Reexamination of the magnetic properties of Cu(2)(dca)(4)(2,5-me(2)pyz) [dca = dicyanamide; me(2)pyz = dimethylpyrazine]: isolated spin-1/2 dimers versus long-range magnetic ordering

The magnetic properties of Cu(2)(dca)(4)(2,5-me(2)pyz) have been reexamined. The extended structure of Cu(2)(dca)(4)(2,5-me(2)pyz) can be viewed in terms of Cu(2)(2,5-me(2)pyz)(4+) dimer units interconnected via mu(1,5)-dca ligands. The bulk magnetic susceptibility chi(T) and the isothermal M(H) of Cu(2)(dca)(4)(2,5-me(2)pyz) are shown to be well described by an isolated dimer model. This finding was confirmed by carrying out a spin dimer analysis based on tight-binding calculations, which shows that the 2,5-me(2)pyz ligand provides a substantial spin exchange interaction between the Cu(2+) ions while the dca ligands do not.     

Influence of substrate morphology on organic layer growth: PTCDA on Ag(1 1 1)

By UV-excited photoelectron emission microscopy (UV-PEEM) we investigated the microscopic growth behavior of organic thin films using 3,4,9,10-perylene-tetracarboxylicacid dianhydride (PTCDA) on a Ag(1 1 1) single crystal substrate as example. Direct, real time observation allows to correlate the initial growth modes and the related kinetic parameters with substrate properties like terrace width, step density, and step bunches from the submonolayer range up to 5 layers or more. Above room temperature PTCDA grows in a Stranski–Krastanov fashion: after completion of the first two stable layers three-dimensional islands are formed. The nucleation density strongly depends on the temperature and the substrate morphology thus affecting the properties of the organic film.     

Spin dimer analysis of the spin exchange interactions in paramelaconite Cu(4)O(3) and its analogue Ag(2)Cu(2)O(3) and the spin ordering of the Cu(2)O(3) spin lattice leading to their magnetic phase transitions

The magnetic structures of the Cu(2)O(3) spin lattices present in Cu(4)O(3) and Ag(2)Cu(2)O(3) were analyzed by studying their spin exchange interactions on the basis of spin dimer analysis. Calculations of spin exchange parameters were calibrated by studying LiCuVO(4) whose intrachain and interchain antiferromagnetic spin exchange parameters are known experimentally. The magnetic phase transition of Cu(4)O(3) at 42.3 K doubles the unit cell along each crystallographic direction. The spin arrangements of the Cu(2)O(3) lattice consistent with this experimental observation are different from conventional antiferromagnetic ordering. Our analysis indicates that spin fluctuation should occur in Cu(4)O(3), low-dimensional magnetism should be more important than magnetic frustration in Cu(4)O(3), and Ag(2)Cu(2)O(3) and Cu(4)O(3) should have similar structural and magnetic properties.     

Synthesis and characterization of a magnetic semiconductor Na(2)RuO(4) containing one-dimensional chains of Ru(6+)

A new ternary ruthenium oxide Na(2)RuO(4) was prepared and shown to crystallize with a new structure type. Single crystal X-ray diffraction measurements reveal that Na(2)RuO(4) consists of RuO(4) chains made up of RuO(5) trigonal bipyramids by sharing axial corners. Na(2)RuO(4) is a magnetic semiconductor with a variable range hopping behavior, and its molar magnetic susceptibility chi(mol) has a broad maximum at approximately 74 K. The derivative d(chi(mol).T)/dT exhibits a peak at 37.7 K which has been confirmed by heat capacity measurement to be due to long-range antiferromagnetic ordering.     

