Electronic structure and spectra of organic molecules

The Pariser-Parr-Pople method is used to predict the singlet-singlet ( ^* type). Electronic transition energies for the anions of hydroxy derivatives of benzene, pyridine and pyrimidine. The core integral for the -O^– substituent was treated as an empirical parameter and its value was chosen to fit results for the phenoxide ion and then applied for the compounds with the -O^– substituents. The results of the calculations for molecules with the -O^– groups are compared with those of the corresponding molecules containing the -OH and -NH₂ substituents as well as with the experimental data. No serious deviations between theoretical and experimental data other than those which could be ascribed to steric hindrances occuring in the molecules were found.

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Zusammenfassung Die Pariser-Parr-Pople-Methode wird benutzt, um die Singlett-Singlett-Übergangsenergien (- ^*-Typ) von Benzol-, Pyridin- und Pyrimidinderivaten zu berechnen, die OH-Gruppen enthalten. Das Rumpfintegral des -O^–-Substituenten wurde wie ein empirischer Parameter behandelt. Sein Wert wurde so gewählt, daß er die Meßergebnisse für das Phenolat-Anion richtig wiedergibt. Die Resultate der Berechnungen für Moleküle mit der -O^–-Gruppe werden mit denjenigen für die entsprechenden Moleküle mit OH- und NH₂-Substituenten als auch mit den experimentellen Daten verglichen. Es werden keine ernsten Abweihungen zwischen theoretischen und experimentellen Daten gefunden, außer solchen, die einer sterischen Hinderung zugeschrieben werden können.

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Résumé La méthode de Pariser, Parr et Pople est utilisée pour prédire les transitions électroniques ( ^*) pour les formes anioniques des derivés hydroxy du benzène, pyridine et pyrimidine. La valeur d'integrale de coeur associée du substituant -O^– a été choisie de façon à reproduire les positions des bandes d'absorption de forme anionique du phenol et après elle a été appliquée pour les composés envisagés. Les resultats des calculs pour l'anions sont mis en comparaison avec les resultats obtenus pour les correspondantes derivés aminés et hydroxy et avec les donnés experimentales. Peu de déviations ont été obtenus, en dehors de ceux que l'on peut attribuer à des encombres steriques.

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Based in part on a M. Sci. thesis by M. Berndt, N. Copernikus University, Toru, 1969 (unpublished, in Polish).     

On strong summability of multiple Fourier series and smoothness properties of functions

_n —n- — ƒ()L _v (T _n ), 1f, - -. -.     

Über substituierte 1,6-Dihydro-1,3,5-triazin-2,4-diamine, 1′,5′,6′,7′-Tetrahydrospiro[cyclopentan-1,4′-cyclopentapyrimidin]-2′(3′ H)-imine und das 6-Phenyl-2,4-pyrimidindiamin

Guanidine reacts with cyclohexanone, cycloheptanone, acetone and 3-pentanone, resp., in a molar ratio 2∶1 to give the 1,3,5-triazaspiro[5.5]undeca-and [5.6]dodeca-1,3-dien-2,4-diamines3 a and3 b resp. and the 6,6-dimethylresp. diethyl-1,6-dihydro-1,3,5-triazin-2,4-diamines3 d and3 e resp. On the contrary, action of guanidine on cyclopentanone yields not3 c, but the 1′,5′,7′-tetrahydrospiro[cyclopentane-1,4′-cyclopentapyrimidine]-2′(3′H)-imines2 c, 5 c and6 c resp., which are 1∶2- and 1∶3-condensates. Phenylacetone is transformed by guanidine (1∶2) to give 6-phenyl-2,4-pyrimidindiamine (8 f). The structure of the compounds cited is proved by NMR-, IR-, and (partially) mass spectra. The different courses of the formation of3 a, b, d, e, 2 c, 5 c and6 c resp. and8 f are also discussed. The structural formulae of some additional bases, which were synthesized from guanidine and cyclopentanone, 3-pentanone and phenylacetone resp. could not be established.     

Zur Längenberechnung der Torsion äusserer Potenzen

Let R be a noetherian ring of dimension d and M a finitely generated R-module of homologic dimension less or equal to one. Assume further that M has a rank r, which equals d or (in case d>0) d?1 and that the r-th Fitting-ideal \(\vartheta _r (M)\) of M has grade ?d. Then the torsion-submodule of the d-th exterior power of M and the module \(R/\vartheta _r (M)\) are equivalent.     

A short note on Dedekind sums

We will give a new proof for the fact that the values of Dedekind sums are dense on the real line.     

C-S Bond Cleavage Reactions of Sulfonediimines

Abstract

Nucleophilic C-S bond cleavage of Sulfonediimines to Sulfinamidine-type Structures is discussed     

Interpolation of Morrey-Campanato and related smoothness spaces

We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.     

1,2- and 1,3-diphosphetanes from alkylidenephosphines

Abstract

Alkyl- or arylbis(trimethylsilyl)phosphines as well as tris(trimethylsilyl)phosphine and the corresponding arsines react with acyl chlorides to give [1-(trimethylsiloxy)alkylidene]phosphines 1 and -arsines 2; most of their 2,2-dimethylpropylidene derivatives are thermally stable at room temperature. With the same class of phosphines as starting compounds and carbon disulfide [bis(trimethylsilylsulfano)methylidene]phosphines 3 are formed, whereas [(dialkylamino)methylidene]-4 and [diarylmethylidene]phosphines 5 or the corresponding arsines 6 and 7 can be obtained from acyl amides or ketones.¹