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This paper describes and develops a fast and accurate path following algorithm that computes the field of values boundary curve ∂F(A)$$ \partial F(A) $$ for every conceivable complex or real square matrix A$$ A $$. It relies on the matrix flow decomposition algorithm that finds a proper block‐diagonal flow representation for the associated hermitean matrix flow ℱA(t)=cos(t)H+sin(t)K$$ {\mathcal{F}}_A(t)=\cos (t)H+\sin (t)K $$ under unitary similarity if that is possible. Here ℱA(t)$$ {\mathcal{F}}_A(t) $$ is the 1‐parameter‐varying linear combination of the real and skew part matrices H=(A+A∗)/2$$ H=\left(A+{A}^{\ast}\right)/2 $$ and K=(A−A∗)/(2i)$$ K=\left(A-{A}^{\ast}\right)/(2i) $$ of A$$ A $$. For indecomposable matrix flows, ℱA(t)$$ {\mathcal{F}}_A(t) $$ has just one block and the ZNN based field of values algorithm works with ℱA(t)$$ {\mathcal{F}}_A(t) $$ directly. For decomposing flows ℱA(t)$$ {\mathcal{F}}_A(t) $$, the algorithm decomposes the given matrix A$$ A $$ unitarily into block‐diagonal form U∗AU=diag(Aj)$$ {U}^{\ast } AU=\operatorname{diag}\left({A}_j\right) $$ with j>1$$ j>1 $$ diagonal blocks Aj$$ {A}_j $$ whose individual sizes add up to the size of A$$ A $$. It then computes the field of values boundaries separately for each diagonal block Aj$$ {A}_j $$ using the path following ZNN eigenvalue method. The convex hull of all sub‐fields of values boundary points ∂F(Aj)$$ \partial F\left({A}_j\right) $$ finally determines the field of values boundary curve correctly for decomposing matrices A$$ A $$. The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices A$$ A $$ due to possible eigencurve crossings of ℱA(t)$$ {\mathcal{F}}_A(t) $$. Tests and numerical comparisons are included. Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and fast when compared with Johnson's Francis QR eigenvalue and Bendixson rectangle based method and compute global eigenanalyses of ℱA(tk)$$ {\mathcal{F}}_A\left({t}_k\right) $$ for large discrete sets of angles tk∈[0,2π]$$ {t}_k\in \left[0,2\pi \right] $$ more slowly. [ABSTRACT FROM AUTHOR]

For a linear matrix function f in X ∈ R m × n we consider inhomogeneous linear matrix equations f (X) = E for E ≠ 0 that have or do not have solutions. For such systems we compute optimal norm constrained solutions iteratively using the Conjugate Gradient and Lanczos’ methods in combination with the More–Sorensen optimizer. We build codes for ten linear matrix equations, of Sylvester, Lyapunov, Stein and structured types and their T-versions, that differ only in two five times repeated equation specific code lines. Numerical experiments with linear matrix equations are performed that illustrate universality and efficiency of our method for dense and small data matrices, as well as for sparse and certain structured input matrices. Specifically we show how to adapt our universal method for sparse inputs and for structured data such as encountered when fusing image data sets via a Sylvester equation algorithm to obtain an image of higher resolution. [ABSTRACT FROM AUTHOR]

For general complex or real 1-parameter matrix flows A(t)n, n and for static matrices A ∈ ℂ n , n alike, this paper considers ways to decompose matrix flows and single matrices globally via one constant matrix similarity Cn, n as A(t) = C− 1 ⋅ diag(A1(t),...,Aℓ(t)) ⋅ C or A = C− 1 ⋅diag(A1,...,Aℓ) ⋅ C with each diagonal block Ak(t) or Ak square and their number ℓ exceeding 1 if this is possible. The theory behind our proposed algorithm is elementary and uses the concept of invariant subspaces for the MATLAB eig computed 'eigenvectors' of one associated flow matrix B(ta) to find the coarsest simultaneous block structure for all flow matrices B(tb). The method works efficiently for all time-varying matrix flows A(t), be they real or complex, normal, with Jordan structures or repeated eigenvalues, differentiable, continuous, or discontinuous in t, and likewise for all fixed entry matrices A. Our intended aim is to discover unitarily diagonal-block decomposable flows as they originate in real-time from sensor given data for time-varying matrix problems that are unitarily invariant. Then, the complexities of their numerical treatments decrease by adopting 'divide and conquer' methods for their diagonal blocks. In the process, we discover and study k-normal fixed entry matrix classes that can be decomposed under unitary similarities into various k-dimensional block-diagonal forms. [ABSTRACT FROM AUTHOR]

