On Rakhmanov's theorem for Jacobi matrices

We prove Rakhmanov's theorem for Jacobi matrices without the additional assumption that the number of bound states is finite. This result solves one of Nevai's open problems.

     

DFT-assisted design and evaluation of bifunctional copper(I) catalysts for the direct intermolecular addition of aldehydes and ketones to alkynes

Bifunctional catalysts containing discrete metal pi-acid and amine sites were designed and investigated for the direct intermolecular addition of aldehydes and ketones to unactivated alkynes. Copper(I)-based catalysts were prioritized based on intramolecular (Conia-ene type) reactions, and complexes were designed with tridentate ligands and potentially hemilabile heterocyclic spacers. The structures of the designed catalysts were computed using density functional theory (DFT), and the relative energies of putative catalytic intermediates were estimated and used to prioritize catalyst designs. Novel bifunctional precatalysts containing a thiazole spacer were synthesized via a 9-step sequence and combined with transition metals before screening for the direct addition of aldehydes and ketones to several internal and terminal alkynes. Despite the lack of desired intermolecular reactions, DFT calculations of putative catalyst intermediates appears to be a promising strategy for the design and prioritization of bifunctional catalysts for CC bond formation.     

Synthesis of 3-fluoro-3-methyl-3-silatetrahydropyran and its conformational preferences in gas and solution by GED,NMR and theoretical calculations

The 3,3-disubstitued 3-silaheterocyclohexane with an electronegative substituent at silicon, 3-fluoro-3-methyl-3-silatetrahydropyran 1, was synthesized, and its molecular structure and conformational properties studied by gas-phase electron diffraction (GED) and low temperature ¹³C and ¹⁹F NMR spectroscopy. Quantum-chemical calculations were carried out both for the isolated species and H-complexes in gas and in polar medium. The predominance of the 1-F_eqMe_ax conformer (1-F_eq:1-F_ax ratio of 65:35, ΔG°?=?0.37?kcal/mol) determined from GED is close to the theoretically estimated conformational equilibrium, especially at the DFT level. In solution, low temperature NMR spectroscopy showed no decoalescence of the signals in ¹³C (down to 95?K) and ¹⁹F NMR spectra (down to 123?K). However, the calculated ¹⁹F chemical shift of ?173.6?ppm for the 1-F_eqMe_ax conformer practically coincides with the experimentally observed value (?173 to ?175?ppm) as distinct from that for the 1-F_axMe_eq conformer (?188.8?ppm), suggesting compound 1 to be anancomeric in solution, in compliance with its theoretical and experimental preference in the gas phase.     

The charge-carrier mobility in disordered organic materials: the long-range one-dimensional diffusion with the memory effect

The transport of charge carriers in disordered organic materials is considered based on the techniques of generalized Langevin equation. We simulate the one-dimensional diffusion of a charge in the ensemble of molecular chains interacting with the acoustic phonon subsystem of bulk environment. The random local charge transitions between chain links are mutually correlated. The full computation of the zero-field charge mobility for the N, N-di(1-naphthyl)-N, N-diphenyl-(1,1-biphenyl)-4,4-diamine (\(\alpha \)-NPD) is performed as an illustration. Several models for the probabilities of local transitions are tested. The individual local diffusion constants are randomly varied along a molecular chain within several orders of magnitude. The stationary diffusion regime establishes for every chain the temperature-dependent partial charge mobility as a frequency-dependent complex-valued response function. It is averaged over the chain ensemble. The computational scheme is simple and efficient. The importance of the memory effect depends on specific properties of a given material. This dependence in terms of the system parameters is discussed.     

Synthesis of 3,5-dimethyl-1-boraadamantane and its transformation into 3,5-dimethyl-1-azaadamantane

The first synthesis of 3,5-dimethyl-1-boraadamantane from its easily available tetrahydrofuran adduct comprised sequential treatment with BuLi, AcCl, (Cy₂BH)₂ and heating. The compound was converted into its electronic ‘antagonist’, namely, 3,5-dimethyl-1-azaadamantane.

