Mono- and dinuclear five-coordinate cyclometalated palladium(II) compounds

Reaction of cyclometalated halide-bridged Pd(II) complexes 1-4 with the tertiary triphosphine ligand (Ph2PCH2CH2)2PPh (triphos) yielded complexes [((Ph2PCH2CH2)2PPh-P,P,P)Pd(N(Cy)=(H)C)C6H2(C(H)=N(Cy))Pd((Ph2PCH2CH2)2PPh-P,P,P)][ClO4]2 5, [Pd(C6H4-N=NC6H5)((Ph2PCH2CH2)2PPh-P,P,P)][ClO4] 6, and [Pd(R-C6H3C(H)=NCy)((Ph2PCH2CH2)2PPh-P,P,P)][ClO4] (7; R = 4-CHO, 8; 3-CHO). Spectroscopic and analytic data suggest five-coordination on the palladium atom, which, for complexes 5, 6, and 7, was confirmed by X-ray crystallography. The geometry around palladium may be view as a distorted trigonal bipyramid, with the palladium, nitrogen, and terminal phosphorus atoms in the equatorial plane. Compound 5 is the first doubly cyclometalated palladium(II) compound with two pentacoordinated metal centers. The structure of 6 comprises two discrete cations with slightly different geometries, showing the importance of crystal packing forces in order to determine the coordination arrangement.     

Operational Solution to the Nonlinear Klein-Gordon Equation

We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.     

Comments on “Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions”

Some results presented in the paper “Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions” [I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999] are discussed in this paper. The slightly modified Grünwald-Letnikov derivative proposed there is used to deduce some interesting results that are in contradiction with those proposed in the referred paper.     

A unified approach to fractional derivatives

A new fractional derivative of the Grüwald–Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Grüwald–Letnikov and the two-sided fractional derivatives. Several properties of such generalized operator are presented, and some particular cases deduced.     

Cyclometallated thiosemicarbazone palladium(II) compounds: The first crystal and molecular structures of mononuclear complexes with a η-diphosphine ligand

Treatment of the thiosemicarbazones 2-XC₆H₄C(Me)NN(H)C(S)NHR (R = Me, X = F, a; R = Et, X = F, b; R = Me, X = Cl, c; R = Et, X = Br, d) with potassium tetrachloropalladate(II) in ethanol, lithium tetrachloropalladate(II) in methanol or palladium(II) acetate in acetic acid, as appropriate, gave the tetranuclear cyclometallated complexes [Pd{2-XC₆H₃C(Me)NNC(S)NHR}]₄ (1a-1d). Reaction of 1a-1d with the diphosphines Ph₂PCH₂PPh₂ (dppm), Ph₂P(CH₂)₂PPh₂ (dppe), Ph₂P(CH₂)₃PPh₂ (dppp) or trans-Ph₂PCHCHPPh₂ (trans-dpe) in 1:2 molar ratio gave the dinuclear cyclometallated complexes [{Pd[2-XC₆H₃C(Me)NNC(S)-NHR]}₂(μ-diphosphine-P,P)] (2a-5a, 3b, 3d, 4c, 5c). Reaction of 1a, 1b with the short-bite or long-bite diphosphines, dppm or cis-dpe, in a 1:4 molar ratio gave the mononuclear cyclometallated complexes [Pd{2-XC₆H₃C(Me)NNC(S)NHR}(diphosphine-P)] (6a, 6b, 7a). The molecular structure of ligand a and of complexes 1a, 3d, 5a, 5c, 6a, 6b and 7a have been determined by X-ray diffraction analysis. The structure of complex 7a shows that the long-bite cis-bis(diphenylphosphino)ethene phosphine appears as monodentate with an uncoordinated phosphorus donor atom.     

Fractional Discrete-Time Signal Processing: Scale Conversion and Linear Prediction

A generalization of the linear prediction for fractional steps isreviewed, widening well-known concepts and results. This prediction isused to derive a causal interpolation algorithm. A reconstructionalgorithm for the situation where averages are observed is alsopresented. Scale conversion of discrete-time signals is studied takingas base the fractional discrete-time system theory. Some simulationresults to illustrate the behaviour of the algorithms will be presented.A new algorithm for performing the zoom transform is also described.     

A Fractional Linear System View of the Fractional Brownian Motion

A definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.     

Chemistry of Tetradentate [C,N : C,N] Iminophosphorane Palladacycles: Preparation,Reactivity and Theoretical Calculations

A theoretical and experimental study of tetradentate [C,N : C,N] iminophosphorane palladacycles was carried out for the purpose of elucidating their behavior as compared to the parent Schiff base analogues to determine the prospect of encountering new A-frame structures for the iminophosphorane derivatives. The DFT calculations were in agreement with the experimental results regarding the performance of these ligands. New insights into the chemistry of the related dinuclear species have been obtained.     

The chemistry of N-benzylidene-1,4-phenylenediamine palladacycles: The crystal and molecular structure of the first tetranuclear palladacycle with bridging Ph2PCH2PPh2 ligands

The reaction of the tetranuclear halide-bridged complexes 1?2(a?d) with Ph₂PCH₂PPh₂ (dppm) or Ph₂PC(CH₂)PPh₂ (vdpp) in 1:2 molar ratio and NH₄PF₆ afforded the novel tetarnuclear palladacycles 3?6 (a, c, d) as 1:2 electrolytes with bridging diphosphine and halogen ligands. The structure of 4a has been determined by X-ray diffraction analysis, and represents the first example of a tetranuclear palladacycle with bridging dppm and halogen ligands. Reaction of 1?2(a?d) with (Ph₂PCH₂CH₂)₂PPh (triphos) in 1:2 molar ratio gave 7(a?d) bearing two pentacoordinated palladium atoms. The structure of 7a, as determined by X-ray diffraction analysis, shows the distorted square pyramidal geometry around the metal centers. Treatment of 1?2(a?d) with dppm, vdpp or Ph₂PN(Me)PPh₂ (dppma) in 1:4 molar ratio gave the dinuclear palladacycles 8?10(a?d) with a chelating diphosphine ligand at each metal center; further treatment of 9(a?c) with the nucleophiles pyrrolidine, piperidine, morpholine or 4-methyl-piperidine gave the Michael addition derivatives 11?12(a?c), 13b, 13c and 14c, promoted by the withdrawing effect of the palladacycle which activates the CCH₂ double bond.