We investigate the eigenvalue curves of 1-parameter Hermitian and general complex or real matrix flows A(t) in light of their geometry and the uniform decomposability of A(t') for all parameters t. The results by Hund and by von Neumann and Wigner in the 1920s for eigencurve crossings of "generic" Hermitian matrix flows A(t) = (A(t))* are clarified. A conjecture on extending these results to general nonnormal or non-Hermitian 1-parameter matrix flows is formulated and investigated. An algorithm to compute the block dimensions of uniformly decomposable Hermitian matrix flows is described and tested. The algorithm uses the Zhang neural network method to compute the time-varying matrix eigenvalue curves of A(t) for to ≤ t ≤ tf. Similar efforts for general complex matrix flows are described. This extension leads to many new and open problems. Specifically, we point to the difficult relationship between the geometry of eigencurves for general complex matrix flows A(t) and a general flow's decomposability into block-di agonal form via one fixed unitary or general matrix similarity for all parameters t. [ABSTRACT FROM AUTHOR]

In this paper, a new and different neural network, called Zhang Neural Network (ZNN) is appropriated from discrete time-varying matrix problems and applied to the angle parameter-varying matrix field of values (FoV) problem. This problem acts as a test bed for newly discovered convergent 1-step ahead finite difference formulas of high truncation error orders. The ZNN method that uses a look-ahead finite difference scheme of error order 6 gives us 15+ accurate digits of the FoV boundary points in record time when applied to hermitian matrix flows A (t). [ABSTRACT FROM AUTHOR]

This paper adapts look-ahead and backward finite difference formulas to compute future eigenvectors and eigenvalues of piecewise smooth time-varying symmetric or hermitean matrix flows A (t). It is based on the Zhang Neural Network (ZNN) model for time-varying problems and uses the associated error function E (t) = A (t) V (t) − V (t) D (t) or e i (t) = A (t) v i (t) − λ i (t) v i (t) with the Zhang design stipulation that E ˙ (t) = − η E (t) or e ˙ i (t) = − η e i (t) with η > 0 so that E (t) and e (t) decrease exponentially over time. This leads to a discrete-time differential equation of the form P (t k) z ˙ (t k) = q (t k) for the eigendata vector z (t k) of A (t k). Convergent look-ahead finite difference formulas of varying error orders then allow us to express z (t k + 1) in terms of earlier A and z data. Numerical tests, comparisons and open questions complete the paper. [ABSTRACT FROM AUTHOR]

Zhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer from low truncation error orders. This paper develops a constructive method to find convergent look-ahead finite difference schemes of higher truncation error orders. The method consists of seeding the free variables of a linear system comprised of Taylor expansion coefficients followed by a minimization algorithm for the maximal magnitude root of the formula's characteristic polynomial. This helps us find new convergent 1-step ahead finite difference formulas of any truncation error order. Once a polynomial has been found with roots inside the complex unit circle and no repeated roots on it, the associated look-ahead ZNN discretization formula is convergent and can be used for solving any discretized ZNN based model. Our method recreates and validates the few known convergent formulas, all of which have truncation error orders at most 4. It also creates new convergent 1-step ahead difference formulas with truncation error orders 5 through 8. [ABSTRACT FROM AUTHOR]

Ionization in the condensed phase and molecular clusters leads to a complicated chain of processes with coupled electron-nuclear dynamics. It is difficult to describe such dynamics with conventional nonadiabatic molecular dynamics schemes since the number of states swiftly increases as the molecular system grows. It is therefore attractive to use a direct electron and nuclear propagation such as the real-time time-dependent density functional theory (RT-TDDFT). Here we report a RT-TDDFT benchmark study on simulations of singly and doubly ionized states of a water monomer and dimer as a prototype for more complex processes in a condensed phase. We employed the RT-TDDFT based Ehrenfest molecular dynamics with a generalized gradient approximate (GGA) functional and compared it with wave-function-based surface hopping (SH) simulations. We found that the initial dynamics of a singly HOMO ionized water dimer is similar for both the RT-TDDFT/GGA and the SH simulations but leads to completely different reaction channels on a longer time scale. This failure is attributed to the self-interaction error in the GGA functionals and it can be avoided by using hybrid functionals with large fraction of exact exchange (represented here by the BHandHLYP functional). The simulations of doubly ionized states are reasonably described already at the GGA level. This suggests that the RT-TDDFT/GGA method could describe processes following the autoionization processes such as Auger emission, while its applicability to more complex processes such as intermolecular Coulombic decay remains limited. [ABSTRACT FROM AUTHOR]

A Correction to this paper has been published: https://doi.org/10.1007/s11075-021-01216-4 [ABSTRACT FROM AUTHOR]

Over any field F every square matrix A can be factored into the product of two symmetric matrices as A = S 1 ⋅ S 2 with S i = S i T ∈ F n , n and either factor can be chosen nonsingular, as was discovered by Frobenius in 1910. Frobenius' symmetric matrix factorization has been lying almost dormant for a century. The first successful method for computing matrix symmetrizers, i.e., symmetric matrices S such that SA is symmetric, was inspired by an iterative linear systems algorithm of Huang and Nong (2010) in 2013 [29,30] . The resulting iterative algorithm has solved this computational problem over R and C , but at high computational cost. This paper develops and tests another linear equations solver, as well as eigen- and principal vector or Schur Normal Form based algorithms for solving the matrix symmetrizer problem numerically. Four new eigendata based algorithms use, respectively, SVD based principal vector chain constructions, Gram–Schmidt orthogonalization techniques, the Arnoldi method, or the Schur Normal Form of A in their formulations. They are helped by Datta's 1973 method that symmetrizes unreduced Hessenberg matrices directly. The eigendata based methods work well and quickly for generic matrices A and create well conditioned matrix symmetrizers through eigenvector dyad accumulation. But all of the eigen based methods have differing deficiencies with matrices A that have ill-conditioned or complicated eigen structures with nontrivial Jordan normal forms. Our symmetrizer studies for matrices with ill-conditioned eigensystems lead to two open problems of matrix optimization. [ABSTRACT FROM AUTHOR]

