Ligand close packing and the geometry of the fluorides of the nonmetals of periods 3, 4, and 5

This paper discusses the geometry of the fluorides of the nonmetals of periods 3, 4, and 5 in terms of the ligand close packing (LCP) model according to which molecular geometry is determined primarily by ligand-ligand repulsions (Pauli closed shell repulsions) rather than by the bonding and lone pair Pauli repulsions of the VSEPR model. The LCP model becomes the dominant factor in determing geometry when the ligands are sufficiently crowded that they may be regarded as essentially incompressible. Ligand close packing is a modification of the VSEPR model in which ligand-ligand repulsion (Pauli closed shell repulsion) is given more emphasis than bonding and nonbonding electron pair Pauli repulsion. The nonmetals of period 3 are large enough to form octahedral six coordinated molecules in which the ligands are close packed. The larger nonmetals of period 4 also have a maximum coordination number of six and an octahedral geometry although the ligands are not close packed. Ligand radii derived from the interligand distances in the molecules of period 3 depend only on the charge of the fluorine ligands and are consistent with the previously derived radii obtained from the fluorides of the close packed tetrahedral molecules of the period 2 elements. Although the ligands in the molecules of the period 4 nonmetals are not close packed, these elements are not large enough to form molecules with a higher coordination number. However, the larger period 5 nonmetals may have coordination numbers of seven and eight. The seven coordinated molecules have a pentagonal bipyramidal geometry in which the equatorial ligands are close packed. The eight coordinated molecules have a square antiprism geometry, which is not a close packed geometry although the fluorine interligand distances are only a little larger than expected for close packing. The difference between the axial and equatorial bond lengths in the trigonal bipyramidal pentafluorides and the pentagonal bipyramidal pentafluorides can be understood on the basis of ligand close packing. Ligand packing prevents the lone pair in AF(6)E molecules from fully entering the valence shell and thereby exerting its full stereochemical effect so that these molecules have a C(3)(v)() distorted octahedral geometry rather than a geometry based on pentagonal bipyramidal seven coordination.     

Dinitration studies of 2,4,5-tribromo-3,6-dimethylphenol: the formation of an acyloin rearrangement product

Dinitration of 2,4,5-tribromo-3,6-dimethylphenol(1) gives either the tribromodinitro-compound(2) or its acyloin rearrangement product(3), depending on the reaction conditions: X-ray crystal structure analyses are reported for compounds (2) and (3).     

The numbers of chiral and achiral alkanes and monosubstituted alkanes

Whereas the theory for the enumeration of the optical isomers of the lakyl radicals and the alkanes has long been understood, this is not the case for the corresponding archiral isomers. We present for the first time recurrence formulae for counting the number of archiral isomers of the alkyl radicals and the alkanes. For chiral and archiral alkanes and monosubstituted alkanes, numerical results up to C₁₄ are tabulated.After presenting the history of the problem and the necessary definitions, we proceed to derive functional equations on the various generating functions, which readily yield the more explicit recurrence formulae usefule for numerical calculations. In the process, we first re-derive Pólya's expression for planted steric trees using his classical enumeration theorem. This result is then extended to the enumeration of free steric trees using the now standard tree-counting method due to Otter and known as a dissimilarity characteristic equation.By definition, a steric tree is a quartic tree (all points having degree 1 or 4) in which the four neighbors of every carbon point are given a tetrahedral configuration. Building on the methods of the first two authors for counting chiral and archiral trees in the plane, we obtain the formula for counting achiral steric trees, thus setting a problem first enunciated by van't Hoff and Le Bel in 1874.     

Micelle studies using a metal ion/murexide indicator system

Summary Complex formation between divalent metal ions and the hydrophilic murexide anion in the presence of anionic micelles has been employed to study aspects of micelle formation, the binding of divalent metal ions to micelles, and the kinetics of metal-complex formation in the presence of micelles.

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Zusammenfassung Die Komplexbildung zweiwertiger Metallionen mit dem hydrophilen Indikator Murexid wurde in Gegenwart anionischer Mizellen untersucht. Die Indikatorreaktion wurde benutzt, um Aussagen über Mizellbildung, Bindung zweiwertiger Metallionen an Mizellen und die Kinetik der Metallkomplexbildung bei Anwesenheit von Mizellen zu erhalten.

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With 8 figures and 1 table

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Dedicated to Prof.G. Rehage on the occasion of his 60th birthday.     

Rates of convergence and optimal spectral bandwidth for long range dependence

Summary For a realization of lengthn from a covariance stationary discrete time process with spectral density which behaves like ^1–2H as 0+ for 1/2<H<1 (apart from a slowly varying factor which may be of unknown form), we consider a discrete average of the periodogram across the frequencies 2j/n,j=1,..., m, wherem andm/n0 asn. We study the rate of convergence of an analogue of the mean squared error of smooth spectral density estimates, and deduce an optimal choice ofm.