Monodromy and nonintegrability in complex Hamiltonian systems

This paper investigates the monodromy representation of the normal variational equation along a phase curve of a two-dimensional complex analytic Hamiltonian system. Geometrical conditions are presented which guarantee reducibility, together with additional hypotheses to ensure complete reducibility. Symmetries in the equations are treated in detail. Applications to establishing the nonintegrability of specific systems are presented.     

Tunability of the M(II)M(III)/M(II)(2) and M(III)(2)/M(II)M(III) (M=Mn, Co) couples in bis-μ-O,O'-carboxylato-μ-OR bridged complexes

A comparison of the electrochemical properties of a series of dinuclear complexes [M(2)(L)(RCO(2))(2)](+) with M = Mn or Co, L = 2,6-bis(N,N-bis-(2-pyridylmethyl)-sulfonamido)-4-methylphenolato (bpsmp(-)) or 2,6-bis(N,N-bis(2-pyridylmethyl)aminomethyl)-4-tert-butylphenolato (bpbp(-)) and R = H, CH(3), CF(3) or 3,4-dimethoxybenzoate demonstrates: (i) The electron-withdrawing sulfonyl groups in the backbone of bpsmp(-) stabilize the [M(2)(bpsmp)(RCO(2))(2)](+) complexes in their M(II)(2) oxidation state compared to their [M(2)(bpbp)(RCO(2))(2)](+) analogues. Manganese complexes are stabilised by approximately 550 mV and cobalt complexes by 650 mV. (ii) The auxiliary bridging carboxylato ligands further attenuate the metal-based redox chemistry. Substitution of two acetato for two trifluoroacetato ligands shifts redox couples by 300-400 mV. Within the working potential window, reversible or quasi-reversible M(II)M(III)? M(II)(2) processes range from 0.31 to 1.41 V for the [Co(2)(L)(RCO(2))(2)](+/2+) complexes and from 0.54 to 1.41 V for the [Mn(2)(L)(RCO(2))(2)](+/2+) complexes versus Ag/AgCl for E(M(II)M(III)/M(II)(2)). The extreme limits are defined by the complexes [M(2)(bpbp)(CH(3)CO(2))(2)](+) and [M(2)(bpsmp)(CF(3)CO(2))(2)](+) for both metal ions. Thus, tuning the ligand field in these dinuclear complexes makes possible a range of around 0.9 V and 1.49 V for the one-electron E(M(II)M(III)/M(II)(2)) couple of the Mn and Co complexes, respectively. The second one-electron process, M(II)M(III)? M(III)(2) was also observed in some cases. The lowest potential recorded for the E°(M(III)(2)/M(II)M(III)) couple was 0.63 V for [Co(2)(bpbp)(CH(3)CO(2))(2)](2+) and the highest measurable potential was 2.23 V versus Ag/AgCl for [Co(2)(bpsmp)(CF(3)CO(2))(2)](2+).     

Synthesis and characterization of diiron dithiolate complexes containing a quinoxaline bridge

A potential model complex for the hydrogenase active site, [Fe(2){(μ-CH(2)S)(2)R}(CO)(6)] (1) (R = quinoxaline), was synthesized by condensation of [(μ-LiS)(2)Fe(2)(CO)(6)] with 2,3-bis(bromomethyl)quinoxaline. Reactions of 1 with bis(diphenylphosphino)methane (dppm) under a range of conditions yielded substituted complexes [Fe(2){(μ-CH(2)S)(2)R}(CO)(5)(dppm)] (2), [Fe(2){(μ-CH(2)S)(2)R}(CO)(4)(k(2)-dppm)] (3) and [Fe(2){(μ-CH(2)S)(2)R}(CO)(4)(μ-dppm)] (4). X-ray crystallography confirms that in 2, the dppm is terminally bonded to an iron atom via one phosphorus atom, whereas in 3, it acts as a chelating ligand to coordinate to an iron center in a dibasal-substituted manner. In 4, the dppm bridges the two iron atoms in a cis basal/basal fashion with one phosphorus bonded to each iron atom. Treatment of 1 with various tertiary phosphines at room temperature in acetonitrile (MeCN) generates a range of mono-substituted products [Fe(2){(μ-CH(2)S)(2)R}(CO)(5)L] (5, L = PEt(3); 6, PMe(3); 7, PPh(3); 8, Me(2)PPh). With Bu(t)NC, mono- and di-substituted [Fe(2){(μ-CH(2)S)(2)R}(CO)(5)(Bu(t)NC)] (9) and [Fe(2){(μ-CH(2)S)(2)R}(CO)(4)(Bu(t)NC)(2)] (10) complexes are generated. All the complexes were characterized by elemental analysis, IR, MS and NMR spectroscopy. IR and NMR spectroscopic studies suggest that addition of excess HBF(4)·OEt(2) acid to 1-4 led to the protonation of quinoxaline nitrogen atoms. In contrast, 5-10 were not stable in acidic media. Electrochemistry of 1-4 was investigated in the acetonitrile medium (0.1 M Bu(4)NPF(6)). The electrochemical instability of the reduced ligand, quinoxaline, and the reduced forms of these complexes revealed from the electrochemical studies suggests that they do not provide ideal models of the hydrogenase active site.     

