Tetradentate vs pentadentate coordination in copper(II) complexes of pyridylbis(aminophenol) ligands depends on nucleophilicity of phenol donors

The ligand binding preferences of a series of potentially pentadentate pyridylbis(aminophenol) ligands were explored. In addition to the previously reported ligands 2,2'-(2-methyl-2-(pyridin-2-yl)propane-1,3-diyl)bis(azanediyl)bis(methylene)diphenol (H(2)L(1)) and 6,6'-(2-methyl-2-(pyridin-2-yl)propane-1,3-diyl)bis(azanediyl)bis(methylene)bis(2,4-di-tert-butylphenol) (H(2)L(1-tBu)), four new ligands were synthesized: 6,6'-(2-methyl-2(pyridine-2-yl)propane-1,3-diyl)bis(azanediyl)bis(methylene)bis(2,4-dibromophenol) (H(2)L(1-Br)), 6,6'-(2-methyl-2(pyridine-2-yl)propane-1,3diyl)bis(azanediyl)bis(methylene)bis(2-methoxyphenol) (H(2)L(1-MeO)), 2,2'-(2-methyl-2(pyridine-2-yl)propane-1,3diyl)bis(azanediyl)bis(methylene)bis(4-nitrophenol) (H(2)L(1-NO2)), and 2,2'-(2-phenylpropane-1,3-diyl)bis(azanediyl)bis(methylene)diphenol (H(2)L(2)). These ligands, when combined with copper(II) salts and base, form either tricopper(II) species or monocopper(II) species depending on the nucleophilicity of the phenol groups in the ligands. All copper complexes were characterized by X-ray crystallography, cyclic voltammetry, and spectroscopic methods in solution. The ligands in trimeric complexes [{CuL(1)(CH(3)CN)}(2)Cu](ClO(4))(2) (1), [{CuL(1)Cl}(2)Cu] (1a), and [{CuL(2)(CH(3)CN)}(2)Cu](ClO(4))(2) (1b) and monomeric complex [CuL(1-tBu)(CH(3)OH)] (2) coordinate in a tetradentate mode via the amine N atoms and the phenolato O atoms. The pyridyl groups in 1, 1a, and 2 do not coordinate, but instead are involved in hydrogen bonding. Monomeric complexes [CuL(1-Br)] (3a), [CuL(1-NO2)] (3b), and [CuL(1-MeO)Na(CH(3)OH)(2)]ClO(4) (3c) have their ligands coordinated in a pentadentate mode via the amine N atoms, the phenolato O atoms, and the pyridyl N atom. The differences in tetradentate vs pentadentate coordination preferences of the ligands correlate to the nucleophilicity of the phenolate donor groups, and coincide with the electrochemical trends for these complexes.     

Structure of the α-phase of solid methanol

The crystal structure of α-methanol at 15K has been determined from neutron powder diffraction measurements. The structure is orthorhombic, space group P2₁2₁2₁. The molecular geometry is found to be very similar to that in the gas phase, but the methyl group no longer has ideal 3-fold symmetry. The crystal is formed by infinite hydrogen-bonded chains of molecules with adjacent chains ‘pointing’ in opposite directions. The O-H … O hydrogen bonds are almost linear. No phase intermediate between the low temperature α-phase and the high temperature β-phase was found, but a new, metastable phase was discovered.     

The uniform convergence of thin plate spline interpolation in two dimensions

Summary. Let be a function from to that has square integrable second derivatives and let be the thin plate spline interpolant to at the points in . We seek bounds on the error when is in the convex hull of the interpolation points or when is close to at least one of the interpolation points but need not be in the convex hull. We find, for example, that, if is inside a triangle whose vertices are any three of the interpolation points, then is bounded above by a multiple of , where is the length of the longest side of the triangle and where the multiplier is independent of the interpolation points. Further, if is any bounded set in that is not a subset of a single straight line, then we prove that a sequence of thin plate spline interpolants converges to uniformly on . Specifically, we require , where is now the least upper bound on the numbers and where , , is the least Euclidean distance from to an interpolation point. Our method of analysis applies integration by parts and the Cauchy--Schwarz inequality to the scalar product between second derivatives that occurs in the variational calculation of thin plate spline interpolation. Received November 10, 1993 / Revised version received March 1994     

The structure of (dichloro) (DI-μ-acetato)(bis-triphenyl phosphine) dimolybdenum(II)

The title compound was obtained in crystalline form suitable for X-ray structure determination. It forms crystals in the monoclinic space group P2₁/c with two centrosymmetric molecules in a unit cell of dimensions, a = 10.888(1) Å, b = 10.182(2) Å, c = 17.929(4) Å, β = 104.33(1)°. The central Mo₂Cl₂(O₂C)₂P₂ core has effectively C_2h-symmetry with the following principal dimensions: MoMo = 2.091(1) Å, MoCl = 2.405 Å, MoP = 2.566(2) Å, MoO(av.) = 2.103[4] Å, MoMoP = 104.38(7)°, and MoMoCl = 116.23(8)°.     

Quadratic termination properties of Davidon's new variable metric algorithm

Davidon [1] provides a variable metric algorithm for minimization calculations that achieves quadratic termination without any line searches by a method that uses positive definite second derivative approximations. We give a new and elementary proof of these termination properties. It shows the great freedom allowed by the algorithm in the choice of search directions and it explains the effect of a restart procedure.     

High pT π0 production from αα and αp collisions at the CERN ISR

The invariant cross sections for π⁰ meson production in alpha—alpha and alpha—proton collisions at the ISR were meas- ured up to transverse momenta of $\text{7}\text{GeV}\text{c}$ and $\text{8}\text{GeV}\text{c}$, respectively. These measurements are compared with π⁰ production in pp collisions at the same values of $\text{s}\text{/}$nucleon, and the variation of the nuclear A-dependence with p_T is determined.     

An algorithm for maximizing entropy subject to simple bounds

An unusual form of the maximum entropy problem is considered, that includes simple bound constraints on the Fourier coefficients of the required image, as well as nonnegativity conditions on the image intensities. The algorithm avoids mixing these constraints by introducing a parameter into the objective function that is adjusted by an outer iteration. For each parameter value an inner iteration solves a large optimization calculation, whose constraints are just the simple bounds, by a combination of the conjugate gradient procedure and an active set method. An important feature is the ability to make many changes to the active set at once. The outer iteration includes a test for inconsistency of all the given constraints. The algorithm is described, a proof of convergence is given, and there are some second-hand remarks on numerical results.