Symmetrie und analytische Struktur der Additionstheoreme räumlicher Funktionen und der Mehrzentren-Molekülintegrale über beliebige Atomfunktionen

Three-dimensional functions f(r) = g(r) · Y _m ^l (, ø), which transform like an irreducible tensor, are transformed simultaneously under rotations and translations. The relationships governing the transformation reveal some general properties. If the addition theorem of a function f(r) can be represented by a one-center expansion in terms of surface spherical harmonics Y _m ^l , each expansion coefficient is given by a Clebsch-Gordan coefficient and a radial function.Because of these properties, addition theorems are especially helpful for the simplification and evaluation of quantum-mechanical matrix elements and multi-center energy integrals in molecular LCAO calculations. The application of addition theorems has two major advantages: First, because addition theorems are equivalent to translation formulas, the number of centers of an integral can be reduced by translation of orbitals and operators. Second, due to the typical analytical structure of the series expansion representing the addition theorem, the dimensionality of a molecular integral can be reduced, because the integration over the angular variables can be executed. Then, a molecular multi-center integral is represented by a series of one-center integrals over functions of the radial variable only.

Herrn Professor Dr. H. Hartmann zum 65. Geburtstag gewidmet.     

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V _xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V _xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.Dedicated to Professor H. Hartmann on the occasion of his 65th birthday.     

The evaluation of ω parameters in contracted density product calculations

General formulas for the rotational averages of two electron integrals with arbitrary combinations of spherical tensors in standard, Cartesian, and equivalent form are presented. The way in which the parameters of CDP type calculations can be obtained from rotational averages is discussed, and it is shown from numerical results that the interpretation of the parameters as space averages is compatible up to d orbitals with the CDP invariance requirements.     

Thermal Behaviour of the Complexes of Zinc Amino Acids

The eight solid complexes of zinc with L--methionine or L--histidine were prepared. The thermal decomposition processes of these complexes were determined by means of TG-DTG. The results show that their decomposition processes can be divided into three steps except for the complex Zn(Met)₂ the decomposition of which is completed in one step. All the final products are ZnO.This revised version was published online in November 2005 with corrections to the Cover Date.     

On simplified spherical harmonics equations for the radiative transfer equation

The radiative transfer equation (RTE) arises in a wide range of applications in sciences and engineering. Due to the high dimension and complicated form of the RTE, it is challenging to solve the equation directly. In the literature, several approximation methods were developed for the RTE. One approximation method, the simplified spherical harmonics (SP _N ) method, provides an efficient way to generate good approximate solutions of the RTE with high absorption and small geometries. The main purpose of the paper is to study well-posedness of the simplified spherical harmonics system. The weak formulation used in the proof of the solution existence and uniqueness provides a starting point for developing the Galerkin finite element method to solve the simplified spherical harmonics system.     

Selective esterolysis of nitrophenyl acetates in crystalline α-cyclodextrin complexes

The esterolysis ofm-nitrophenyl acetate (mNPA) andp-nitrophenyl acetate (pNPA), complexed with -cyclodextrin, was investigated in the solid state. At 117 and 140°C, the initial half-times ofmNPA esterolysis were 30 and 24 h, respectively, whereasp NPA esterolysis was undetectably slow. At 117°C, themNPA reaction proceeded to completion, and cyclodextrin acetate andm-nitrophenol products were identified. At 140°C,the initial rate was followed by a slow phase with a half-time of 130 h, evidently due to a structural change in the complex. Themeta/para selectivity of the solid-state reaction is considerably enhanced over the selectivity reported in aqueous solution.     

Lumineszierende Cu(I)- und Ag(I)-Cluster mit Thionoliganden

Zusammenfassung Cu(I) bildet mit zahlreichen nicht lumineszierenden Thionoliganden (N-monosubstituierten N-Sulfonylthioharnstoffen, N,N-Dialkyl-N-phenylthioharnstoffen und N,N-Dialkylmonothiocarbamaten) rot lumineszierende oktaedrische Cluster (CuL)₆. Die Lumineszenz tritt sowohl im Festzustand als auch in Lösungen auf. Abklingzeiten von 10^–5s deuten auf kurzlebige Phosphoreszenz hin. Der Einfluß verschiedener Strukturelemente auf die Lage der Emissionsmaxima wird diskutiert. Dabei bewirken Veränderungen in der Metall-Ligand-Koordination die stärkste Verschiebung der Lumineszenzbanden. Tetraedrische (CuL)₄-Cluster mit den obigen Thionoliganden zeigen keine Lumineszenz. Generelle Unterschiede in der Struktur oktaedrischer und tetraedrischer Cluster werden diskutiert.Ag(I) bildet nur mit N-Alkyl-N-sulfonylthioharnstoffen lumineszierende Cluster (AgL)₆. Die Lumineszenz ist im Gegensatz zu den Cu-Clustern auf den Festzustand beschränkt.

