Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances

Rules for molecular cyclicity based on the global indices resulting from reciprocal distances (Harary number, H) or from resistance distances (Kirchhoff number, Kf) were tested in comparison with those elaborated earlier by means of the Wiener index, W. The Harary number and the Wiener number were found to match molecular cyclicity in an almost identical manner. The Kirchhoff number also generally follows cyclicity trends described previously. H is slightly less degenerate than is W, but Kf has practically no degeneracy in the graphs investigated here. Being much more discriminating than the Wiener number (i.e., practically nondegenerate), Kf allowed the formulation of new rules for systems formed from linearly condensed ribbons of even-membered rings with different sizes as well as for branched ribbons. The topological cyclicity patterns are thus reformulated in an extended basis, proceeding from three different graph metrics. © 1994 John Wiley & Sons, Inc.     

Synthesis of new non‐symmetrical substituted 7,7′‐bisindolizines by the direct reaction of 4,4′‐bipyridinium‐ylides with dimethyl acetylenedicarboxylate

We report here on the synthesis of some novel non‐symmetrical substituted bisindolizines by 3+2 dipolar cycloaddition reaction. New compounds were prepared by the direct reaction of isolated non‐symmetrical substituted 4,4′‐bipyridinium bisylides with dimethyl acetylenedicarboxy late (DMAD). The obtained compounds can be used as precursors of fluorescent markers in fluorometric analysis.     

Single point activation of pyridines enables reductive hydroxymethylation

The single point activation of pyridines, using an electron-deficient benzyl group, facilitates the ruthenium-catalysed dearomative functionalisation of a range of electronically diverse pyridine derivatives. This transformation delivers hydroxymethylated piperidines in good yields, allowing rapid access to medicinally relevant small heterocycles. A noteworthy feature of this work is that paraformaldehyde acts as both a hydride donor and an electrophile in the reaction, enabling the use of cheap and readily available feedstock chemicals. Removal of the activating group can be achieved readily, furnishing the free NH compound in only 2 steps. The synthetic utility of the method was illustrated with a synthesis of (±)-Paroxetine.

Pyridines can be activated at a single point with a new benzyl group, followed by dearomative functionalisation at C3 using formaldehyde.     

Search for nondegenerate real vertex invariants and derived topological indexes

Two new types of real (i.e., noninteger) local vertex invariants (LOVIs), denoted by c_i and c′_i and called distance-enhanced exponential connectivities, are defined via eqs. (1)–(3) and (1′)–(3′), respectively. Only the case when the exponent z equals 1 in eqs. (3) and (3′) is discussed in detail. Both these LOVIs span the range from 0–1, but their dependence upon topology is fairly different, as seen from Table II, where c_i and c′_i values for all heptane and octane isomers are displayed. From these LOVIs, by simple summation over all graph vertices two new topological indexes (TIs), denoted by XC and XC′, respectively, are obtained. Their intermolecular ordering of all alkanes with four to nine carbon atoms is discussed. On their basis, correlations with boiling points and critical pressures of alkanes are presented. © 1993 John Wiley & Sons, Inc.     

Molecular topology. IV. Regressive vertex degrees (new graph invariants) and derived topological indices

New local graph invariants, “regressive vertex degrees” (which are slightly augmented vertex degrees) are introduced on the basis of decreasing contributions of more remote vertexes to the classical vertex degrees. Several such invariants are proposed (BR, ER, SR) where t (either t = 1 or t = 2) is an operator expressing the attenuation with increasing topological distance, according to formula (1) or (2). With the aid of these new local invariants, new topological indices (global graph invariants), Y (namely BY, EY or SY) are introduced and exemplified. Their ability to express the branching and to order alkanes is investigated. An appendix gives some recursive relationships for computing these indices.     

Synthesis of 3-arylpiperidines by a radical 1,4-aryl migration

[reaction: see text] A route to 3-arylpiperidines, 3-arylpyridines, and 5-arylpiperidin-2-ones involving a radical 1,4-aryl migration has been explored. The sequence requires a xanthate addition to an N-allylarylsulfonamide, followed by acetylation and treatment with dilauroyl peroxide to give the 1,4-aryl transfer product, which upon acidic hydrolysis affords the desired piperidine derivative.     

