Interaction of 6,6′′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)-2,2′:6′,2′′-terpyridine (CyMe4-BTTP) with some trivalent ions such as lanthanide(iii) ions and americium(iii)

The new ligand 6,6 ''-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)2,2':6 ',2 ''-terpyridine (CyMe4-BTTP) has been synthesized in 4 steps from 2,2':6',2 ''-terpyridine. Detailed NMR and mass spectrometry studies indicate that the ligand forms 1 : 2 complexes with lanthanide(III) perchlorates where the aliphatic rings are conformationally constrained whereas 1 : 1 complexes are formed with lanthanide(III) nitrates where the rings are conformationally mobile. An optimized structure of the 1 : 2 solution complex with Yb(III) was obtained from the relative magnitude of the induced paramagnetic shifts. X-Ray crystallographic structures of the ligand and of its 1 : 1 complex with Y(III) were also obtained. The NMR and mass spectra of [Pd(CyMe4-BTTP)](n)(2n+) are consistent with a dinuclear double helical structure (n = 2). In the absence of a phase-modifier, CyMe4-BTTP in n-octanol showed a maximum distribution coefficient of Am(III) of 0.039 (+/-20%) and a maximum separation factor of Am(III) over Eu(III) of 12.0 from nitric acid. The metal(III) cations are extracted as the 1 : 1 complex from nitric acid. The generally low distribution coefficients observed compared with the BTBPs arise because the 1 : 1 complex of CyMe4-BTTP is considerably less hydrophobic than the 1 : 2 complexes formed by the BTBPs. In M(BTTP)(3+) complexes, there is a competition between the nitrate ions and the ligand for the complexation of the metal.

A square-planar nickel(II) monoradical complex with a bis(salicylidene)diamine ligand

The new square-planar Ni-II-N2O2 complex [Ni(L-Me)] (1(Me)), where L-Me, stands for the dianionic phenolato form of N,N'bis(3,5-di-tert-butyl-salicylidene)-4,5-dimethyl-1,2-phenyl- enediamine ((LH2)-L-Me), has been synthesised and fully characterised. X-ray crystallography was also used for the characterisation. The electrochemical one-electron oxidation of 1(Me) produces the thermally stable (within the temperature range 10-295 K) cationic species (1(Me))(+). The UV/Vis and X-band EPR experimental data, supported by DFT calculations, indicate that (1(Me))(+), is best described as a Ni-II monoradical complex and, thus, does NOT exist in a Ni-III ground state, in contrast to its demethylated counterpart [Ni(L-H)](+) (1(H))(+) below 170 K.

Strongly nucleophilic RhI centre in square-planar complexes with terdentate (κ3) 2,2′:6′,2′′-terpyridine ligands: crystallographic, electrochemical and density functional theoretical studies

Rh-I-terpyridine complexes have been unambiguously formed for the first time. The 2,21:6',2"-terpyridine (tpy), 4'-chloro-2,2':6',2"-terpyridine (4'-Cl-tpy) and 4'-(tert-butyldimethylsilyl-ortho-carboranyl)-2,2':6',2"-terpyridine (carboranyl-tpy) ligands were used for successful syntheses and characterisation of the corresponding Rh-I complexes with halide coligands, [Rh(X)(4'-Y-terpyridine)] (X = Cl, Y = H, Cl, carboranyl; X = Br, Y = H). All four neutral Rh-tpy complexes are square planar, with Rh-X bonds in the plane of the 4'-Y-terpyridine ligands. Full characterisation of these dark blue, highly air-sensitive compounds was hampered by their poor solubility in various organic solvents. This is mainly due to the formation of pi-stacked aggregates, as evidenced by the crystal structure of [Rh(Cl)(tpy)]; in addition, [Rh(Cl)(carboranyl-tpy)] merely forms discrete dimers. The (bonding) properties of the novel Rh-I-terpyridine complexes have been studied with single-crystal X-ray diffraction, (time-dependent) density functional theoretical (DFT) calculations, far-infrared spectroscopy, electronic absorption spectroscopy and cyclic voltammetry. From DFT calculations, the HOMO of the studied Rh-I-terpyridine complexes involves predominantly the metal centre, while the LUMO resides on the terpyridine ligand. Absorption bands of the studied complexes in the visible region (400-900 nm) can be assigned to MLCT and MLCT/XLCT transitions. The relatively low oxidation potentials of [Rh(X)(tpy)] (X = Cl, Br) point to a high electron density on the metal centre. This makes the Rh-I-terpyridine complexes strongly nucleophilic and (potentially) highly reactive towards various (small) substrate molecules containing carbon-halide bonds.