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Luminescent Cu(I) and Ag(I) clusters with thiono ligands

Summary Octahedrical (CuL)₆ clusters with several non luminescent thiono ligands (N-monosubstituted N-sulfonylthioureas, N,N-dialkyl-N-phenylthioureas and N,N-dialkylmonothiocarbamates) show red luminescence in the solid state and in solution. The luminescence lifetimes of 10^–5s are typical of short lived phosphorescence. The emission bands are affected by structural variation of the ligand. Changes of the coordination bonds cause the strongest shifts of the luminescence maxima. Tetrahedrical (CuL)₄ clusters with the same thiono ligands are not luminescent. General structural differences between octahedral and tetrahedral clusters are discussed.(AgL)₆ clusters are only luminescent in the solid state and if the ligand is a N-monosubstituted N-sulfonylthiourea

     

Expansion of potential 1/r12 of c‐spherical harmonics

The expansion coefficient C^D_|L| of Coulomb potential 1/r₁₂ of atomic system in hyper‐spherical harmonics is derived and the explicit expression is given.     

Use of ESR for characterizing exchange-coupled polynuclear μ-oxo complexes of iron(iii)

ESR spectra of 13 bi-, tri- and tetranuclear -oxo complexes of Fe(III) were studied in the solid state and in solution. On the basis of the data obtained, the broad signal observed nearg=2 for all the complexes was interpreted as resulting from thermal populating of paramagnetic excited states.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 470–472, March, 1993.     

Molecular one-electron integrals over slater-type atomic orbitals and irregular solid spherical harmonics

The one-electron integral over Slater-type atomic orbitals centered at A and B and irregular solid spherical harmonics as operator centered at C is evaluated analytically by using elliptical coordinates and translation of the solid spherical harmonics from center C to either focus A or B. A special case is the three-center nuclear attraction integral which is also evaluated by means of the Neumann expansion and expressed without associate Legendre functions of the second kind. The strict observation of the charge distribution concept leads to compact expressions for the integral. It has the further advantage that the charge density distributions which have been developed for the two-center cases and used in calculations for diatomic molecules can be utilized.     

Nitrosation of mefenorex in the presence of cyclodextrins

- and -Cyclodextrin (CD) and heptakis-2,6-di-O-methyl--cyclodextrin (DIMEB) form soluble inclusion compounds with mefenorex (MEF); with -CD a partial inclusion occurs. No solid inclusion compound could be obtained with the four CDs. -, -CD and DIMEB, but not -CD, enhance the nitrosation rate of MEF if the nitrosation assay procedure (NAP test) is applied. During this reaction with - and -CD, solid inclusion compounds of the CDs and nitrosomefenorex (NMEF) precipitate.Part of the Ph.D. thesis of V. Wedelich, Freie Universität Berlin, 1985.     

Equivalent spherical harmonics

It is known that the 2l+1 spherical harmonics Y_lm can be transformed into cyclically equivalent orbitals, of which only a few examples have so far been given explicitly. In this article the totality of such cyclic sets is derived. It is demonstrated that other kinds of equivalent spherical harmonics do not exist. Finally a set of five equivalent d orbitals related to icosahedral symmetry is introduced.     

In vitro nitrosation of ephedrine in the presence of cyclodextrins

-, and -cyclodextrin and heptakis-2,6-di-O-methyl--cyclodextrin enhance the nitrosation rate of l-ephedrine if the nitrosation assay procedure (NAP test) is applied. During this reaction with -cyclodextrin a solid inclusion compound of -cyclodextrin andN-nitrosoephedrine precipitates. Solubilities and stabilities of inclusion compounds of the cyclodextrins with ephedrine and nitrosoephedrine, respectively, explain especially the catalytic effects of some cyclodextrins on ephedrine.Part of the PhD thesis of V. Wedelich, Freie Universität Berlin, 1985.     