Alkali metals can react explosively with water and it is textbook knowledge that this vigorous behaviour results from heat release, steam formation and ignition of the hydrogen gas that is produced. Here we suggest that the initial process enabling the alkali metal explosion in water is, however, of a completely different nature. High-speed camera imaging of liquid drops of a sodium/potassium alloy in water reveals submillisecond formation of metal spikes that protrude from the surface of the drop. Molecular dynamics simulations demonstrate that on immersion in water there is an almost immediate release of electrons from the metal surface. The system thus quickly reaches the Rayleigh instability limit, which leads to a 'coulomb explosion' of the alkali metal drop. Consequently, a new metal surface in contact with water is formed, which explains why the reaction does not become self-quenched by its products, but can rather lead to explosive behaviour. [ABSTRACT FROM AUTHOR]

The optical spectrum of the hydrated(aqueous) electron, eaq–, is theprimary observable by means of which this species is detected, monitored,and studied. In theoretical calculations, this spectrum has most oftenbeen simulated using one-electron models. Here, we present ab initiosimulations of that spectrum in both bulk water and, for the firsttime, at the water/vapor interface, using density functional theoryand its time-dependent variant. Our results indicate that this approachprovides a reliable description, and quantitative agreement with theexperimental spectrum for the bulk species is obtained using a “tuned”long-range corrected functional. The spectrum of the interfacial electronis found to be very similar to the bulk spectrum. [ABSTRACT FROM AUTHOR]

It is generally assumed that the hydrated electron occupies a quasi-spherical cavity surrounded by only a few water molecules in its equilibrated state. However, in the very moment of its generation, before water has had time to respond to the extra charge, it is expected to be significantly larger in size. According to a particle-in-a-box picture, the frequency of its absorption spectrum is a sensitive measure of the initial size of the electronic wavefunction. Here, using transient terahertz spectroscopy, we show that the excess electron initially absorbs in the far-infrared at a frequency for which accompanying ab initio molecular dynamics simulations estimate an initial delocalization length of ≈40 Å. The electron subsequently shrinks due to solvation and thereby leaves the terahertz observation window very quickly, within ≈200 fs. [ABSTRACT FROM AUTHOR]

We revisit an earlier idea of Marcus and Pesce from 1987 for generating fields of values ofbymatricesvia 2 by 2 matrix compressions and their easily constructed elliptical field of values. This approach is used to reduce the cost of finding the FOV boundary curve of a matrixand makes it more accurate at the same time. The new algorithm succeeds by using fewer eigenanalyses and constructing 2 by 2 matrix compression ellipses offor approximatinginstead of only eigenanalyses. An application to verify a counterexample to theZemanek Conjecture for companion matrices of monic polynomials and their normalized derivatives inand, respectively, in dimension 4 is given. [ABSTRACT FROM PUBLISHER]

By a theorem of Frobenius (F.G. Frobenius,Über die mit einer Matrix vertauschbaren Matrizen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (1910), pp. 3–15 (also in Gesammelte Abhandlungen, Band 3, Springer 1968. pp. 415–427)), every matrixAn,nover any field 𝔽 is the product of two symmetric ones. Using the algorithm of Huang and Nong (J. Huang and L. Nong,An iterative algorithm for solving finite-dimensional linear operator equations T(x) = f with applications, Linear Algebra Appl. 432 (2010), pp. 1176–1188) for linear systems, we develop an algorithm to compute a symmetric matrixS = ST ∈ 𝔽n,nfor whichSAis symmetric for any given square matrixA ∈ 𝔽n,nwhere 𝔽 = ℝ or ℂ. The algorithm is implemented and tested in MATLAB. [ABSTRACT FROM AUTHOR]

Abstract: We use methods of geometric computing combined with hermitean matrix eigenvalue/eigenvector evaluations to find the generalized Crawford number of a pair of hermitean matrices and quickly and to high precision. The classical Crawford number is defined as the minimal distance from zero in to the field of values of the associated complex matrix if zero lies outside the field of values of A. We describe, test, and compare a geometry based MATLAB code for finding for the generalized Crawford number that measures the smallest distance of zero from the boundary of the field of values of A even if zero lies inside. [Copyright &y& Elsevier]

Fifty years after the invention of the QR algorithm by John Francis and Vera Kublanovskaya we reconstruct the ideas and the influences that led to its genesis from the originators’ own recollections and their sources and give an account of some of its subsequent developments. [ABSTRACT FROM PUBLISHER]

Abstract: This overview covers the development in synthesis and reactivity of tin(IV) and tin(II) silicon derivatives made during the last decade. Attention is directed towards compounds with at least more than one silicon–tin bond, i.e. compounds with Siph name="sbnd" />Si, Snph name="sbnd" />Sn, Snph name="sbnd" />Si or Siph name="sbnd" />Sn sequences in the molecule. Some spectroscopic and structural features will be discussed in addition to their preparation and reactivity. [Copyright &y& Elsevier]

Focuses on the author's response to comments made by mathematician Frank Uhlig on how to teach a first course on linear algebra published in the 50th volume of the journal "Educational Studies in Mathematics."

