Interacting Multiple Try Algorithms with Different Proposal Distributions

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space

Spontaneous self-assembly of an unsymmetric trinuclear triangular copper(II) pyrazolate complex, [Cu3(μ3-OH)(μ-pz) 3(MeCOO)2(Hpz)] (Hpz = pyrazole). Synthesis, experimental and theoretical characterization, reactivity, and catalytic activity

The almost quantitative formation of the triangular trinuclear copper derivative [Cu3(μ3-OH)(μ-pz)3(MeCOO) 2(Hpz)] (1) (Hpz = pyrazole), has been simply achieved by adding Hpz to an ethanol solution of Cu(MeCOO)2·H2O. An X-ray molecular structure determination shows that 1 is completely unsymmetric and that trinuclear units result assembled in an extended bidimensional network formed through acetate bridges and hydrogen bonds. EPR and magnetic measurements are consistent with the presence of a single unpaired electron. Theoretical density functional calculations carried out for S = 1/2 provide a thorough description of the electronic structure of 1, allowing a detailed assignment of its UV-vis absorption spectrum. Compound 1 reacts with MeONa, yielding [Cu 3(μ3-OH)(μ-pz)3(MeCOO)(MeO)(Hpz)] (2) and [Cu3(μ3-OH)(μ-pz)3(MeO) 2(Hpz)] (3) through the substitution of one and two acetate ions, respectively, with MeO- ion(sS). The spontaneous self-assembly of the triangular trinuclear Cu3 moiety seems to occur only with pyrazole as can be inferred by the results obtained in the reactions of copper(II) acetate with some substituted pyrazoles leading to the formation of mononuclear [Cu(MeCOO)2(L)2] (4-8) and dinuclear [Cu(MeCOO) 2(L)]2 (9-11) (L = substituted pyrazole) compounds. Also the presence of acetate ions seems to play a leading role in determining the formation of the trinuclear triangular arrangement, as indicated by the formation of a mononuclear derivative, [Cu(CF3COO) 2(Hpz)]2 (compound 12), in the reaction of copper(II) trifluoroacetate with pyrazole. Compounds 1-3, as well as some other mono- and dinuclear copper(II)-substituted pyrazole complexes, have been tested as catalyst precursors in cyclopropanation reaction, observing the formation of products in a syn:anti ratio opposite that normally reported