Adaptive least mean square CDMA detection with Gram–Schmidt pre-processing

The Gram-Schmidt (GS) orthogonalisation procedure has been used to improve the convergence speed of least mean square (LMS) adaptive code-division multiple-access (CDMA) detectors. However, this algorithm updates two sets of parameters, namely the GS transform coefficients and the tap weights, simultaneously. Because of the additional adaptation noise introduced by the former, it is impossible to achieve the same performance as the ideal orthogonalised LMS filter, unlike the result implied in an earlier paper. The authors provide a lower bound on the minimum achievable mean squared error (MSE) as a function of the forgetting factor λ used in finding the GS transform coefficients, and propose a variable-λ algorithm to balance the conflicting requirements of good tracking and low misadjustment.

[Pr(NO3)3L]: a mononuclear ten-coordinate lanthanide(III) complex with a tetradentate di-Schiff base

The novel praseodymium(III) complex [Pr(NO3)3L] (1), where L=N,N′-bis[1-(pyridin-2-yl)ethylidene]ethane-1,2-diamine, has been obtained by direct reaction of the Schiff base and the metal salt; the gadolinium(III) homologue has also been prepared and so far characterized only spectroscopically. The crystal structure resembles those reported for hexadentate macrocyclic Schiff bases.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Complexation of lanthanides, actinides and transition metal cations with a 6-(1,2,4-triazin-3-yl)-2,2′:6′,2′′-terpyridine ligand: implications for actinide(III)/lanthanide(III) partitioning

The quadridentate N-heterocyclic ligand 6-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin- 3-yl)-2,2′ : 6′,2′′-terpyridine (CyMe4-hemi-BTBP) has been synthesized and its interactions with Am(III),U(VI), Ln(III) and some transition metal cations have been evaluated by X-ray crystallographic analysis, Am(III)/Eu(III) solvent extraction experiments, UVabsorption spectrophotometry, NMR studies and ESI-MS. Structures of 1 : 1 complexes with Eu(III), Ce(III) and the linear uranyl (UO2 2+) ion were obtained by X-ray crystallographic analysis, and they showed similar coordination behavior to related BTBP complexes. In methanol, the stability constants of the Ln(III) complexes are slightly lower than those of the analogous quadridentate bis-triazine BTBP ligands, while the stability constant for the Yb(III)complex is higher. 1H NMR titrations and ESI-MS with lanthanide nitrates showed that the ligand forms only 1 : 1 complexes with Eu(III), Ce(III) and Yb(III), while both 1 : 1 and 1 : 2 complexes were formed with La(III) and Y(III) in acetonitrile. A mixture of isomeric chiral 2 : 2 helical complexes was formed with Cu(I), with a slight preference (1.4 : 1) for a single directional isomer. In contrast, a 1 : 1 complex was observed with the larger Ag(I) ion. The ligand was unable to extract Am(III) or Eu(III) from nitric acid solutions into 1-octanol, except in the presence of a synergist at low acidity. The results show that the presence of two outer 1,2,4-triazine rings is required for the efficient extraction and separation of An(III)from Ln(III) by quadridentate N-donor ligands.

