Crystalline Nitridophosphates by Ammonothermal Synthesis

Nitridophosphates are a well-studied class of compounds with high structural diversity. However, their synthesis is quite challenging, particularly due to the limited thermal stability of starting materials like P₃N₅. Typically, it requires even high-pressure techniques (e.g. multianvil) in most cases. Herein, we establish the ammonothermal method as a versatile synthetic tool to access nitridophosphates with different degrees of condensation. α-Li₁₀P₄N₁₀, β-Li₁₀P₄N₁₀, Li₁₈P₆N₁₆, Ca₂PN₃, SrP₈N₁₄, and LiPN₂ were synthesized in supercritical NH₃ at temperatures and pressures up to 1070 K and 200 MPa employing ammonobasic conditions. The products were analyzed by powder X-ray diffraction, energy dispersive X-ray spectroscopy, and FTIR spectroscopy. Moreover, we established red phosphorus as a starting material for nitridophosphate synthesis instead of commonly used and not readily available precursors, such as P₃N₅. This opens a promising preparative access to the emerging compound class of nitridophosphates.     

An SR1/BFGS SQP algorithm for nonconvex nonlinear programs with block-diagonal Hessian matrix

We present a quasi-Newton sequential quadratic programming (SQP) algorithm for nonlinear programs in which the Hessian of the Lagrangian function is block-diagonal. Problems with this characteristic frequently arise in the context of optimal control; for example, when a direct multiple shooting parametrization is used. In this article, we describe an implementation of a filter line-search SQP method that computes search directions using an active-set quadratic programming (QP) solver. To take advantage of the block-diagonal structure of the Hessian matrix, each block is approximated separately by quasi-Newton updates. For nonconvex instances, that arise, for example, in optimum experimental design control problems, these blocks are often found to be indefinite. In that case, the block-BFGS quasi-Newton update can lead to poor convergence. The novel aspect in this work is the use of SR1 updates in place of BFGS approximations whenever possible. The resulting indefinite QPs necessitate an inertia control mechanism within the sparse Schur-complement factorization that is carried out by the active-set QP solver. This permits an adaptive selection of the Hessian approximation that guarantees sufficient progress towards a stationary point of the problem. Numerical results demonstrate that the proposed approach reduces the number of SQP iterations and CPU time required for the solution of a set of optimal control problems.     

A Factor Analysis Perspective on Linear Regression in the ‘More Predictors than Samples’ Case

Linear regression (LR) is a core model in supervised machine learning performing a regression task. One can fit this model using either an analytic/closed-form formula or an iterative algorithm. Fitting it via the analytic formula becomes a problem when the number of predictors is greater than the number of samples because the closed-form solution contains a matrix inverse that is not defined when having more predictors than samples. The standard approach to solve this issue is using the Moore–Penrose inverse or the L2 regularization. We propose another solution starting from a machine learning model that, this time, is used in unsupervised learning performing a dimensionality reduction task or just a density estimation one—factor analysis (FA)—with one-dimensional latent space. The density estimation task represents our focus since, in this case, it can fit a Gaussian distribution even if the dimensionality of the data is greater than the number of samples; hence, we obtain this advantage when creating the supervised counterpart of factor analysis, which is linked to linear regression. We also create its semisupervised counterpart and then extend it to be usable with missing data. We prove an equivalence to linear regression and create experiments for each extension of the factor analysis model. The resulting algorithms are either a closed-form solution or an expectation–maximization (EM) algorithm. The latter is linked to information theory by optimizing a function containing a Kullback–Leibler (KL) divergence or the entropy of a random variable.     

Manifolds with almost nonnegative curvature operator and principal bundles

We study closed manifolds with almost nonnegative curvature operator (ANCO) and derive necessary and/or sufficient conditions for the total spaces of principal bundles over (A)NCO manifolds to admit ANCO connection metrics. In particular, we provide first examples of closed simply connected ANCO manifolds which do not admit metrics with nonnegative curvature operator.     

The NiII,HgII and CuII complexes of 12‐membered‐ring mixed‐donor macrocycles

The structures of di­aqua(1,7‐dioxa‐4‐thia‐10‐aza­cyclo­do­decane)­nickel dinitrate, [Ni(C₈H₁₇NO₂S)(H₂O)₂](NO₃)₂, (I), bis­(nitrato‐O,O′)(1,4,7‐trioxa‐10‐aza­cyclo­do­decane)­mercury, [Hg(NO₃)₂(C₈H₁₇NO₃)], (II), and aqua­(nitrato‐O)(1‐oxa‐4,7,10‐tri­aza­cyclo­do­decane)copper nitrate, [Cu(NO₃)(C₈H₁₉N₃O)(H₂O)]NO₃, (III), reveal each macrocycle binding in a tetradentate manner. The conformations of the ligands in (I) and (III) are the same and distinct from that identified for (II). These differences are in agreement with molecular‐mechanics predictions of ligand conformation as a function of metal‐ion size.     

