Characterizing the dynamics of coupled pendulums via symbolic time series analysis

We propose a novel method of symbolic time-series analysis aimed at characterizing the regular or chaotic dynamics of coupled oscillators. The method is applied to two identical pendulums mounted on a frictionless platform, resembling Huygens’ clocks. Employing a transformation rule inspired in ordinal analysis [C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002)], the dynamics of the coupled system is represented by a sequence of symbols that are determined by the order in which the trajectory of each pendulum intersects an appropriately chosen hyperplane in the phase space. For two coupled pendulums we use four symbols corresponding to the crossings of the vertical axis (at the bottom equilibrium point), either clock-wise or anti-clock wise. The complexity of the motion, quantified in terms of the entropy of the symbolic sequence, is compared with the degree of chaos, quantified in terms of the largest Lyapunov exponent. We demonstrate that the symbolic entropy sheds light into the large variety of different periodic and chaotic motions, with different types synchronization, that cannot be inferred from the Lyapunov analysis.     

Reversible Carbene Insertion into a Ge−N Bond and Insights into CO and Carbene Substitution Reactions Involving Amidinatogermylenes and Fischer Carbene Complexes

The formation of the five-membered-ring germylene complexes [M(CO)₅{Ge(tBu₂bzamC(OEt)Me)tBu}] ( 3_M ; M=Cr, W), which occurs readily at room temperature from the germylene Ge(tBu₂bzam)tBu ( 1 _{t Bu} ) and Fischer carbenes [M(CO)₅{C(OEt)Me}] ( 2_M ; M=Cr, W), has been found to be reversible. Upon heating at 60 °C, complexes 3_M undergo epimerization to an equilibrium mixture of 3_M and 3′_M . At that temperature, the chromium epimers (but not the tungsten ones) release CO to end in the mixed germylene–Fischer carbene complexes [Cr(CO)₄{C(OEt)Me}{Ge(tBu₂bzam)tBu}] (cis- 4_Cr and trans- 4_Cr ). The latter decompose at 120 °C to [Cr(CO)₅{Ge(tBu₂bzam)tBu}] ( 6_Cr ). Because the formation of cis- 4_Cr and trans- 4_Cr from 3_Cr or 3′_Cr requires the presence of free 1 _{t Bu} and 2_Cr in the reaction solutions, the reactions of 1 _{t Bu} with 2_M to give 3_M (and 3′_M at 60 °C) should be reversible. This proposal has been proven by germylene-exchange crossover reactions in which free 1 _{t Bu} and [M(CO)₅{Ge(tBu₂bzamC(OEt)Me)CH₂SiMe₃}] ( 5′_M ; M=Cr, W) were formed when complexes 3_M were treated at room temperature with the germylene Ge(tBu₂bzam)CH₂SiMe₃ ( 1_tmsm ). A clear differential behavior between N-heterocyclic carbenes (NHCs) and amidinatogermylenes ( 1 _{t Bu} and 1_tmsm ) in their reactivity against group 6 metal Fischer carbene complexes is demonstrated. The higher electron-donor capacity of amidinatogermylenes with respect to NHCs and the bias of the former to get involved in ring expansion processes are responsible for this differential behavior.     

Densities and derived thermodynamic properties of ternary mixtures 1-butyl-3-methyl-imidazolium tetrafluoroborate + ethanol + water at seven pressures and two temperatures

This work is a continuation of our studies on experimental measurements of physical properties on binary mixtures of the ionic liquid (IL) family 1-alkyl-3-methyl imidazolium tetrafluoroborate (CnMIM-BF₄) with water and ethanol. Here, we present density for the ternary system Butyl-MIM-BF₄ + ethanol + water at two temperatures (298.15 K and 323.15 K) and seven pressures (from 0.1 to 30 MPa). It should be noted that BMIM-BF₄ is the only IL of the family CnMIM-BF₄ that can be mixed with water and ethanol in all range of concentrations at room conditions. From the density data measured in function of pressure and temperature other important derived thermodynamic properties can be calculated, such us excess molar volumes, isothermal compressibility, isobaric expansion and the thermal pressure coefficients. These properties for selected ternary mixtures will be discussed and compared with data from the scarce number of published results for similar ternary mixtures with this same IL.     

