Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Calculations of the electronic structures of cage molecules using free-electron orbitals as a basis

A non-empirical molecular orbital method, particularly suitable for calculations on cage-like molecules, is described. The method uses as basis functions the set of free-electron functions which are the solutions of Schrödinger's equation for an electron confined between two concentric, spherical potential energy barriers. Application of the theory to the SCF calculation of the energies of the delocalized electrons in benzene and tetrasulphur tetranitride shows that the model is capable of interpreting the properties of such systems. However, it does highlight a difficulty in the calculation of excited state energies with one-centre models which appears to be largely unrecognized.Extension of the method to a consideration of all the valence electrons, using P₄ as an example, reveals problems the origin of which is an inadequate treatment of the core electrons. It is suggested that these problems may best be dealt with by use of a suitable pseudo potential.     

Effect of ‘Transannular Transmission’ in Dibenzo-18-Crown-6

The effect of the nature of the substituent in the monosubstituted derivatives of dibenzo-18-crown-6 on the reactivity and direction of the electrophilic substitution reaction of the unsubstituted benzene ring has been determined. This transfer is carried out via the macrocycle and therefore is called transannular transmission. The possible mechanism of this transmission is discussed.     

Triphenylphosphan-Nickel(0)-Komplexe mit Isocyanid-Liganden — [(RNC)nNi(PPh3)4–n] (n = 1–3)

Triphenylphosphane Nickel(0) Complexes with Isocyanide Ligands — [(RNC)_nNi(PPh₃)_4–n] (n = 1–3) Synthesis and properties of the isocyanide triphenylphosphane nickel(0) complexes [(RNC)Ni(PPh₃)₃], [(RNC)₂Ni(PPh₃)₂] and [(RNC)₃Ni(PPh₃)] (R = ^tBu, Cy, PhCH₂, p-TosCH₂) are described. I.r. and ³¹P n.m.r. spectra were recorded and the X-ray crystal structure of [(PhCH₂NC)₂Ni(PPh₃)₂] was determined.     

1H NMR Detection of σ-Adducts in S NH Reactions of Nitroquinolines with Chloromethyl Phenyl Sulfone

The intermediate -adducts of chloromethyl phenyl sulfone with 3-nitro-, 5-nitro-, 6-nitro-, 7-nitro- and 8-nitroquinoline are detected by ¹H NMR spectroscopy.     

Investigation of the phosphinyl analog of α-ketoglutaric acid

It was shown by³¹P and¹³C NMR spectroscopy that methyl(3-carboxy-3-oxopropyl)phosphinic acid (4-methylhydroxyphosphinyl-2-oxobutyric acid) (1) and the amide (2) of the latter exist in keto forms in non-aqueous solutions. In aqueous solutions an equilibrium between the keto,gem-diol, and enol forms has been observed. The proportions of the diol and enol forms increase as the acidity of the media increases. Silylation of acid 1 with hexamethyldisilazane gives the tris(trimethylsilyl) derivative of enol form (3) (Z- andE-isomers).Translated fromIzyestiya Akadetnii Nauk. Seriya Khimicheskaya, No. 1, pp. 125–128, January, 1994.     

Synthesis and properties of functional derivatives ofN′-phosphoryl- andN′-phosphonoyldiazeneN-oxides; molecular structure ofN-(2,2-dimethyl-5-nitro-1,3-dioxan-5-yl)-N′-[methoxy(phenyl)phosphoryl]diazeneN-oxide

Methods for the synthesis of polyfunctionalN-phosphoryl- andN-phosphonoyldiazeneN-oxides containing hydroxyl, acetoxyl, and nitrate groups, and dibromoallyl and dibromopropyl fragments have been developed. The molecular structure ofN-(2,2-dimethyl-5-nitro-1,3-dioxan-5-yl)-N-[methoxy(phenyl)phosphoryl)diazeneN-oxide was established by X-ray structural analysis.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1284–1289, July, 1994.     

Aminomethylation of (ω-alkylthioalkyl)phenols

The reactions of ()-alkylthioalkyl)phenols with formaldehyde and secondary amines afforded the corresponding aminomethyl derivatives, in which the dimethylamino group may be replaced by the alkylthio group.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1504–1507, June, 1996.     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.