A potential-function reduction algorithm for solving a linear program directly from an infeasible “warm start”

This paper develops an algorithm for solving a standard-form linear program directly from an infeasible “warm start”, i.e., directly from a given infeasible solution \(\hat x\) that satisfies \(A\hat x = b\) but \(\hat x \ngeqslant 0\) . The algorithm is a potential function reduction algorithm, but the potential function is somewhat different than other interior-point method potential functions, and is given by $$F(x,B) = q\ln (c^T x - B) - \sum\limits_{j = 1}^n {\ln (x_j + h_j (c^T x - B))}$$ where \(q = n + \sqrt n\) is a given constant,h is a given strictly positive shift vector used to shift the nonnegativity constaints, andB is a lower bound on the optimal value of the linear program. The duality gapc ^T x ? B is used both in the leading term as well as in the barrier term to help shift the nonnegativity constraints. The algorithm is shown under suitable conditions to achieve a constant decrease in the potential function and so achieves a constant decrease in the duality gap (and hence also in the infeasibility) in O(n) iterations. Under more restrictive assumptions regarding the dual feasible region, this algorithm is modified by the addition of a dual barrier term, and will achieve a constant decrease in the duality gap (and in the infeasibility) in \(O(\sqrt n )\) iterations.     

Polynomial-time algorithms for linear programming based only on primal scaling and projected gradients of a potential function

This paper presents extensions and further analytical properties of algorithms for linear programming based only on primal scaling and projected gradients of a potential function. The paper contains extensions and analysis of two polynomial-time algorithms for linear programming. We first present an extension of Gonzaga's O(nL) iteration algorithm, that computes dual variables and does not assume a known optimal objective function value. This algorithm uses only affine scaling, and is based on computing the projected gradient of the potential function $$q\ln (x^T s) - \sum\limits_{j = 1}^n {\ln (x_j )} $$ wherex is the vector of primal variables ands is the vector of dual slack variables, and q = n + \(\sqrt n \) . The algorithm takes either a primal step or recomputes dual variables at each iteration. We next present an alternate form of Ye's O( \(\sqrt n \) L) iteration algorithm, that is an extension of the first algorithm of the paper, but uses the potential function $$q\ln (x^T s) - \sum\limits_{j = 1}^n {\ln (x_j ) - \sum\limits_{j - 1}^n {\ln (s_j )} } $$ where q = n + \(\sqrt n \) . We use this alternate form of Ye's algorithm to show that Ye's algorithm is optimal with respect to the choice of the parameterq in the following sense. Suppose thatq = n + n ^t wheret?0. Then the algorithm will solve the linear program in O(n ^r L) iterations, wherer = max{t, 1 ? t}. Thus the value oft that minimizes the complexity bound ist = 1/2, yielding Ye's O( \(\sqrt n \) L) iteration bound.     

Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which interpolate between the zonal spherical functions of related real andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

Importance of supersuperexchange interactions in determining the dimensionality of magnetic properties. Determination of strongly interacting spin exchange paths in A(2)Cu(PO(4))(2) (A = Ba, Sr), ACuP(2)O(7) (Ba, Ca, Sr, Pb), CaCuGe(2)O(6), and Cu(2)UO(2)(PO(4))(2) on the basis of qualitative spin dimer analysis

The patterns of the Cu(2+) ion arrangements in the magnetic oxides A(2)Cu(PO(4))(2) (A = Ba, Sr), ACuP(2)O(7) (Ba, Ca, Sr, Pb), CaCuGe(2)O(6), and Cu(2)UO(2)(PO(4))(2) are quite different from the patterns of the strongly interacting spin exchange paths deduced from their magnetic properties. This apparently puzzling observation was explained by evaluating the strengths of the Cu-O-Cu superexchange and Cu-O...O-Cu supersuperexchange interactions of these oxides on the basis of qualitative spin dimer analysis. Supersuperexchange interactions are found to be crucial in determining the dimensionality of magnetic properties of these magnetic oxides.     

Analysis of bonding properties in molecular ground and excited states by a Cohen-type bond order

We propose a Cohen-type bond order analysis in terms of orthogonalized atomic basis functions which can be used to analyze NDO wave functions of large organic and metal–organic molecules. It is shown that for small molecules the results gained with this method are in excellent agreement with the same analysis based on ab initio STO -3G wavefunctions. For large planar aromatic systems these all-valence electron bond orders are found to be a consistent generalization of the π-bond order. A simple relation between these bond orders and the corresponding covalent bond energies is established. The method can be easily extended to study excited state multiconfiguration wave functions. We present calculations for C₂H₂, C₂H₄, C₂H₆, and Mn₂(CO)₁₀. The results indicate that the method can be used to discuss the photochemistry of organic and metal–organic compounds.