We develop the philosophical and practical background for teaching an elementary Linear Algebra course from the requirements that are particular to the subject. It mixes the inner workings and logic of Linear Algebra and matrices with concepts, hands-on computational schemes, and applications for a satisfying comprehensive teaching and learning experience. [Copyright &y& Elsevier]

Examines the false mathematical statement familiar to teachers and students. Ways to interpret complex numbers; Use of standard operations for matrix addition and multiplication matrices.

We describe how elementary Linear Algebra can be taught successfully while introducing students to the concept and practice of `mathematical proof'. This is done badly with a sophisticated Definition–Lemma–Proof–Theorem–Proof–Corollary (DLPTPC) approach; badly – since students in elementary Linear Algebra courses have very little experience with proofs and mathematical rigor. Instead, the subjects and concepts of Linear Algebra can be introduced in an exploratory and fundamentally reasoned way. One seemingly successful way to do this is to explore the concept of solvability of linear systems first via the row echelon form (REF). Solvability questions lead to row and column criteria for a REF that can be used repeatedly to: compute subspaces, settle linear (in)dependence, find inverses, perform basis change, compute determinants, analyze eigensystems etc. If these subjects are explained heuristically from the first principles of linear transformations, linear equations, and the REF, students experience the power of a concept–built approach and reap the benefit of deep math understanding. Moreover, early `salient point' proofs lead to an intuitive understanding of `math proof'. Once the basic concept of `proof' is ingrained in students, more abstract proofs, even DLPTPC style expositions, on normal matrices, the SVD etc. become accessible and understandable to sophomore students. With the help of this gentle early approach, the concept and construct of a `math proof' becomes firmly embedded in the students' minds and helps with future math courses and general scientific reasoning. [ABSTRACT FROM AUTHOR]

Recent experimental results indicate that the stability of non‐Watson‐Crick DNA i‐motif structures can be influenced by the presence of various metal cations. Whereas Au+, Cu+, and Ag+ are stabilizing agents, alkali metal ions like Na+ or Li+ are known to destabilize the i‐motif. In terms of reduced ion‐cytosine complexes, we rationalize the experimental observations with the help of standard and conceptual density functional theory (DFT) calculations. Our results highlight the importance of coordinating electrostatic bonds with partially covalent character for the stability of the ion‐cytosine complex. The occurrence of these bonds can be mainly attributed to charge transfer processes between two cytosines and the transition metal ions, which can be either explained by frontier molecular orbital theory in combination with a bond critical point analysis, or by the concept of chemical reactivity indices within a conceptual DFT approach. The results of our calculations establish a consistent theoretical framework to understand the experimentally observed behavior, and are also important in order to achieve more detailed insights into nucleobase pairing mechanisms in general. [ABSTRACT FROM AUTHOR]

Investigation of the solubility behavior of para‐substituted (H, Me, t‐Bu, n‐Bu) meso‐tetraarylporphyrins as well as meso‐tetraalkylporphyrins (Me, n‐Pr, n‐Bu) were performed. An increase of solubility in chloroform and benzene is detected according to the higher functionality in para position of the phenyl ring for meso‐tetraarylporphyrins or in meso position on meso‐tetraalkylporphyrins. Furthermore, the series of bis(chlorido)tin(IV) meso‐tetraarylporphyrin and bis(chlorido)tin(IV) meso‐tetraalkylporphyrin was investigated via UV/Vis spectroscopy, 119Sn‐NMR and single crystal X‐ray diffraction. [ABSTRACT FROM AUTHOR]

Finite difference schemes have been widely studied because of their fundamental role in numerical analysis. However, most finite difference formulas in the literature are not suitable for discrete time-varying problems because of intrinsic limitations and their relatively low precision. In this paper, a high-precision 1-step-ahead finite difference formula is developed. This 5-instant finite difference (5-IFD) formula is used to approximate and discretize first-order derivatives, and it helps us to compute discrete time-varying generalized matrix inverses. Furthermore, as special cases of generalized matrix inverses, time-varying matrix inversion, and scalar reciprocals are generally deemed as independent problems and studied separately, which are solved unitedly in this paper. The precision of the 5-IFD formula and the convergence behavior of the corresponding discrete-time models are derived theoretically and shown in numerical experiments. Conventional useful formulas, such as the Euler forward finite difference (EFFD) formula and the 4-instant finite difference (4-IFD) formula are also used for comparisons and to show the superiority of the 5-IFD formula. [ABSTRACT FROM AUTHOR]

