Carbamoylation of B6 vitamins

The reaction of B₆ vitamins 1–3 with cyanate, in the presence of equivalent amounts of hydrochloric acid, yields different adducts according to the structure of the starting material. Regiospecific attack on the amino group or the phenolic hydroxy group was found for 2a,b and 3a,b , respectively. From the aldehydes 1a,b , the 2H-pyrido[3,4-e]-1,3-oxazin-2-ones 7a,b were obtained through an attack on both the phenolic and aldehyde group.     

Note on the atomic correlation energy

In the introductory section, we compare the total, kinetic, nuclear-electron, Coulomb, exchange, and correlation energies of ground-state atoms. From the analyses of the data, one can conclude that the Hartree-Fock (HF) model is notably good and might require only a small perturbation to become essentially an “accurate” model. For this reason and considering past literature, we present a semiempirical extension of the HF model. We start with a calibration of three independent models, each one with an effective Hamiltonian, which introduces a small perturbation on the kinetic, the nuclear-electron, or the Coulomb HF operators. The perturbations are expressed as very simple functions of products of orbital probability density. The three perturbations yield very equivalent results and the computed ground-state energies are reasonably near to the accurate nonrelativistic energies recently provided by E. Davidson and his collaborators for the 2–18 electron systems and the estimates by Clementi and his collaborators for the 19–54 electron systems. The first ionization potentials from He to Cs, the second ionization potentials from Li to Zn, and excitation energies for npⁿ, 3dⁿ, and 4s¹3dⁿ configurations are used as additional verification and validation. The above three effective Hamiltonians are then combined in order to redistribute the correlation energy correction in a way which exactly satisfies the virial theorem and maintains the HF energy ratios between kinetic, nuclear-electron, and electron-electron interaction energies; the resulting effective Hamiltonian, named “virial constrained,” yields good quality data comparable to those obtained from the three independent effective operators. Concerning excitation energies, these effective Hamiltonians yield values only in modest agreement with experimental data, even if definitively superior to HF computations. To further improve the computed excitation energies, we applied an empirical scaling in the vector coupling coefficient; this correction yields very reasonable excitations for all the configurations that we have considered. We conclude that the use of effective potentials to introduce small perturbations density-dependent onto the HF model constitutes a broad class of practical and reliable semiempirical solutions to atomic many-electron problems, can provide an alternative to popular proposals from density functional theory, and should prepare the ground for “generalized HF models.” © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 571–591, 1997     

Application of nanosized zeolites in methanol conversion processes: A short review

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Photoluminescence-Based Techniques for the Detection of Micro- and Nanoplastics

The growing numbers related to plastic pollution are impressive, with ca. 70 % of produced plastic (>350 tonnes/year) being indiscriminately wasted in the environment. The most dangerous forms of plastic pollution for biota and human health are micro- and nano-plastics (MNPs), which are ubiquitous and more bioavailable. Their elimination is extremely difficult, but the first challenge is their detection since existing protocols are unsatisfactory for microplastics and mostly absent for nanoplastics. After a discussion of the state of the art for MNPs detection, we specifically revise the techniques based on photoluminescence that represent very promising solutions for this problem. In this context, Nile Red staining is the most used strategy and we show here its pros and limitations, but we also discuss other more recent approaches, such as the use of fluorogenic probes based on perylene-bisimide and on fluorogenic hyaluronan nanogels, with the added values of biocompatibility and water solubility.     

Extremal Curves in Nilpotent Lie Groups

We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin maximum principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specific type. We also extend the results to the nonfree case.     

Lipschitz and path isometric embeddings of metric spaces

We prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curves in the manifold. The result is an extension of Nash C ¹ Embedding Theorem. For more general metric spaces the same result is false, e.g., for Finsler non-Riemannian manifolds. However, we also show that any metric space of finite Hausdorff dimension can be embedded in some Euclidean space via a Lipschitz map.