Systematic Study of the Interaction Between VIV Centres and LnIII Ions in Well Defined {V 2 IV LnIII}{AsIIIW9O33}2 Sandwich-Type Clusters: Part 2

The gadolinium (Gd) member of a new type of heteropolytungstates that contain one lanthanide and two transition metal ions in a triangular arrangement is reported. The compound NaK₆Gd_0.33 [((VO)₂Gd(H₂O)₄K₂(H₂O)₂(Na)(H₂O)₂)(α-B-AsW₉O₃₃)₂]·24H₂O (1) was prepared from acidified aqueous solutions of Na₂WO₄·2H₂O, As₂O₃ and VOSO₄·5H₂O to which Gd³⁺ ions were added. The single crystal X-ray structure analysis (monoclinic, space group P2₁/m) shows that the anion consists of two [α-B-As^IIIW₉O₃₃]^9? trilacunary Keggin-type units linked by two VO²⁺, one Gd³⁺ as well as weakly by two K⁺ and one Na⁺ ions, resulting in a sandwich-type structure with idealized C _2v symmetry. The problem of positioning crystal lattice and special polyoxometalate sites with different cations is discussed also in connection with supramolecular chemistry aspects and as an option for further research. A fit of the magnetic susceptibility yielded exchange coupling constants of J _VV = ?2.55 cm^?1 (anti-ferromagnetic) between the vanadium ions and J _GdV = 0.6 cm^?1 (ferromagnetic) between the Gd and each of the two vanadium ions. The complete magnetochemical analysis also revealed a partial occupancy of the Na⁺ sites in the counter-cation–water system by Gd³⁺ ions (0.33 Gd³⁺ ions in total).     

Binomial transforms and integer partitions into parts of <Emphasis Type="Italic">k</Emphasis> different magnitudes

A relationship between the general linear group of degree n over a finite field and the integer partitions of n into parts of k different magnitudes was investigated recently by the author. In this paper, we use a variation of the classical binomial transform to derive a new connection between partitions into parts of k different magnitudes and another finite classical group, namely the symplectic group Sp. New identities involving the number of partitions of n into parts of k different magnitudes are introduced in this context.     

On the Number of Even Parts in All Partitions of $$\varvec{n}$$n into Distinct Parts

Annals of Combinatorics - A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. The even parts in partitions of n into...     

Mimicking biological cation-transport based on sphere-surface supramolecular chemistry: simultaneous interaction of porous capsules with molecular plugs and passing cations

Spherical capsules of the type [{(Mo)Mo(5)}(12){Mo(2)(ligand)}(30)](n-) exhibiting 20 {Mo(9)O(9)} pores with crown ether functions allowed us to perform a sophisticated study of the title phenomenon based on synthetic work as well as NMR spectroscopy. The pores of the host system interact in solution specifically with guests that can be noncovalently bonded, such as formamidinium and acetamidinium cations, while having different affinities to the pores. The exchange between the guest species present in solution and in the pores was investigated, including, besides the extreme scenarios of complete pore closing and complete opening, that of stepwise pore plugging. Because of this option it was possible to model for the first time passive transmembrane cation transport based on gated pores/channels. These have the appropriate dimensions and can even adopt different structure flexibilities in response to different cations. The present investigation is based on related syntheses as well as on numerous detailed (7)Li NMR studies of Li(+) transport/exchange equilibria in dependence of the pore environment/guest situations. One compound containing capsules with sulfate ligands (2) could be obtained in which all the pores are plugged with formamidinium cations and another corresponding one was obtained with additionally encapsulated Ca(2+) ions (3); these were taken up after temporary release of some of the formamidinium plugs/guests upon short heating of the related solution.     

Cation behavior at an artificial cell interface: binding distinguished by ion hydration energetics and size

The unique molybdenum oxide-based nucleophilic porous capsule/artificial cell [{(MoVI)MoVI5O21(H2O)6}12{MoV2O4(SO4)30}]72-, according to an X-ray crystallographic study, traps [Al(H2O)6]3+ complexes above the pores while interacting with the latter via hydrogen bonds; this is supported by 27Al NMR studies of the interaction of the capsule with hydrated Al3+ cations in aqueous solution.