Stable heteroleptic complexes of divalent lanthanides with bulky pyrazolylborate ligands--iodides, hydrocarbyls and triethylborohydrides

The reaction of YbI(2) with KTp(Me2) gives (Tp(Me2))YbI(THF)(2) (1-Yb) as a thermally unstable product. Use of the more hindered KTp(tBu,Me) gave (Tp(tBu,Me))LnI(THF)(n) (Ln = Sm, n = 2, 2-Sm; Ln = Yb, n = 1, 2-Yb). The crystal structures of both these compounds are reported. Adducts with neutral ligands such as pyridines and isonitriles can be prepared and the crystal structures of [(Tp(tBu,Me))YbIL(n)] (L = CN(t)Bu, n = 1; L = 3,5-lutidine, n = 2) are described. 2-Sm can be oxidized using AgBPh(4) to give [(Tp(tBu,Me))SmI(THF)(2)]BPh(4). Compounds 2-Sm and 2-Yb are useful starting materials for the preparation of heteroleptic compounds by metathesis with appropriate potassium reagents. The preparations and characterization of the hydrocarbyls (Tp(tBu,Me))Ln{CH(SiMe(3))(2)} (Ln = Sm, 5-Sm; Yb, 5-Yb) and [(Tp(tBu,Me))Ln{CH(2)(SiMe(3))}(THF)] (Ln = Yb, 6a-Yb) and the triethylborohydrides [(Tp(tBu,Me))Ln(HBEt(3))(THF)(n)] (Ln = Sm, n = 0, 7-Sm; Yb, n = 1, 7-Yb) are reported, as well as the crystal structures of 5-Sm and 5-Yb, and the THF adducts 6a-Yb and [(Tp(tBu,Me))Sm{CH(SiMe(3))(2)}(THF)], 5a-Sm.     

Anion dependent redox changes in iron bis-terdentate nitroxide {NNO} chelates

The reaction of [Fe(II)(BF(4))(2)]·6H(2)O with the nitroxide radical, 4,4-dimethyl-2,2-di(2-pyridyl) oxazolidine-N-oxide (L(?)), produces the mononuclear transition metal complex [Fe(II)(L(?))(2)](BF(4))(2) (1) which has been investigated using temperature dependent susceptibility, Mo?ssbauer spectroscopy, electrochemistry, density functional theory (DFT) calculations, and X-ray structure analysis. Single crystal X-ray diffraction analysis and Mo?ssbauer measurements reveal an octahedral low spin Fe(2+) environment where the pyridyl donors from L(?) coordinate equatorially while the oxygen containing the radical from L(?) coordinates axially forming a linear O(?)··Fe(II)··O(?) arrangement. Magnetic susceptibility measurements show a strong radical-radical intramolecular antiferromagnetic interaction mediated by the diamagnetic Fe(2+) center. This is supported by DFT calculations which show a mutual spatial overlap of 0.24 and a spin density population analysis which highlights the antiparallel spin alignment between the two ligands. Similarly the monocationic complex [Fe(III)(L(-))(2)](BPh(4))·0.5H(2)O (2) has been fully characterized with Fe-ligand and N-O bond length changes in the X-ray structure analysis, magnetic measurements revealing a Curie-like S = 1/2 ground state, electron paramagnetic resonance (EPR) spectra, DFT calculations, and electrochemistry measurements all consistent with assignment of Fe in the (III) state and both ligands in the L(-) form. 2 is formed by a rare, reductively induced oxidation of the Fe center, and all physical data are self-consistent. The electrochemical studies were undertaken for both 1 and 2, thus allowing common Fe-ligand redox intermediates to be identified and the results interpreted in terms of square reaction schemes.     

Solvent and hydrogen confinement in molecular capsules-Hirshfeld surface and molecular simulation analysis

Hirshfeld surface analysis of the 'ordered' inner phase of the molecular capsule complex, [(chloroform)(6)@C-n-butylpyrogallol[4]arene)(6)], provides insight into the intermolecular contacts and orientation of the solvent molecules. Molecular simulations show that adding two or three hydrogen molecules to the six solvent molecules is energetically favoured, and this correlates with NMR studies.     

Poly[tetrakis(n‐propylammonium) [octa‐μ‐chlorido‐dichloridotrinickelate(II)]]: a hybrid organic–inorganic layer compound in the Cs4Mg3F10 structure type

The title compound, {(C₃H₁₀N)₄[Ni₃Cl₁₀]}_n, contains zigzag layers of tri‐μ‐chlorido‐bridged linear 2/m‐symmetric Ni₃Cl₁₂ segments, linked by mono‐μ‐chlorido quasi‐linear bridges to two other segments at each end. These inorganic layers are interleaved with interdigitated bilayers of mirror‐symmetric n‐propylammonium cations, the ammonium head groups of which are directed into the inorganic layers to form multiple N—H...Cl hydrogen bonds, while the propyl tail groups pack together in a tongue‐and‐groove manner in the center of the bilayer. The propyl groups are ordered at 100 K but disordered with opposite conformations on the mirror plane at 240 K.     

Infant speech-sound discrimination in noise

The effects of noise on 7- to 11-month-old infants' speech-sound discrimination (/ba/vs/ga/) were determined using a conditioned head-turn procedure. Variation in performance as a function of signal-to-noise ratio (S/N) was estimated by testing each infant at four S/N's (-8, 0, 8, and 16 dB). Adults were tested for comparison at four S/N's (-12, -8, -4, and 0 dB). The S/N's were chosen based on pilot data. Performance varied monotonically with S/N for both age groups, but infants required greater S/N than adults to achieve comparable levels of performance. Both groups were also tested using an adaptive (1-up, 1-down) threshold procedure with a 3-dB step size. There was a group mean difference in threshold of 5.8-dB S/N favoring the adults. Weighted group psychometric functions, derived from the responses obtained in the adaptive runs, showed good correspondence with the data points at the four S/N's. The slopes of these functions were the same (7.5%/dB) for infants and adults. The results suggest that infants are at a greater disadvantage than adults when processing speech in noise and that concern over the effects of a noisy environment on the acquisition of language is justified. In addition, the adaptive threshold procedure can be used as an efficient way to estimate the limits of discrimination ability as a function of S/N or intensity, both for individual subjects and for groups of subjects, in developmental research.