In the past, the electrochemical properties of organosilicon compounds were investigated for both fundamental reasons and synthesis purposes. Little is, however, known about the electrochemical behaviour of hydrogen-bearing arylsilanes. Here, we throw light on the electrochemical properties of 11 arylsilanes compounds, 2 of them synthesized for the first time. The oxidation potentials are found to depend on both the nature and number of the aryl groups. Based on these findings it was possible to establish some variation trends that match the expected structure–property correlations. Furthermore, we present first insights into the electrochemical reaction kinetics behind and identify several soluble electrochemical oxidation products. • Electrochemical properties of single, double and triple substituted arylsilanes • Thermodynamics and kinetics of anodic oxidation • The influence of the aryl residue and the oxidation potential variation trends [ABSTRACT FROM AUTHOR]

Abstract A new method was developed to achieve highly selective monochlorination of α,ω-dihydridosiloxanes, ((H)Me 2 SiO-(SiMe 2 O) n -SiMe 2 (H), n = 0–2; (H)R 2 Si O-SiR 2 (H); R = Me, i Pr, Ph; 3,5-dihydridooctamethyltetrasiloxane, Me 3 SiO-(Si(H)MeO) 2 SiMe 3) with trichloroisocyanuric acid (TCCA). The dependence of the selectivity of the monochlorination on the siloxane chain length is also discussed. Graphical abstract Image 1 Highlights • High yield selective chlorination of oligomeric siloxanes containing more than one Si-H unit. • Selectivity is depending on the chain length between the Si-H unit. • Selectivity is depending on the organic substituents at the silicon atoms. • Easy to use, upscaling possible, TCCA is inexpensive and non-toxic. • Workup and chlorination procedures are depending on the desired target compounds. [ABSTRACT FROM AUTHOR]

Amphiphilic copolymer self-assembly is a straightforward approach to obtain responsive micelles, nanoparticles, and vesicles that are particularly attractive for biomedicine, i.e., for the delivery of functional molecules. Here, amphiphilic copolymers of hydrophobic polysiloxane methacrylate and hydrophilic oligo (ethylene glycol) methyl ether methacrylate with different lengths of oxyethylenic side chains were synthesized via controlled RAFT radical polymerization and characterized both thermally and in solution. In particular, the thermoresponsive and self-assembling behavior of the water-soluble copolymers in water was investigated via complementary techniques such as light transmittance, dynamic light scattering (DLS), and small-angle X-ray scattering (SAXS) measurements. All the copolymers synthesized were thermoresponsive, displaying a cloud point temperature (Tcp) strongly dependent on macromolecular parameters such as the length of the oligo(ethylene glycol) side chains and the content of the SiMA counits, as well as the concentration of the copolymer in water, which is consistent with a lower critical solution temperature (LCST)-type behavior. SAXS analysis revealed that the copolymers formed nanostructures in water below Tcp, whose dimension and shape depended on the content of the hydrophobic components in the copolymer. The hydrodynamic diameter (Dh) determined by DLS increased with the amount of SiMA and the associated morphology at higher SiMA contents was found to be pearl-necklace-micelle-like, composed of connected hydrophobic cores. These novel amphiphilic copolymers were able to modulate thermoresponsiveness in water in a wide range of temperatures, including the physiological temperature, as well as the dimension and shape of their nanostructured assemblies, simply by varying their chemical composition and the length of the hydrophilic side chains. [ABSTRACT FROM AUTHOR]

Nonlinear optimization is widely important for science and engineering. Most research in optimization has dealt with static nonlinear optimization while little has been done on time-varying nonlinear optimization problems. These are generally more complicated and demanding. We study time-varying nonlinear optimizations with time-varying linear equality constraints and adapt Z-type neural-dynamics (ZTND) for solving such problems. Using a Lagrange multipliers approach we construct a continuous ZTND model for such time-varying optimizations. A new four-instant finite difference (FIFD) formula is proposed that helps us discretize the continuous ZTND model with high accuracy. We propose the FDZTND-K and FDZTND-U discrete models and compare their quality and the advantage of the FIFD formula with two standard Euler-discretization ZTND models, called EDZTND-K and EDZTND-U that achieve lower accuracy. Theoretical convergence of our continuous and discrete models is proved and our methods are tested in numerical experiments. For a real world, we apply the FDZTND-U model to robot motion planning and show its feasibility in practice. [ABSTRACT FROM AUTHOR]

Amphiphilic fluorinated copolymers PEGMAx‐co‐FAy and TEGMAx‐co‐FAy are prepared by activators regenerated by electron transfer atom transfer radical polymerization (ARGET‐ATRP). All polymers present a reversible thermoresponsive lower critical solution temperature‐type behavior, and a cloud point temperature (Tc) in the range of 30–60 °C strictly dependent on the length of the oxyethylene side chain, the content of the hydrophobic counits, and the concentration of the solution. Combined small angle X‐ray scattering (SAXS) and dynamic light scattering measurements are used to study the self‐assembly behavior in water, organic solvents (tetrahydrofuran [THF] and dimethylformamide [DMF]), and a fluorinated solvent (hexafluorobenzene [HFB]). SAXS confirms the formation of compact‐globular single‐chain self‐folded unimer micelles in water below Tc, which generally presents small hydrodynamic diameters (Dh ≤ 8 nm) as a result of the folding of the hydrophobic perfluorohexylethyl acrylate counits. The copolymers are also able to form reverse unimer micelle in HFB. The copolymers are not able to self‐assemble in unimer micelles in THF or DMF solutions, in which they adopt conventional random coil conformations. [ABSTRACT FROM AUTHOR]

