Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

Topology and topological sequence entropy

Let X be a compact metric space and T:X-→X be continuous.Let h*(T)be the supremum of topological sequence entropies of T over all the subsequences of Z+and S(X)be the set of the values h*(T)for all the continuous maps T on X.It is known that{0}■S(X)■{0,log 2,log 3,...}∪{∞}.Only three possibilities for S(X)have been observed so far,namely S(X)={0},S(X)={0,log 2,∞}and S(X)={0,log 2,log 3,...}∪{∞}.In this paper we completely solve the problem of finding all possibilities for S(X)by showing that in fact for every set{0}?A?{0,log 2,log 3,...}∪{∞}there exists a one-dimensional continuum XAwith S(XA)=A.In the construction of XAwe use Cook continua.This is apparently the first application of these very rigid continua in dynamics.We further show that the same result is true if one considers only homeomorphisms rather than continuous maps.The problem for group actions is also addressed.For some class of group actions(by homeomorphisms)we provide an analogous result,but in full generality this problem remains open.     

Molecular, supramolecular and solution structures of peroxovanadium complexes with ON and O3N donor set ligands: two new types of cationic-anionic peroxovanadium(V) peroxovanadates(V)

The complexes, [VO(O(2))(pa)(2)]ClO(4).3H(2)O (1), [VO(O(2))(pa)(2)][VO(O(2))(2)(pa)].3H(2)O (2), [VO(O(2))(pa)(2)][VO(O(2))(ada)].2H(2)O (3) and [VO(O(2))(pa)(pca)].H(2)O (4)[pa = picolinamide, ada = carbamoylmethyliminodiacetate(2-) and pca = 2-pyrazinecarboxylate(1-)], were synthesized. 2 and 3 are new types of peroxovanadium complexes: monoperoxovanadium diperoxovanadate (2) and monoperoxovanadium monoperoxovanadate (3). The complexes were characterized by chemical analysis and IR spectroscopy, and 1, 3 and 4 also by X-ray analysis. The structure of 1 is disordered, with alternating positions of the oxo and peroxo ligands. The peroxo oxygen atoms, O(p), in 1 are involved in weak hydrogen bonds with water molecules and close intramolecular C-HO...(p) bonds [d(HO(p)) approximately 2.0 A]. The supramolecular structure of 1 is formed by a network of hydrogen bonds and strong attractive intermolecular pi-pi interactions between the pyridine rings. The supramolecular architecture in 4 is constructed by (N,O)-H...O hydrogen bonds between the neutral complex molecules and water of crystallization. The peroxo oxygen atoms in 4 form intramolecular C-H...O(p) bonds [d(H...O(p))= 2.303 A]. The pa and pca ligands are ON coordinated via the oxygen atoms of the C(NH(2))=O and COO(-) groups, respectively, and nitrogen atoms of the heterocyclic rings, and ada as a tetradentate O(3)N ligand. The thermal analysis of 4 showed that the loss of water of crystallization and the active oxygen release (T(min)/ degrees C 82, T(max)/degrees C 165) are, under given conditions, individual processes separated by the temperature interval 90-132 degrees C. The solution structures and stability were studied by UV-VIS and (51)V NMR spectroscopies.     

Triangular,ferromagnetically-coupled CuII 3-pyrazolato complexes as possible models of particulate methane monooxygenase (pMMO)

Magnetic susceptibility and EPR studies show that trinuclear Cu(II)-pyrazolato complexes with a Cu(3)(mu3-X)2 core (X = Cl, Br) are ferromagnetically coupled: J(Cu-Cu) = +28.6 cm(-1) (X = Cl), +3.1 cm(-1) (X = Br). The orderly transition from an antiferromagnetic to a ferromagnetic exchange among the Cu centers of Cu(3)(mu3-X) complexes, X = O, OH, Cl, Br, follows the change of the Cu-X-Cu angle from 120 degrees to approximately 80 degrees. The crystal structures of [Bu4N]2"[Cu3(mu3-Br)2(mu-pz*)3Br3] (pz* = pz (1a) or 4-O2N-pz (1b), pz = pyrazolato anion, C(3)H(3)N(2)(1-)) are presented.     

The mean free path and mobility of electrons in ionic crystals

Relations are found for the mean free path and mobility of an electron or hole in ionic crystals. The results are compared with experiment.