Ab initio CPHF calculations of the static polarizability and second hyperpolarizability of small molecules: Comparisons between standard and moderately large basis sets augmented with diffuse functions

Static polarizability and second hyperpolarizability have been calculated for a number of small molecules? CO₂, OCS, CS₂, C₂H₂, C₂H₆, C₃H₈, cyclo-C₃H₆, C₃H₄, C₃H₆, SiH₄, Si₂H₆? in the framework of the coupled-perturbed Hartree-Fock (CPHF ) theory. The linear and nonlinear coefficients have been calculated with standard Gaussian basis sets and 3-21G bases moderately enlarged with diffuse functions. It is shown that the parallel component of the polarizability saturates rapidly, which suggests that a 3-21G basis containing s and p diffuse functions is sufficient to reproduce α_zz. For the α_xx and α_yy components, a 3-21G basis with s, p, and d diffuse functions is required. In general, the concordance between α computed with this basis set and the experimental static polarizability is at least of the order of 80%. On the contrary, the computation of the second hyperpolarizability with the same basis set for CO₂, CS₂, and C₂H₂ gives values that are 30% too low, compared to the experimental value. Better results are observed for ethane, propane, and cyclopropane for which the error is lower than 50%. The better agreement observed for the saturated compounds can probably be explained by their saturated character.     

Channel inclusion of potassium and tetrachloroplatinate ions in a complex formed between 1,3-diamino-2-propanone and K2PtCl4 in an acidic medium

The crystalline complex dipotassium 1,3-diammonio-2-propanone tetrachloroplatinate trihydrate, formulated as K₂[(NH₃CH₂C)₂O][PtCl₄]₂ · 3H₂O, has been prepared while synthesizing complexes analogous tocis-dichlorodiamine Pt(II). Its structure is orthorhombic, space groupPnma,M _r = 896.1,F(000) = 1640,a = 8.428(4),b = 20.360(10),c = 12.141(7)A,V = 2083.3ų,Z = 4,D _x = 2.860 g cm^–3, (MoK _x) = 196 cm^–1, finalR = 0.083 for 1379 unique reflections. The structure consists of a very extended hydrogen bonded network which involves half of the PtCl₄ ^2– ions, the organic molecules and the water molecules of hydration, leaving large oval channels which accommodate potassium cations and tetrachloroplatinate anions. Within the channel the potassium and tetrachloroplatinate ions pack in columns extending along the a axis. The dense packing is rather reminiscent of that found in the neat salt where each potassium ion is surrounded by six chlorine atoms which describe a polyhedron of a distorted trigonal prism with K⁺ —C1 distances ranging between 3.163–3.187 Å. There is some indirect evidence for the formation of 1,3-diammonio-2-propanone dications which counterbalance the charges of half of the PtCl₄ ^2– ions by protonation of each of the amino nitrogens. The carbonyl oxygens, however, are involved only in a very weak O-C-O interactions along thea axis.     

A new look at the John–Nirenberg and John–Strömberg theorems for BMO

We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John–Nirenberg inequality and of related inequalities due to John and to Wik. Our approach enables us to pose a simply formulated “geometric” question, for which an affirmative answer would lead to a version of the John–Nirenberg inequality with dimension free constants.     

Kinetic deconjugation: a gateway to the synthesis of Xxx-Gly (E)-alkene dipeptide isosteres

A new method for the preparation of Xxx-Gly (E)-alkene dipeptide isosteres (EADIs), using LDA deprotonation followed by 1 N HCl quench, was explored. The method, named kinetic deconjugation, enabled the synthesis of Tyr-Gly, Gly-Gly, Ser-Gly, Pro-Gly, and Phe-Gly EADIs, as well as one Tyr-Gly trisubstituted alkene dipeptide isostere (TADI). Overall, this method, based on commercially available materials, leads to high yields, requires few synthetic steps and works on the gram scale in the synthesis of a wide variety of EADIs.     

Cyclic Peptide–Polymer Complexes and Their Self‐Assembly

Pepped up polymers : The synthesis and properties of novel chiral cyclic peptides designed to complex with suitable polymers through hydrogen bonding are described. A substituted cyclic peptide self‐assembles into supramolecular nanotubes and develops noncovalent interactions with poly(vinyl alcohol) (PVA) by means of its carboxyl side chains.

     

Sobolev type embeddings in the limiting case

We use interpolation methods to prove a new version of the limiting case of the Sobolev embedding theorem, which includes the result of Hansson and Brezis-Wainger for W _n ^k/k as a special case. We deal with generalized Sobolev spaces W _A ^k , where instead of requiring the functions and their derivatives to be in L_n/k, they are required to be in a rearrangement invariant space A which belongs to a certain class of spaces “close” to L_n/k. We also show that the embeddings given by our theorem are optimal, i.e., the target spaces into which the above Sobolev spaces are shown to embed cannot be replaced by smaller rearrangement invariant spaces. This slightly sharpens and generalizes an, earlier optimality result obtained by Hansson with respect to the Riesz potential operator. In memory of Gene Fabes. Acknowledgements and Notes This research was supported by Technion V.P.R. Fund-M. and C. Papo Research Fund.