Secondary bonding interactions in biomimetic [2Fe-2S] clusters

A series of synthetic [2Fe-2S] complexes with terminal thiophenolate ligands and tethered ether or thioether moieties has been prepared and investigated in order to provide models for the potential interaction of additional donor atoms with the Fe atoms in biological [2Fe-2S] clusters. X-ray crystal structures have been determined for six new complexes that feature appended Et (1(C)), OMe (1(O)), or SMe (1(S)) groups, or with a methylene group (2(C) ), an ether-O (2(O)), or an thioether-S (2(S)) linking two aryl groups. The latter two systems provide a constrained chelate arrangement that induces secondary bonding interactions with the ether-O and thioether-S, which is confirmed by density functional theory (DFT) calculations that also reveal significant spin density on those fifth donor atoms. Structural consequences of the secondary bonding interactions are analyzed in detail, and effects on the spectroscopic and electronic properties are probed by UV-vis, M?ssbauer, and (1)H NMR spectroscopy, as well by SQUID measurements and cyclic voltammetry. The potential relevance of the findings for biological [2Fe-2S] sites is considered.     

P-hydrogen-substituted 1,3,2-diazaphospholenes: molecular hydrides

P-Hydrogen-substituted 1,3,2-diazaphospholenes 1 were prepared by an improved procedure from diazadienes and were characterized by spectroscopy and in one case by X-ray diffraction. A unique hydride-type reactivity of the P-H bonds was documented by extensive reactivity studies. Aldehydes and ketones were readily reduced to diazaphospholene derivatives of the corresponding alcohols, with alkyl-substituted ketones being converted at much lower rates than aldehydes or diaryl ketones. Reactions with the tetrachlorides of group 14 elements proceeded via hydride/chloride metathesis to give either partially chlorinated derivatives EH(n)Cl(4-n) (n = 0-3 for E = C, Si) or HCl and phosphenium salts 16c[ECl3] (for E = Ge, Sn) which were characterized by spectroscopic and X-ray diffraction studies. Tin dichloride was readily reduced to the element. Reactions of 1c with the P-chloro-diazaphospholene 3c and the salt 16c[OTf] allowed the first experimental detection of intermolecular exchange of a hydride, rather than a proton, between phosphine derivatives. Computational studies indicated that the hydride transfer between 1c and the cation 16c involves a transient H-bridged species with bonding properties similar to those of B2H7-. The preference for the formation of these bridged intermediates over P-P bonded phosphenium-phosphine adducts is attributed to the low electrophilicity of the diazaphospholenium cations and characterizes a novel reaction mode for phosphenium ions.     

Phase behavior and viscoelastic properties of entangled block copolymer gels

Triblock copolymers in midblock‐selective solvents can form physical gels. However, at low triblock contents (near the percolation threshold), the bridging of chains between micelles can lead to macrophase separation. Adding a styrene–isoprene diblock to a styrene–isoprene–styrene triblock copolymer in squalane can eliminate macrophase separation, yielding a wide range of stable, single‐phase gels with a disordered arrangement of micelles. The plateau modulus of these triblock gels scales with the 2.2 power of polymer content, indicating the importance of entanglements in dictating the modulus. Comparing gels made from the midblock‐saturated derivative of the same polymer [styrene‐(ethylene‐alt‐propylene)‐styrene] in squalane reveals that the modulus differences in the gels are a direct consequence of the difference in the entanglement molecular weight of the midblock homopolymer in bulk. Finally, the broad relaxation spectrum of these triblocks is well‐described by a recent theory for the dynamics of entangled star polymers, with the breadth of the relaxation spectrum dictated by the number of entanglements per midblock in the gel. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2183–2197, 2001     

Binding of β-lactam antibiotics to a bioinspired dizinc complex reminiscent of the active site of metallo-β-lactamases

Metallo-β-lactamases (mβls) cause bacterial resistance toward a broad spectrum of β-lactam antibiotics by catalyzing the hydrolytic cleavage of the four-membered β-lactam ring, thus inactivating the drug. Minutiae of the mechanism of these enzymes are still not well understood, and reports about binding studies of the substrates to the enzymes as well as to synthetic model systems are rare. Here we report a new pyrazolate-based bioinspired dizinc complex (1) reminiscent of the active site of binuclear mβls. Since 1 does not mediate hydrolytic degradation of β-lactams, the binding of a series of common β-lactam antibiotics (benzylpenicillin, cephalotin, 6-aminopenicillanic acid, ampicillin) as well as the inhibitor sulbactam and the simplest β-lactam, 2-azetidinone, to the dizinc core of 1 could now be studied in detail by NMR and IR spectroscopy as well as mass spectrometry. X-ray crystallographic information was obtained for 1 and its complexes with 2-azetidinone (2) and sulbactam (3); the latter represents the first structurally characterized dizinc complex with a bound β-lactam drug. While 2-azetidinone was found deprotonated and bridging in the clamp of the two zinc ions in 2, in 3 and all other cases the substrates preferentially bind via their carboxylate group within the bimetallic pocket. The relevance of this binding mode for mβls and consequences for the design of functional model systems are discussed.