Effect of a methyl group on the spontaneous resolution of a square-pyramidal coordination compound: crystal packing and conglomerate formation

Reaction of [Cu(pic)2]·2H2O (where pic stands for 2-picolinato) with 2-({[2-(dimethylamino)ethyl]amino}methyl)phenol (HL1) produces the square-pyramidal complex [CuL1(pic)] (1), which crystallizes as a conglomerate (namely a mixture of optically pure crystals) in the Sohncke space group P212121. The use of the methylated ligand at the benzylic position, i.e. (±)-2-(1-{[2-(dimethylamino)ethyl]amino}ethyl)phenol (HL2), yields the analogous five-coordinate complex [CuL2(pic)] (2) that crystallizes as a true racemate (namely the crystals contain both enantiomers) in the centrosymmetric space group P21/c. Density functional theory (DFT) calculations indicate that the presence of the methyl group indeed leads to a distinct crystallization behaviour, not only by intramolecular steric effects, but also because its involvement in non-covalent C–H···π and hydrophobic intermolecular contacts appears to be an important factor contributing to the crystal-lattice (stabilizing) energy of 2

Lanthanide speciation in potential SANEX and GANEX actinide/ 2 lanthanide separations using Tetra-N-Donor extractants

Lanthanide(III) complexes with N-donor ex-tractants, which exhibit the potential for the separation of minor actinides from lanthanides in the management of spent nuclear fuel, have been directly synthesized and characterized in both solution and solid states. Crystal structures of the Pr3+, Eu3+, Tb3+, and Yb3+ complexes of 6,6′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin3-yl)-1,10-phenanthroline(CyMe4-BTPhen) and the Pr3+, Eu3+, and Tb3+ complexes of 2,9-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotria-zin-3-yl)-2,2′-bypyridine (CyMe4-BTBP) were obtained. The majority of these structures displayed coordination of two ofthe tetra-N-donor ligands to each Ln3+ ion, even when in some cases the complexations were performed with equimolar amounts of lanthanide and N-donor ligand. The structures showed that generally the lighter lanthanides had their coordination spheres completed by a bidentate nitrate ion, giving a 2+ charged complex cation, whereas the structures of the heavier lanthanides displayed tricationic complex species with a single water molecule completing their coordination environments. Electronic absorption spectroscopic titrations showed formation of the 1:2 Ln3+/LN4‑donor species (Ln = Pr3+, Eu3+, Tb3+) in methanol when the N-donor ligand was in excess. When the Ln3+ ion was in excess, evidence for formation of a 1:1 Ln3+/LN4‑donor complex species was observed. Luminescent lifetime studies of mixtures of Eu3+ with excess CyMe4-BTBP and CyMe4-BTPhen in methanol indicated that the nitrate-coordinated species is dominant in solution. X-ray absorption spectra of Eu3+ and Tb3+ species, formed by extraction from an acidic aqueous phase into an organic solution consisting of excess N-donor extractant in pure cyclohexanone or 30% tri-n-butyl phosphate (TBP) in cyclohexanone, were obtained. The presence of TBP in the organic phase did not alter lanthanide speciation. Extended X-ray absorption fine structure data from these spectra were fitted using chemical models established by crystallography and solution spectroscopy and showed the dominant lanthanide species in the bulk organic phase was a 1:2 Ln3+/LN‑donor species.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

Chemistry and structure by design: ordered CuNi(CN)4 sheets with copper(II) in a square-planar environment

Layered copper–nickel cyanide, CuNi(CN)4, a 2-D negative thermal expansion material, is one of a series of copper(II)-containing cyanides derived from Ni(CN)2. In CuNi(CN)4, unlike in Ni(CN)2, the cyanide groups are ordered generating square-planar Ni(CN)4 and Cu(NC)4 units. The adoption of square-planar geometry by Cu(II) in an extended solid is very unusual.

Synthesis and evaluation of a novel hydrophilic 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine ligand for separating actinide(III) from lanthanide(III)

We report the synthesis and evaluation of a novel hydrophilic 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine (BTBP) ligand containing carboxylate groups as a selective aqueous complexing agent for the minor actinides over lanthanides. The novel ligand is able to complex and separate Am(III) from Eu(III) in alkaline solutions selectively.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.