On matrices with operator entries

In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated.     

Geometry prediction of hafnocenes by quantum chemical methods

The performance of quantum chemical methods for geometry prediction of hafnocenes was evaluated. HF, B3LYP and MP2 in combination with nonrelativistic (MHF) and relativistic (MWB and LANL2DZ) basis sets for hafnium together with standard basis sets 3-21G*, 6-31G* and 6-311G** for other elements were applied. Five basic structural parameters of the optimized structures of the hafnocenes were compared with experimental crystal structures obtained from the Cambridge structural database. Altogether 80 hafnocenes were included in the analysis. The results show that relativistic corrections are necessary for Hf atom. However, even the Hartree–Fock (HF) method, when combined with relativistic pseudopotentials, reproduces the experimental crystal structures with significant accuracy. The good performance of the HF method can be understood to originate from the absence of significant near-degeneracy correlations for hafnium. On average, the B3LYP and MP2 methods provide structural parameters somewhat closer to the experimental ones.     

Ab initio molecular orbital calculations on large lattice cluster models: Use of translational symmetry

Summary Translational symmetry has been shown to be useful in the calculation of electronic structures of large lattice models. The number of unique integrals has been derived for cases of different dimensionality. For the unique integrals zero screening and approximation methods are described. The method has been applied to arrays of hydrogen atoms and to a zincblende surface model. When the size of the system is increased the translationally unique integrals are shown to become either zero or they can be calculated by simple coulombic approximations.     

Novel coordination of a hydroxamic acid : Crystal structures of bis(glycinohydroxamoto)nickel(II) and tris(glycinohydroxamoto)cobalt(III)

The structures of two glycinohydroxamoto (GHA) complexes of Ni(II) and Co(III) have been determined by single-crystal X-ray diffraction methods. The crystals of Ni(GHA)₂ are monoclinic with a = 5.360(1), b = 7.315(4), c = 10.194(4) Å, β = 96.57(3), Z = 2, and space group P2₁/c. The crystals of Co(GHA)₃•1/2 H₂O are monoclinic with a = 22.467(19), b = 8.041(4), c = 13.700(11) Å, β = 116.01(7), Z = 8, and space group C2/c. The values of the final residuals R for Ni(GHA)₂ and Co(GHA)₃•1/2 H₂O are 0.0275 and 0.032, respectvely. The molecular structures of Ni(GHA)₂ and Co(GHA)₃ consist of a square planar and an octahedral coordination, respectively, with the glycinohydroxamato (NH₂CH₂CONOH⁻) ligands coordinating to the metal ion via the N (amino) and the N (NOH⁻). These two complexes are the first well-established cases of coordination of the NHO⁻ group of a hydroxamic acid to a transition metal via the nitrogen atom.     

Anion and Additive Effects on the Structure of Mercury(II) Halides Complexes with Tripodal Ligand

The metal complexes [Hg₂(tbim)₂Br₄]·2DMF ( 1 ) and [Hg₂(tbim)I₄]·1.5DMF ( 2 ) were prepared by reactions of 1,3,5‐tris(benzimidazol‐1‐ylmethyl)‐2,4,6‐trimethylbenzene (tbim) with HgBr₂, HgI₂, respectively, and [Hg₂(tbim)I₄]·0.5(FeCp₂)·H₂O ( 3 ) was obtained by the same method with addition of ferrocene (FeCp₂) as additive. Their structures were determined by X‐ray crystallographic analyses. Complex 1 has a macrocyclic binuclear structure with one benzimidazole arm of the ligand free of coordination and the binuclear units are further connected by C‐H···N hydrogen bonds to give an infinite zigzag chain. Complexes 2 and 3 have a 2D network structure in which tbim serves as a tridentate ligand. The results showed that the halides of bromide and iodide have remarkable impact on the structure of the complexes. The FeCp₂ molecules are trapped in the voids of framework 3 .     

Synthesis and structural characterization of two novel heterometallic clusters: [Rh4Pt2(CO)11(dppm)2] and [Ru2Rh2Pt2(CO)12(dppm)2

Two novel heterometallic octahedral clusters [Rh(4)Pt(2)(CO)(11)(dppm)(2)](1) and [Ru(2)Rh(2)Pt(2)(CO)(12)(dppm)(2)](2) were synthesized by the reaction of [Rh(2)Pt(2)(CO)(6)(dppm)(2)] with [Rh(6)(CO)(14)(NCMe)(2)] and Ru(3)(CO)(12), respectively. Solid state structures of 1 and 2 have been established by a single crystal X-ray diffraction study. Two dppm ligands in 1 are bonded to one platinum and three rhodium atoms, which form an equatorial plane of the Rh(4)Pt(2) octahedron. Two rhodium and two platinum atoms bound to the diphosphine ligands in 2 are nonplanar to give an octahedral C2 symmetric Ru(2)Rh(2)Pt(2)(dppm)2 framework. The (31)P NMR investigation of and (1D, (31)P COSY, (31)P-[(103)Rh] HMQC) and simulation of 1D spectral patterns showed that in both clusters the structures of the M(6)(PP)(2) fragments found in the solid state are maintained in solution.     

Ligand substitution of FeRu2(CO)12 and Fe2Ru(CO)12 with tertiary phosphines and phosphites

Ligand substitution of the mixed-metal clusters FeRu₂(CO)₁₂ and Fe₂Ru(CO)₁₂ with triphenylphosphine and trimethylphosphite has been studied. Mono- and di-substituted derivatives have been synthesized and characterized structurally. The following crystal and molecular structures are reported: Fe₂Ru(CO)₁₁PPh₃: triclinic, space group P$\text{1}$, a 9.203(2), b 11.903(3), c 15.117(4) Å, α 81.54(2), β 87.28(2), γ 66.72(2)°, Z = 2; Fe₂Ru(CO)₁₁P(OMe)₃: orthorhombic, space group Pna2₁, a 17.220(5), b 14.572(4), c 8.708(6) Å, Z = 4, FeRu₂(CO)₁₁PPh₃: monoclinic, space group P2₁/n, a 11.435(3), b 16.034(5), c 16.642(4) Å, β 93.35(2)°, Z = 4; FeRu₂(CO)₁₀(PPh₃)₂: orthorhombic, space group Pccm, a 14.854(4), b 17.180(7), c 16.786(12) Å, Z = 4.Ligand substitution is found to occur preferentially at the ruthenium centers of the FeRu₂ and Fe₂Ru clusters. Monosubstitution causes expansion of both of the clusters while the overall geometry is practically unchanged. Disubstitution of FeRu₂(CO)₁₂ causes contraction of the cluster and leads to a formation of carbonyl bridges. The structural trends have been interpreted in terms of electronic and packing effects of ligand substitution. The X-ray structures of Fe₂Ru(CO)₁₂ and FeRu₂(CO)₁₂ are not known; the ligand substitution studies indicate that Fe₂Ru(CO)₁₂ has the same structure as Fe₃(CO)₁₂, and that FeRu₃(CO)₁₂ does not have a Ru₃(CO)₁₂ structure as postulated previously from the IR studies.