Wave model for conservative bound systems

In the hidden variable theory, Bohm proved a connection between the Schrodinger and Hamilton-Jacobi equations and showed the existence of classical paths, for which the generalized Bohr quantization condition is valid. In this paper we prove similar properties, starting from the equivalence between the Schrodinger and wave equations in the case of the conservative bound systems. Our approach is based on the equations and postulates of quantum mechanics without using any additional postulate. Like in the hidden variable theory, the above properties are proven without using the approximation of geometrical optics or the semiclassical approximation. Since the classical paths have only a mathematical significance in our analysis, our approach is consistent with the postulates of quantum mechanics.     

K11[HSn(PWO34)2] · 27 H2O – Synthese und Struktur

K₁₁[HSn (PW O₃₄)₂] · 27 H₂O – Synthesis and Structure K₁₁[HSn (PWO₃₄)₂] · 27 H₂O 1 can be synthesized in an “one-pot reaction” from commercially obtainable educts (SnCl₂; Na₂HPO₄ · 7 H₂O, Na₂WO₄ · 2 H₂O) in high yields and has been characterized by elemental analysis, IR/Raman-, UV/Vis-spectroscopy as well as by X-ray crystal structure analysis. The example of 1 again demonstrates the validity of our working hypothesis, that polyoxometalates can be obtained by linking highly charged, transferable building blocks by cationic centres within the scope of an optimal charge control. For structural details see “Inhaltsübersicht”.     

Hindered rotation around the N(sp2)-C(sp3) single bond in 2,4,6-trimethyl-N-alkylpyridinium cations:H DNMR analysist

Pairwise chemical shift nonequivalence of the 2,6-methyl and 3,5-protons in ¹H NMR spectra, as well as of the 2,6-methyl, 2,6-ring and 3,5-ring carbons in ¹³C NMR spectra, was observed for N-alkyl-2,4,6-trimethylpyridinium salts 2. Dynamic NMR spectroscopy demonstrates appreciably higher activation free energies ΔG^# for rotation around the N(sp²)-C(sp³ bond than ΔG# for the analogously substituted mesityl derivatives, in agreement with the shorter N-C bond distance than for the C-C bond.     

Cis-/Trans-Isomerie bei Bis-(trisalkoxy)-hexavanadaten: cis-Na2[VO7(OH)6{(OCH2)3CCH2OH}2] · 8 H2O,cis-(CN3H6)3[VIVVO13{(OCH2)3CCH2OH}2] · 4,5 H2O und trans-(CN3H6)2[VO13{(OCH2)3CCH2OH}2] · H2O

Cis-/Trans-Isomerism of Bis-(trisalkoxy)-hexavanadates: cis-Na₂[V O₇(OH)₆{(OCH₂)₃CCH₂OH}₂] · 8 H₂O, cis-(CN₃H₆)₃[V^IVV O₁₃{(OCH₂)₃CCH₂OH}₂] · 4.5 H₂O and trans-(CN₃H₆)₂[V O₁₃{(OCH₂)₃CCH₂OH}₂] · H₂O Polyoxovanadates with distorted Lindquist-structure, in which six of the twelve μ₂-oxygen atoms are formally replaced by the oxygen atoms of two coordinated pentaerythritol ligands, can be prepared by a simple method in an aqueous medium. The “fully reduced”, six-fold protonated compound cis-Na₂[VO₇(OH)₆{(OCH₂)₃CCH₂OH}₂] · 8 H₂O ( 1 ), the mixed valence species cis-(CN₃H₆)₃[V^IVVO₁₃{(OCH₂)₃CCH₂OH}₂] · 4.5 H₂O ( 2 ) containing one localized V^IV centre and the “fully oxidized” compound trans-(CN₃H₆)₂[VO₁₃{(OCH₂)₃CCH₂ · OH}₂] · H₂O ( 3 ) have been synthesized and characterized by UV/VIS-, IR- and EPR-spectroscopy, by magnetic measurements, cyclic voltammetry and by a single-crystal X-ray structure analysis. The organic {(CH₂)₃CCH₂OH}³⁺-groups tend to cap the triangular faces formed by μ₂-oxygen atoms of the central approximately octahedral {V₆O₁₉}-unit. Therefore the anions of bis-(trisalkoxy)-hexavanadates can exist in a trans-form as well as in an isomeric cis-form referring to a “basic” plane of four vanadium atoms of the {V₆}-octahedron. The different relative positions of the ligands have a significant influence on the redox potentials of the compounds. For structural details see “Inhaltsübersicht”.