The reaction of phenylphosphine (PhPH2) with ketones showed conversion into a 5-membered heterocyclic ring of the type P2SOC if 2–2.5 equivalents of sulfur (S8) were used. X-Ray data and31P,13C,1H NMR spectra proved the formation of the (Z) diastereomer of 1,3,2,4-oxathiadiphospholane1((PhPS)2SOCMe2) if acetone is used. Mechanistic studies displayed that small changes in the reaction pathway lead toward the formation and characterization of intermediates including 1,3,2,4,5-dithiatriphospholane, 2,4,5-triphenyl-2-sulfide (PhP)3S3and 1,3,2,4-oxathiadiphospholane, and 5,5-dimethyl-2,4-diphenyl-2-sulfide ((PhPS)(PhP)SOCMe2), which undergo reactions with acetone, subsequently yielding the abovementioned heterocyclic ring. [ABSTRACT FROM PUBLISHER]

Liquid-phase exfoliation (LPE) is a widely used and promising method for the production of 2D nanomaterials because it can be scaled up relatively easily. Nevertheless, the yields achieved by this process are still low, ranging between 2% and 5%, which makes the large-scale production of these materials difficult. In this report, we investigate the cause of these low yields by examining the sonication-assisted LPE of graphene, boron nitride nanosheets (BNNSs), and molybdenum disulfide nanosheets (MoS2 NS). Our results show that the low yields are caused by an equilibrium that is formed between the exfoliated nanosheets and the flocculated ones during the sonication process. This study provides an understanding of this behaviour, which prevents further exfoliation of nanosheets. By avoiding this equilibrium, we were able to increase the total yields of graphene, BNNSs, and MoS2 NS up to 14%, 44%, and 29%, respectively. Here, we demonstrate a modified LPE process that leads to the high-yield production of 2D nanomaterials. [ABSTRACT FROM AUTHOR]

The reaction of dialkyltinhydrides with dialkylzinc results in a tin metal bond formation. Crystal structures of 1,1,1,2,3,3,3-hepta-phenyl-2-(ethylzincio)tristannane *TMEDA 1, 1,1,2,2,3,3,4,4-octaphenyl-1,4-(ethylzincio)tetrastannane*2TMEDA 2, and triphenyl(phenylzincio)stannane*TMEDA 3 could be obtained. Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file. GRAPHICAL ABSTRACT[image omitted] [ABSTRACT FROM AUTHOR]

The coordination chemistry of the bis(diphenylmethytsilyt)amine ligand, HN(SiMePh2)2, with the heavy alkali metals potassium and rubidium has been investigated to Study its effect on the structure of the resulting compounds. The compounds exhibit extensive intra- and intermolecular M—π interactions, creating 1-D coordination polymers, [K(N(SiMePh2)2)]∞ (1) and IRb(N(SiMePh2)2)]∞ (3). This motif is maintained in the presence of tetrahydroturan (THF), as seen in [K(N(SiMePh2)2)thf]∞ (2). In contrast, use of the tridenlate PMDTA allows isolation of a monomeitc species, K(pmdta)N(SiMePh2)2 (4), which exhibits both agostic and M—π interactions. The incorporation of macrocyclic 18-crown-6, results in the formation of a rare non-metal bound amido species, ([K(18-crown-6)N-(SiMePh2)2])∞ (5), stabilized by M—π interactions from adjacent [N(SiMePh2)2]- ligands propagating 1-D coordination polymers. [ABSTRACT FROM AUTHOR]

It is known that for every real square matrix A there exists a nonsingular real symmetric matrix S such thatSA=A′S,where A′ denotes the transpose of A.Using the notion of an M-matrix we derive a criterion for A to satisfy the above equality with a diagonal S of signature k. Such a matrix A will be called Dk-symmetrizable and the paper presents some results on this concept. In particular we show that a Dk-symmetrizable matrix shares many properties with a real symmetric matrix and that any real matrix A, up to an orthogonal similarity, is Dk-symmetrizable for some k. [Copyright &y& Elsevier]

[Display omitted] A series of novel arylgermanium hydrides Ar n GeH 4 –n (n = 1–3) and diaryl(chloro)germanium hydrides Ar 2 Ge(Cl)H were synthesized and characterized. Systematic preparation and purification were achieved via the lithium chloride–triflic acid and the optimized Grignard route. Arylgermanium hydrides Ar n GeH 4– n (Ar = 2,5-Me 2 C 6 H 3 , n = 1–3) were characterized by 1H and 73Ge NMR spectroscopy and single crystal X-ray diffractometry. [ABSTRACT FROM AUTHOR]