Reactions of phthalazine, quinazoline, 4,7-phenanthroline and 2,3'-bipyridine with ruthenium carbonyl

The reactions of [Ru(3)(CO)(12)] with four aromatic diazines have been studied in THF at reflux temperature. With phthalazine (L(1)), the compound [Ru(3)(μ-κ(2)N(2)N(3)-L(1))(μ-CO)(3)(CO)(7)] (1), which contains an intact phthalazine ligand in an axial position bridging an Ru-Ru edge through both N atoms, is initially formed but it reacts with more phthalazine to give [Ru(3)(κN(2)-L(1))(μ-κ(2)N(2)N(3)-L(1))(μ-CO)(3)(CO)(6)] (2), in which a π-π stacking interaction between the aromatic rings of both ligands determines their position in cluster axial sites on the same face of the Ru(3) triangle. With quinazoline (HL(2)), the cyclometalated hydrido decacarbonyl derivative [Ru(3)(μ-H)(μ-κ(2)N(3)C(4)-L(2))(CO)(10)] (3) is initially produced but it partially decarbonylates under the reaction conditions to give [Ru(6)(μ-H)(2)(μ-κ(2)N(3)C(4)-L(2))(μ(3)-κ(3)-N(1)N(3)C(4)-L(2))(CO)(19)] (4), which results from the displacement of a CO ligand of 3 by the uncoordinated N(1) atom of another molecule of 3. With 4,7-phenanthroline (H(2)L(3)), the stepwise formation of the cyclometalated derivatives [Ru(3)(μ-H)(μ-κ(2)N(4)C(3)-HL(3))(CO)(10)] (5) and two isomers of [Ru(6)(μ-H)(2)(μ(4)-κ(4)N(4)C(3)N(7)C(8)-L(3))(CO)(20)] (6a, 6b) takes place. In compounds 6a and 6b, two Ru(3)(μ-H)(CO)(10) trinuclear units are symmetrically (C(2) in 6a or C(S) in 6b) bridged by a doubly-cyclometalated 4,7-phenanthroline ligand. With 2,3'-bipyridine (HL(4)), two products have been isolated, [Ru(3)(μ-H)(μ-κ(2)N(3')C(4')-L(4))(CO)(10)] (7) and [Ru(3)(μ-H)(μ-κ(3)N(2)N(3')C(2')-L(4))(CO)(9)] (8). While compound 7 contains an N(3')C(4')-cyclometalated 2,3'-bipyridine, in compound 8 an N(3')C(2')-cyclometalation is accompanied by the coordination of the N(2) atom of the remaining pyridine fragment. The structures of compounds 2, 3, 4, 6a and 8 have been determined by X-ray diffraction crystallography.     

The adsorption of 1,3-butadiene on Pd/Ni multilayers: The interplay between spin polarization and chemisorption strength

The adsorption of 1,3-butadiene (BD) on the Pd/Ni(1 1 1) multilayers has been studied using the VASP method in the framework of the density functional theory (DFT). The adsorption on two different configurations of the Pd_n/Ni_m(1 1 1) systems were considered. The most stable adsorption sites are dependent on the substrate composition and on the inclusion or not of spin polarization. On Pd₁Ni₃(1 1 1) surface, di-π-cis and 1,2,3,4-tetra-σ adsorption structures are the most stable for non-spin polarized (NSP) and spin polarized (SP) levels of calculation, respectively. Conversely, on Pd₃Ni₁(1 1 1) surface, the 1,2,3,4-tetra-σ adsorption structure is the most stable for both NSP and SP levels, respectively. The magnetization of the Pd atoms strongly modifies the adsorption energy of BD and its most stable adsorption mode. On the other hand, as a consequence of BD adsorption, the Pd magnetization decreases. The smaller adsorption energies of BD and 1-butene on the Pd₁Ni₃(1 1 1) surface than on Pd(1 1 1) can be associated to the strained Pd overlayer deposited on Ni(1 1 1).     

Unexpected Zwitterionic Allenyls from Silylenes and a Fischer Alkynylcarbene: A Remarkable Silylene-Promoted Rearrangement

The silylenes Si(tBu₂bzam)R (tBu₂bzam=N,N′-bis(tertbutyl)benzamidinate; R=mesityl, CH₂SiMe₃) attack the C_carbene atom of the Fischer alkynyl(ethoxy)carbene complex [W(CO)₅{C(OEt)C₂Ph}] to give, after a striking rearrangement, zwitterionic σ-allenyl complexes in which the original carbene C atom forms part of the allene C₃ fragment and also of a Si-C-N-C-N five-membered ring after insertion into a Si−N bond of the original amidinatosilylene. These remarkable allenyl products, which contain two stereogenic groups, are selectively formed as single diastereomers.     

Crystallographic report: [N,N′‐Bis‐(6‐methylpyrid‐2‐ylium)‐(1R,2R)‐1,2‐diaminocyclohexane] bis‐[(p‐cymene)‐ trichlororuthenate(II)]

The chiral compound (H₂cydiampy)[RuCl₃(p‐cymene)]₂ has been obtained in high yield by treating [RuCl₂(p‐cymene)]₂ with an excess of hydrochloric acid in the presence of one equivalent of N,N′‐bis‐(6‐methylpyrid‐2‐yl)‐(1R,2R)‐1,2‐diaminocyclohexane (cydiampy). It crystallizes in the chiral tetragonal space group P4₃2₁2, with half of the atoms of the dication related to the other half by a crystallographic C₂ axis that also makes equivalent the two anionic metal moieties. Copyright © 2005 John Wiley & Sons, Ltd.