Rayleigh light scattering in molecular crystals of succinonitrile and trimethylacetonitrile

Two representatives of molecular crystals exhibiting plastic phase : succinonitrile NCCH₂CH₂CN and trimethylacetonitrile |CH₃|₃CCN were studied. For these crystals the horizontally and vertically polarized components of the scattered radiation were measured in the temperature range from the plastic phase to liquid, and the depolarization degrees were determined. The isotropic component V_V was also measured as a function of temperature changing from liquid to plastic phase. In both phases the squares of effective anisotropy of optical polarizability were found from the measurements of the anisotropic component H_V.     

On symmetry of discrete polynomial hypergroups

Let be a discrete polynomial hypergoup on with Plancherel measure If the hypergroup is symmetric, the set of characters can be identified with a compact subset of the real line which contains the support of We show that the lower and upper bounds of and coincide. In particular, the trivial character belongs to the support of the Plancherel measure.

     

Gradient discontinuities in calculations involving molecular surface area

The free energy of solvation of a polypeptide or a protein can be expressed in terms of the accessible surface area of the molecule. Algorithms for energy minimization or for molecular dynamics, which involve the first derivatives of the energy, including the free energy of solvation, are commonly used in the conformational analysis of proteins. Discontinuities of the first derivatives, which occur in the accessible surface area and, hence, in the solvation energy, can cause serious numerical problems. In this paper, we describe all the situations in which the gradient of the molecular surface area becomes discontinuous.     

(1Z,3Z)-1,4-Di(pyridin-2-yl)buta-1,3-diene-2,3-diol: the planar highly conjugated symmetrical enediol with multiple intramolecular hydrogen bonds

1H, (13)C, and (15)N NMR spectral data show that in chloroform solution (1Z,3Z)-1,4-di(pyridin-2-yl)buta-1,3-diene-2,3-diol, OO, is in ca. 9:1 equilibrium with (3Z)-3-hydroxy-1,4-di(pyridin-2-yl)but-3-en-2-one, OK, while no 1,4-di(pyridin-2-yl)-2,3-butanedione, KK, was detected. The species present in the tautomeric mixture were identified by comparing their experimental chemical shifts with those known for similar compounds as well as with the theoretically calculated (GIAO-HF/DFT) values. Ab initio calculations show that OK and especially the highly conjugated OO forms are preferred in the tautomeric mixtures both in vacuo and in chloroform solution. Comparison of experimental (Arrhenius) and calculated (ab initio) energies of OK shows that the MP2/6-31G//RHF/6-31G method gives the most precise results. There are one and two strong O-H.N hydrogen bonds present in the molecules of the former and latter compound, respectively. Other tautomeric forms, e.g., dienaminedione [(1Z,4Z)-1,4-di[pyridin-2(1H)-ylidene]butane-2,3-dione], and their rotamers were found to have higher energies. The single-crystal X-ray diffraction studies show that dienediol OO is the only tautomeric form present in the crystal at 173 K. Its almost perfectly planar molecule is stabilized by two strong intramolecular O-H.N hydrogen bonds.     

Autoassociates and tautomerism of 2-oxo-5-halogenopyrimidines: theoretical and experimental investigations

Theoretical calculations (on a semi-empirical level) of energy and geometry of the autoassociates of two tautomeric forms of 2-oxo-5X-pyrimidines (X = H, Cl, Br) are presented. On the basis of the calculated energies of autoassociates it is possible to explain the enol—keto tautomeric transition between the gas phase and condensed phases. We propose a double-proton transfer reaction as a possible mechanism for the tautomeric transition.

Infrared absorption spectra of 2-oxo-5X-pyrimidines in the v(NH …) and v(C=O) regions in solid phases and in low-temperature argon matrices are also presented and discussed. Comparison of IR spectra and results of the theoretical calculations with known crystallographic structures of 2-oxo-5X-pyrimidines (X = H, F, Cl) lead to the conclusion that the crystal structure of the 5-bromo derivative should be similar to that of the 5-chloro derivative.     

Studies on the application of the Passerini reaction and enzymatic procedures to the synthesis of tripeptide mimetics

A new, efficient method for the multicomponent synthesis of tripeptide mimetics is presented. Simple, chemoenzymatic transformations of Passerini reaction products enable the introduction of varied amino acid moieties into the tripeptide scaffold, with control of the stereochemistry. Additionally, this method allows the convenient introduction of a methyl group to the amide nitrogen, leading to derivatives of N-methylated amino acids—compounds of interest for medicinal chemistry.     

Effect of a Carboxylic Group on the Conformational Properties of Some Gemini Surfactants

Molar volumes of derivatives of N,N-bisdimethyl-1,2-ethanediamine of general formula [C _n H_2n+1OOCCH₂(CH₃)₂N⁺CH₂CH₂N⁺(CH₃)₂CH₂COOC _n H_2n+1]2Cl⁻ (bis-C _n BEC), and betaine ester derivatives of general formula N⁺(CH₃)₃CH₂COOC _n H_2n+1Cl⁻ (C _n BEC), were calculated by means of molecular connectivity indices and an additivity scheme. The COO group contribution in the β-position to the molar volume of bis-C _n BEC was found from experimental data to be significantly lower from that for C _n BEC and was estimated to be 13.5 cm³⋅mol⁻¹. It is suggested that this effect is due to hydrogen bonding between the carboxyl groups via water molecules. Molecular dynamics simulations of bis-C₁₂BEC and 14–2–14 molecules in water were performed and suggest that the upper part of the bis-C₁₂BEC, containing the carboxyl groups, is stiffened by its hydration shell.     

Linearization and connection coefficients of orthogonal polynomials

Let {P _n } _n ^=0/ be a system of orthogonal polynomials.Lasser [5] observed that if the linearization coefficients of {P _n } _n ^=0/ are nonnegative then each of theP _n (x) is a linear combination of the Tchebyshev polynomials with nonnegative coefficients. The aim of this paper is to give a partial converse to this statement. We also consider the problem of determining when the polynomialsP _n can be expressed in terms ofQ _n with nonnegative coefficients, where {Q _n } _n ^=0/ is another system of orthogonal polynomials. New proofs of well known theorems are given as well as new results and examples are presented.