Methods for the selective chlorination of organogermylhydrides are given by the selective functionalization of organogermylhydrides of types R3GeH, R2GeH2 and RGeH3 (R = alkyl, aryl). The use of trichloroisocyanuric acid (TCCA) allows the direct conversion of Ge‐H functions into their monochlorinated derivatives R2Ge(Cl)H and RGe(Cl)H2. [ABSTRACT FROM AUTHOR]

• A synthetic strategy overview for 3-aminopropyl-phenyl germanes is displayed in this work. • Novel salt metathesis and hydrogermylation routes were explored for the formation of 3-aminopropyl-phenyl germanes. • New promising bifunctional 3-aminopropyl-diphenyl germane building blocks are synthesized. Novel synthetic pathways for different 3-aminopropyl germanes are shown in this work. For this purpose, in Synthetic Route A, a corresponding germanium compound was metalated and, via salt metathesis, the corresponding protected 3-aminopropyl germane was formed. After the deprotection, the corresponding amino hydrochlorides were isolated. After a neutralization reaction, the 3-aminopropyl germanes were formed. With 3-aminopropyl-diphenyl-germanium hydride, (H 2 N(CH 2) 3)Ph 2 GeH, a new bifunctional building block was isolated. To form the corresponding 3-aminopropyl‑chloro germanes ((CyHN(CH 2) 3)Ph 2 GeCl and (H 2 N(CH 2) 3)Ph 2 GeCl), diphenyl‑chloro germane was used in a hydrogermylation to form the corresponding amines (Synthetic Route B). All compounds were characterized by state-of-the-art techniques, including single crystal X-ray diffraction for selected compounds. Diphenyl germanes are reacted in a hydrogermylation or salt metathesis with the corresponding substituent. After various steps the corresponding 3-aminopropyl germanes were isolated. These compounds are new promising building blocks in organogermanium chemistry. Moreover, the amino hydrochlorides are crystalized and studied by single crystal X-ray analysis. R = H or Cyclohexyl; RPG = Protection Group (CH- t -Bu) [Display omitted] [ABSTRACT FROM AUTHOR]

The rational control of the electronic and optical properties of small functionalized diamond-like molecules, the diamondoids, is the focus of this work. Specifically, we investigate the single- and double- functionalization of the lower diamondoids, adamantane, diamantane, and triamantane with -NH2 and -SH groups and extend the study to N-heterocyclic carbene (NHC) functionalization. On the basis of electronic structure calculations, we predict a significant change in the optical properties of these functionalized diamondoids. Our computations reveal that -NH2 functionalized diamondoids show UV photoluminescence similar to ideal diamondoids while -SH substituted diamondoids hinder the UV photoluminescence due to the labile nature of the S-H bond in the first excited state. This study also unveils that the UV photoluminescence nature of -NH2 diamondoids is quenched upon additional functionalization with the -SH group. The double-functionalized derivative can, thus, serve as a sensitive probe for biomolecule binding and sensing environmental changes. The preserved intrinsic properties of the NHC and the ideal diamondoid in NHC-functionalized-diamondoids suggests its utilization in diamondoid-based self-assembled monolayers (SAM), whose UV-photoluminescent signal would be determined entirely by the functionalized diamondoids. Our study aims to pave the path for tuning the properties of diamondoids through a selective choice of the type and number of functional groups. This will aid the realization of optoelectronic devices involving, for example, large-area SAM layers or diamondoid-functionalized electrodes. [ABSTRACT FROM AUTHOR]

A novel synthetic pathway involving the desilylation of a tin trimethylsilyl species (Ph2Sn(SiMe3)2) towards nonprotected di(3-aminopropyl)tin dichloride ((H2N(CH2)3)2SnCl2) is described. Di(3-aminopropyl)tin dichloride is then converted to the respective dicarboxylates species (H2N(CH2)3)2Sn(OCOR)2 containing carboxylic acids of different lengths (R = -CH3, -(CH2)10CH3). Depending on the nature of R, discrete packing effects are observed in the solid state of di(3-aminopropyl)tin dicarboxylate derivatives. All the synthesized substances were characterized by 1H, 13C, and 119Sn nuclear magnetic resonance data and also single crystal X-ray analysis. These compounds are a promising class of substances for biological, pharmaceutical, and technical applications. [ABSTRACT FROM AUTHOR]

A series of novel and previously published tetraarylgermanes aryl 4 Ge (aryl = m -tolyl, 3,4-xylyl, 3,5-xylyl, 2-naphthyl) and triarylgermanium halides aryl 3 GeX (aryl = o -tolyl, 2,4-xylyl, 2,5-xylyl, 2,6-xylyl, 1-naphthyl, 2,4,6-mesityl, X = Cl, Br) were synthesized and characterized. All solids were investigated using single crystal X-ray diffractometry in order to elucidate the molecular structures. Effects of the substitution pattern of the aryl residue employed have been studied in terms of the impact on the product formation. [ABSTRACT FROM AUTHOR]

