenfunction for a second order elliptic operator

We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold when the diffusion constant ε goes to zero. We assume that the first order term is given by a vector field b, whose recurrent components are either hyperbolic points or cycles or two dimensional torii. The limits of the normalized eigenfunctions concentrate on the recurrent sets of maximal dimension where the topological pressure [Y. Kifer, Principal eigenvalues, topological pressure and stochastic stability of equilibrium states, Israel J. Math. 70 (1990) (1) 1–47] is attained. On the cycles and torii, the limit measures are absolutely continuous with respect to the invariant probability measure on these sets. We have determined these limit measures, using a blow-up analysis. To cite this article: D. Holcman, I. Kupka, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Die vibronische Kopplung in Koordinationsverbindungen am Beispiel von Hexahalogenokomplexen

Ohne Zusammenfassung

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The vibronic coupling in coordination compounds. hexahalogeno complexes as example