The complete symmetrization of quantum operators: new thoughts on an old problem

The complete symmetrization with respect to x, p _x,... of the operators associated with dynamical properties can sometimes lead to results different from those obtained by the conventional quantum formalism based on the rule op (A ²)=(op A)². For example, angular momentum operators M _z ² and M ² are modified by the additive constants ²/2 and 3 ²/2 respectively (M ²0 for electron in the ground state of H atom, rotator never at rest, but spectra unchanged); the average quadratic dispersion of energy is different from zero. These results can be interpreted by assuming that the system is never strictly isolated but communicates with the other systems of the universe by means of electromagnetic interactions. Quantum mechanics would give only average values over a sufficiently long time and would exhibit a quasi-ergodic character. Examples supporting this possibility are given, in particular that of arsines for which quantum forecasts correspond to average values over one year.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Synthesis and 1H NMR study of 3,4-di ethyl-1,2,3,3a,4,5-hexahydro-canthinone-6

The racemic mixtures of the two epimers of 3,4-diethyl-l,2,3,3a,4,5-hexahydro-canthinone-6 (3,4-diethyl-2,3,3a,4,5,6-hexahydro-6-oxo-1H-indolo-(3,2,1 ,de) (1,5)naphtyridine) have been prepared. They were separated by crystallization of one of the synthesis intermediates. Identification of the configuration was possible by 1h NMR spectroscopy after running a 2D J-resolved spectrum of the “cis”-isomer.     

A proposal for the molecular basis of μ and δ opiate receptor differentiation based on modeling of two types of cyclic enkephalins and a narcotic alkaloid

Summary The molecular basis underlying the divergent receptor selectivity of two cyclic opioid peptides Tyr-c[N -d-Orn²-Gly-Phe-Leu-] (c-ORN) and [d-Pen², l-Cys⁵]-enkephalinamide (c-PEN) was investigated using a molecular modeling approach. Ring closure and conformational searching procedures were used to determine low-energy cyclic backbone conformers. Following reinsertion of amino acid side chains, the narcotic alkaloid 7-[(1R)-1-methyl-1-hydroxy-3-phenylpropyl]-6,14-endoethenotetrahydro oripavine (PEO) was used as a flexible template for bimolecular superpositions with each of the determined peptide ring conformers using the coplanarity and cocentricity of the phenolic rings as the minimum constraint. A vector space of PEO, accounting for all possible orientations for the C₂₁-aromatic ring of PEO served as a geometrical locus for the aromatic ring of the Phe⁴ residue in the opioid peptides. Although a vast number of polypeptide conformations satisfied the criteria of the opiate pharmacophore, they could be grouped into three classes differing in magnitude and sign of the torsional angle values of the tyrosyl side chain. Only class III conformers for both c-ORN and c-PEN, having tyramine dihedral angles ₁ =–150° ± 30° and ₂=–155° ± 20°, had significant structural and conformational properties that were mutually compatible while respecting the PEO vector space. Comparison of these properties in the context of the divergent receptor selectivity of the studied opioid peptides suggests that the increased distortion of the peptide backbone in the closure region of c-PEN together with the pendant ,-dimethyl group, combine to generate a steric volume which is absent in c-ORN and that may be incompatible with a restrictive topography of the receptor. The nature and stereo-chemistry of substituents adjacent to the closure region of the peptides could also modulate receptor selection by interacting with a charged () or neutral () subsite.     

Configurational conditions and digraphs

Configurational conditions (Schließungsaussagen) of a noncommutative space will be developped from pairs (, ) of digraphs where is a partial digraph of . In this way we obtain an extensive generalization of Pfalzgraf 's q-simplex-conditions Sim_q.In Memoriam Hans Zassenhaus     

Recherches sur la structure électronique et les caractéristiques des différentes formes tautomères de la purine

Résumé Les caractéristiques électroniques (énergie, charges , géométrie, moment dipolaire, énergie de transition) des quatre formes tautomères de la purine et des phényl-8 N(1)H et N(3)H purines ont été déterminées par la méthode LCAO améliorée. La forme 9 est trouvée la plus stable à l'état isolé. Une interprétation nouvelle des bandes d'absorption est proposée.

---

Researches on the electronic structure and the characteristics of various tautomer forms of Purine

The electronic characteristics (energy, charge , geometry, dipole moment, transition energy) of the four tautomeric forms of the purine and of the phenyl-8 N(1)H and N(3)H purines have been determined by the improved LCAO method. The form 9 is considered as the most stable at the isolated state. A new interpretation of the absorption bands is proposed.

---

Zusammenfassung Die elektronischen Charakteristiken (Energie, Ladung , Geometrie, Dipolmoment, Übergangsenergie) der vier Tautomerformen des Purins und der Phenyl-8 N(1)H und N(3)H Purine sind durch die verbesserte LCAO-Methode bestimmt worden. Die Form 9 ist, zum isolierten Stand, als am meisten beständig zu betrachten. Eine neue Erklärung der Absorptionsbänder ist vorgeschlagen.

---

---

Les auteurs remercient le Professeur B. Pullmann (Paris) de l'intérêt qu'il a porté à ce travail, ainsi que Madame H. Feilchenfeld (Jérusalem) pour les résultats inédits qu'elle a bien voulu leur communiquer.     

Magnetic properties on holmium iron garnet in high magnetic field. Optical absorption spectra in the infra-red region

On single crystals of holmium iron garnet (HoIG), magnetic properties have been studied in magnetic field up to 150kOe applied parallel to the main crystallographic directions in the 4.2–300K temperature range. Above 130 K, the magnetization is isotropic and linear magnetic field dependent as previously found in polycrystals and predicted by Néel's ferrimagnetic theory. Nevertheless the paramagnetic Curie temperature is much higher than the polycrystal value. Below 130K, due to the onset of the umbrella structure, the ferrite magnetization presents a non linear field variation with [111] as easy direction. The field evolutions of the anisotropy constants (K ₁ andK ₂) were calculated. Optical absorption measurements of both 5₈5I ₆ and 5I ₈5I ₇ transitions are reported and compared to the results of the literature in terms of inequivalent magnetic sites.     

2-Amino-4-bromobutanoic Acid

(2S)- and (2R)-2-Amino-4-bromobutanoic acid were prepared starting from N-Boc-glutamic acid α tert-butyl ester. The double tert-butyl protection was necessary to prevent a partial racemisation during Barton’s radical decarboxylation used to transform the γ-carboxylic group into a bromide. This bromide reacted with different nitrogen, oxygen and sulphur nucleophiles to give nonnatural amino acids characterised by basic or heterocyclic side chains. The title compound was also used to prepare a conformationally constrained peptidomimetic.     

Regioselectivity in methylation and phenylation of the zwitterionic pyrido[2,1-f]-as-triazinium-1- and 3-olates and thiolates

Substituted derivatives of the title ring system have been synthesized and the regioselectivity in methylation and phenylation of the zwitterionic pyrido[2,1-f]-as-triazinium 1- and 3-olates 4a-g and 10 and thiolates 7a,b and 12 has been studied by nmr techniques. Depending on the soft or hard nature of the used reagent (methyl iodide, trimethyloxonium hexafluorophosphate or diphenyliodonium tetrafluoroborate), the reaction yielded NMe 5 and/or OMe 6,11a and NPh 14 or OPh 11b products in the case of olates; while thiolates gave NMe 8 and/or SMe 9,13a and SPh 13b, 15 compounds. Mechanistic suggestions are given to rationalize the observed phenomena.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.