A series of bis(phenylacetylido)(porphyrinato) E(IV) (E = Si, Ge, Sn) derivatives were obtained by reacting lithium phenylacetylide with the corresponding bis(chlorido)(porphyrinato) E(IV) precursors. Crystal structure determinations demonstrated that the transcoordinated acetylide ligands deviate from their expected ideal geometry. Density functional theory calculations and comparison of the packing of the molecules among the homologous series of Si(IV), Ge(IV) and Sn(IV) revealed causes for the deviation from the simple valence shell electron pair repulsion model. Fluorescence and phosphorescence of these organometallic group 14 derivatives were studied and the results are compared to the literature-known properties of the related bis(chlorido) (porphyrinato) E(IV) compounds (E = Si, Ge, Sn). The first crystal structure of a porphyrinato Ge(IV) compound with σ-bonded acetylide ligands is reported. [ABSTRACT FROM AUTHOR]

The first hybrid crown ether with two adjacent disilane fragments was synthesized through reaction of O(Si2Me4Cl)2 (3) with O(C2H4OH)2. By means of DFT calculations, the complexation ability of 1,2,4,5-tetrasila[12]crown-4 (7) towards Li+ was determined to be considerably higher compared to [12]crown-4. [ABSTRACT FROM AUTHOR]

The series of oligogermanes Pri3Ge(GePh2)nGePri3 (n = 0, 2; n = 1, 3; n = 2, 4; n = 3, 5) were prepared by the hydrogermolysis reaction. All four species were characterized by NMR (¹H and 13C) and UV/visible spectroscopy as well by cyclic voltammetry and differential pulse voltammetry. The oligogermanes exhibited a successive red shift in their absorbance maxima as the length of the Ge-Ge chain was increased, and these molecules also became easier to oxidize as the chain length was increased. The X-ray crystal structures of 4 and 5 as well as the trigermane HPh2GeGePh2GePh2H (6) were determined. The pentagermane 5 was shown to be dichroic in the solid state due to the packing of the individual molecules in a columnar fashion in the crystal. Pentagermane 5 is also luminescent in solution, exhibiting an emission maximum at 380 nm. The physical properties of 5, like the hexagermane Pri3Ge(GePh)4GePri3, mimic the properties of the larger polygermane systems. [ABSTRACT FROM AUTHOR]

A series of novel and previously published silicon dihydrides, R2SiH2(R = benzyl, fluorenyl,p-tolyl,p-n-butyl,p-biphenyl,m-tolyl,o-tolyl, 2,4-xylyl, 2,6-xylyl,p-biphenyl, 1-naphthyl, 9-anthracenyl), were synthesized and characterized using1H,13C, and29Si NMR spectroscopy. Effects of substituent bulk on29Si NMR shifts are compared between reported silicon dihydrides species and novel dihydrides herein. In addition, single crystal X-ray diffraction was employed to elucidate the molecular structure of all solid silicon dihydrides and the at room temperature liquid p-tolyl2SiH2. These compounds display non-covalent intermolecular interactions in the form of edge to face, π−π stacking, and CH3···π interactions. The dependency of substituent type on the nature of interactions present will be highlighted and discussed. [ABSTRACT FROM AUTHOR]

Microorganisms accumulate molar concentrations of compatible solutes like ectoine to prevent proteins from denaturation. Direct structural or spectroscopic information on the mechanism and about the hydration shell around ectoine are scarce. We combined surface plasmon resonance (SPR), confocal Raman spectroscopy, molecular dynamics simulations, and density functional theory (DFT) calculations to study the local hydration shell around ectoine and its influence on the binding of a gene-5-protein (G5P) to a single-stranded DNA (dT25). Due to the very high hygroscopicity of ectoine, it was possible to analyze the highly stable hydration shell by confocal Raman spectroscopy. Corresponding molecular dynamics simulation results revealed a significant change of the water dielectric constant in the presence of a high molar ectoine concentration as compared to pure water. The SPR data showed that the amount of protein bound to DNA decreases in the presence of ectoine, and hence, the protein-DNA dissociation constant increases in a concentration-dependent manner. Concomitantly, the Raman spectra in terms of the amide I region revealed large changes in the protein secondary structure. Our results indicate that ectoine strongly affects the molecular recognition between the protein and the oligonucleotide, which has important consequences for osmotic regulation mechanisms. [ABSTRACT FROM AUTHOR]

A series of novel and previously published silicon dichlorides, R2SiCl2(R = benzyl, fluorenyl, p-tolyl p-n-butyl, p-biphenyl, m-tolyl, o-tolyl, 2,4-xylyl, 2,6-xylyl, p-biphenyl, 1-naphthyl, 9-anthracenyl), were synthesized and characterized using1H-,13C- and29Si NMR spectroscopy. Effects of substituent bulk on both experimental and calculated29Si NMR shifts are compared between reported silicon dichlorides species and novel dichlorides herein. In addition, single crystal X-ray diffraction was employed to elucidate the molecular structure of all solid diorgano silicon dichlorides. These compounds display non-covalent intermolecular interactions in the form of edge to face, π–π stacking, and CH3···π interactions. Dependency of substituent type on the nature of interactions present will be highlighted and discussed. [ABSTRACT FROM PUBLISHER]