No abstract

No abstract

The implementation of global optimization algorithms, using the arithmetic of infinity, is considered. A relatively simple version of implementation is proposed for the algorithms that possess the introduced property of strong homogeneity. It is shown that the P-algorithm and the one-step Bayesian algorithm are strongly homogeneous.

A study of the enantiomers of bicyclo[3.3.1]nonane-2,7-dione, a chiral molecule containing two carbonyl chromophores, was performed. Enantiomers of this structure were obtained by HPLC resolution and the (+)-(1R,5S)-enantiomer by enantiospecific synthesis from(+)-(1S,5S)-bicyclo[3.3.1]nonane-2,6-dione. The title structure is an interesting molecule to demonstrate the validity of the octant rule. The location of the major chair-chair conformer into octants placing each chromophore into the origin of the octants led to the opposite configuration assignments. In order to prove unequivocally absolute configuration, enantiospecific synthesis of the title compound was carried out. The kinetic resolution of racemic bicyclo[3.3.1]nonane-2,6-dione using baker's yeast afforded (+)-(1S,5S)-2,6-dione. Employing a reaction sequence analogous to one developed earlier by us with racemic substrates led to carbonyl group shift giving enantiomerically pure (+)-(1R,5S)-bicyclo[3.3.1]nonane-2,7-dione. The absolute configuration of the investigated compound was established by combined use of the octant rule and chemical correlation.

No abstract

The synthesis of a C2-symmetric cleft molecule 2 based on the fused framework between bicyclo[3.3.1]nonane and 4-oxo-5-azaindole, incorporating a self-complementary hydrogen-bonding motif, in both racemic and enantiomerically pure forms is reported. This cleft molecule is reminiscent of analogues of Tröger's base though with different cleft dimensions and tilt angles. The framework of 2 provides a building block for the construction of self-assembled hydrogen-bonded supramolecular structures. The solid-state structure of 2 is highly influenced by the limited solubility of (+/-)-2 and (-)-2. The solvents interact with the potential hydrogen-bonding motifs of (+/-)-2 and (-)-2, forming different three-dimensional structures as revealed by X-ray diffraction analysis. In the solid state (+/-)-(2)2 x 5DMF forms hydrogen-bonded pleated band structures that build up three-dimensional pens between adjacent bands in which two molecules of DMF are trapped. In contrast, the aggregate obtained from (-)-2, (-)-2 x 2AcOH, showed infinite bands of complex constitution.

The enantiospecific synthesis of several bicyclic enones starting from enantiomerically pure (+)‐(1S,5S)‐bicyclo[3.3.1]nonane‐2,6‐dione (1) was accomplished. The target enones 7–9 were obtained in high yield and purity by using a catalytic amount of benzeneselenic anhydride. (+)‐(1S,5R)‐bicyclo[3.3.1]nonane‐2,3,6‐trione was obtained from diketone 1 by α‐hydroxylation involving the use of iodine under basic conditions. The reaction included a ring closure/reopening sequence via oxatricyclo[4.3.1.03,8]decane‐10‐one. It was shown that the latter triketone exists in enone/enol form. Chiroptical properties of the enantiomerically pure compounds were studied, and the sign of the Cotton effect was related to the absolute configuration of the enones. The positive Cotton effect in the bisignate CD curve is accounted for by the nonplanarity of the chromophore in enones (1S,5R)‐4 and (1S,5S)‐8. The circular dichroism spectra provided evidence for interchromophoric interaction in dichromophoric bis(enone) 9. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.