Multipole expansion of Cartesian Gaussian orbitals about a new origin

Cartesian Gaussian orbitals (CGO) about one center are expanded as a series of spherical harmonics around a new origin. Radial coefficients are given in analytical form. Developments of solid harmonic Gaussian orbitals (SHGO) are also obtained and used to study the convergence properties of expansions of s, p, d, and f Gaussians in terms of a single dimensionless parameter λ. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 647–653, 1997     

Calculation of overlap integrals over Slater-type orbitals using translational and rotational transformations for spherical harmonics

Using translation and rotation formulas for spherical harmonics the finite sums through the basic overlap integrals and spherical harmonics are derived for the arbitrary overlap integrals over Slater-type orbitals (STOs). The recurrence relations for the evaluation of basic overlap integrals have been established recently [Guseinov II, Mamedov BA (1999) J Mol Struct (THEOCHEM) 465:1]. By the use of the derived expressions the overlap integrals can be calculated most efficiently and accurately, especially for large quantum numbers of STOs. Received: 2 May 2000 / Accepted: 31 May 2000 / Published online: 11 September 2000     

Solubility characteristics ofβ-cyclodextrin inclusion complexes

Some inclusion complexes of-cyclodextrin (cyclomaltoheptaose) have been investigated, particularly with respect to their solubility. The mathematical characterization of the equilibrated host-guest system containing both solid and solution phases is discussed (first of all those, which contain 1:1 or 1:1 + 2:1 species) and demonstrated by different examples.     

Transition Metal Halide Salts of 1,3-bis(4-Pyridyl)propane: Synthesis and Structural Characterization

The resulting salts of (H₂bpp)MX₄ · n H₂O (M = Zn, X = Cl, n = 1, 1; M = Cd, X = Br, n = 0, 2; M = Hg, X = Cl, n = 1, 3; M = Cu, X = Cl, n = 0, 4; M = Cu, X = Br, n = 1, 5; M = Pt, X = Cl, n = 1, 6) were crystallized from the reaction mixture prepared by adding MX₂ to the HX solution of 1,3-bis(4-pyridyl)propane (bpp), while the salt of colorless (H₂bpp)SnCl₆, 7, was crystallized from the reaction mixture prepared by adding SnCl₂ to the HCl solution of bpp. Their structures have been determined by X-ray crystallography. All the compounds show supramolecular structures in the solid state by intermolecular hydrogen bondings and aromatic – interactions. The H₂bpp²⁺ cations in these metal salts adopt the gauche–gauche and anti–anti conformations with different dihedral angles for the two pyridyl rings.     

Colloidal copper in aqueous solutions: radiation-chemical reduction,mechanism of formation,and properties

Colloidal copper has been obtained by -irradiation of aqueous solutions of copper (II) perchlorate in the presence of alcohol and polyethyleneimine (PEI). The sols are spherical particles about 4 nm in diameter, which are quickly oxidized by oxygen or other oxidants. When Cu^II is not entirely incorporated into the complex with PEI, disproportionation of Cu^I aqua complexes formed affords the metal, along with Cu₂O. Reduction of the PEI complex of Cu^I by hydrated electrons gives only colloidal copper. The copper ions can be reduced on the surface of silver sols. Optical parameters of the resulting bimetallic particles have been studied. The presence of copper ions leads to broadening of the absorption band associated with the silver sols and shifts it to the UV region, which is due to the transfer of electrons from copper to silver. Three copper monolayers are enough to cause plasmon absorption of colloidal copper.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 25–30, January, 1994.     

Relativistic electric and magnetic property operators for two‐component transformed Hamiltonians

A general procedure is presented for the derivation of property operators for electric and magnetic perturbations for Hamiltonians derived from the Dirac Hamiltonian by a partially block‐diagonalizing unitary transformation. The procedure involves a regularized expansion in powers of p ²/m²c². Property operators are expressed in terms of the solid spherical harmonics. Expressions for the free‐particle Foldy–Wouthuysen, Douglas–Kroll, and Barysz–Sadlej–Snijders transformations are compared with the well‐known Pauli results. Explicit examples of a constant electric field and a constant magnetic field are given. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 412–421, 2000     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001