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DFT study of small aluminum and boron hydrides: isomeric composition and physical properties

The structure, energetics, and physical properties, including rotational constants, characteristic vibrational temperatures, dipole moment, static polarizability, HOMO-LUMO gap, formation enthalpy and collision diameter of different isomeric forms of atomic Al _n H _m and B _n H _m clusters with n = 1..4 and all feasible m numbers are studied within the density functional theory framework. The search of isomer structures has been accomplished using multistep hierarchical algorithm. Temperature dependences of thermodynamic functions (enthalpy, entropy and specific heat capacity) have been calculated both for the individual isomers and for the ensemble of isomers with equilibrium composition for each class of clusters, taking into account the anharmonicity of cluster vibrations and the contribution of excited electronic states. The prospects of the application of small atomic Al _n H _m and B _n H _m clusters as the components of energetic and hydrogen storage materials are also discussed.     

Regioselective Friedel–Crafts deacylations of polycyclic aromatic ketones in the pyrene series

1,3,6,8-tetrabenzoylpyrene (1,3,6,8-Bz ₄ PY) and 1,3,6-tribenzoylpyrene (1,3,6-Bz ₃ PY) were synthesized and their crystal structures were determined. The Friedel–Crafts deacylations in PPA of 1,3,6,8-Bz ₄ PY (at 120–200 °C) and of 1,3,6-Bz ₃ PY (at 80–160 °C) have been studied. The mono-deacylation of 1,3,6-Bz ₃ PY was regioselective and led to three dibenzoylpyrenes in the following order of relative amounts: 1,8-Bz ₂ PY > 1,6-Bz ₂ PY > 1,3-Bz ₂ PY. 1,3,6,8-Bz ₄ PY was resistant to deacylation at 120–160 °C. The deacylations of 1,3,6,8-Bz ₄ PY at 200 °C gave the polycyclic aromatic ketone (PAK) 8H-dibenzo[def,qr]chrysen-8-one (DBCO) via an intramolecular Scholl reaction. Two plausible pathways of the Friedel–Crafts deacylation of 1,3,6,8-Bz ₄ PY to give DBCO are proposed. A density functional theory (DFT) B3LYP/6-311(d,p) computational study of the conformational spaces of 1,3,6-Bz ₃ PY and 1,3,6,8-Bz ₄ PY was performed. The estimated energy barriers of formation of dibenzoylpyrenes by deacylation of 1,3,6-Bz ₃ PY increase in the following order: 1,8-Bz ₂ PY < 1,3-Bz ₂ PY < 1,6-Bz ₂ PY. A mechanism of the Friedel–Crafts deacylation of 1,3,6-Bz ₃ PY in PPA via the respective O-protonated ketone and σ-complexes is presented.     

More Than 12 % Polarization and 20 Minute Lifetime of 15N in a Choline Derivative Utilizing Parahydrogen and a Rhodium Nanocatalyst in Water

Hyperpolarization techniques are key to extending the capabilities of MRI for the investigation of structural, functional and metabolic processes in vivo. Recent heterogeneous catalyst development has produced high polarization in water using parahydrogen with biologically relevant contrast agents. A heterogeneous ligand‐stabilized Rh catalyst is introduced that is capable of achieving ¹⁵N polarization of 12.2±2.7 % by hydrogenation of neurine into a choline derivative. This is the highest ¹⁵N polarization of any parahydrogen method in water to date. Notably, this was performed using a deuterated quaternary amine with an exceptionally long spin‐lattice relaxation time (T₁) of 21.0±0.4 min. These results open the door to the possibility of ¹⁵N in vivo imaging using nontoxic similar model systems because of the biocompatibility of the production media and the stability of the heterogeneous catalyst using parahydrogen‐induced polarization (PHIP) as the hyperpolarization method.