Identifying aspirin polymorphs from combined DFT-based crystal structure prediction and solid-state NMR

A combined experimental and computational approach was used to distinguish between different polymorphs of the pharmaceutical drug aspirin. This method involves the use of ab initio random structure searching (AIRSS), a density functional theory (DFT)-based crystal structure prediction method for the high-accuracy prediction of polymorphic structures, with DFT calculations of nuclear magnetic resonance (NMR) parameters and solid-state NMR experiments at natural abundance. AIRSS was used to predict the crystal structures of form-I and form-II of aspirin. The root-mean-square deviation between experimental and calculated ¹H chemical shifts was used to identify form-I as the polymorph present in the experimental sample, the selection being successful despite the large similarities between the molecular environments in the crystals of the two polymorphs.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Gas-phase 21Ne NMR studies and the nuclear magnetic dipole moment of neon-21

Gas-phase ²¹Ne nuclear magnetic resonance spectra were measured at the natural abundance of ²¹Ne isotope for samples consisting of pressurized neon up to 60 bar at room temperature and applying the magnetic field of the strength B₀ = 11.7574 T. It showed that the nuclear magnetic resonance frequency is linearly dependent on the density of gaseous neon. The resonance frequency was extrapolated to the zero-density point, and it permitted the determination of the ²¹Ne nuclear magnetic moment, μ(²¹Ne) = 0.6617774(10) μ_N. The present value of μ(²¹Ne) is not influenced by the bulk magnetic susceptibility of neon and interactions between neon atoms; therefore, it is more precise and reliable than the previous result obtained for μ(²¹Ne).     

PtII-Catalyzed Hydroxylation of Terminal Aliphatic C(sp3)−H Bonds with Molecular Oxygen

The practical application of Shilov-type Pt catalysis to the selective hydroxylation of terminal aliphatic C−H bonds remains a formidable challenge, due to difficulties in replacing Pt^IV with a more economically viable oxidant, particularly O₂. We report the potential of employing FeCl₂ as a suitable redox mediator to overcome the kinetic hurdles related to the direct use of O₂ in the Pt reoxidation. For the selective conversion of butyric acid to γ-hydroxybutyric acid (GHB), a significantly enhanced catalyst activity and stability (turnover numbers (TON)>30) were achieved under 20 bar O₂ in comparison to current state-of-the-art systems (TON<10). In this regard, essential reaction parameters affecting the overall activity were identified, along with specific additives to attain catalyst stability at longer reaction times. Notably, deactivation by reduction to Pt⁰ was prevented by the addition of monodentate pyridine derivatives, such as 2-fluoropyridine, but also by introducing varying partial pressures of N₂ in the gaseous atmosphere. Finally, stability tests revealed the involvement of Pt^II and FeCl₂ in catalyzing the non-selective overoxidation of GHB. Accordingly, in situ esterification with boric acid proved to be a suitable strategy to maintain enhanced selectivities at much higher conversions (TON>60). Altogether, a useful catalytic system for the selective hydroxylation of primary aliphatic C−H bonds with O₂ is presented.     

Directing-Group-Free C7-Alkylations of N-Alkylindoles Mediated by Cationic Zirconium Complexes: Role of Brønsted Acid for Catalytic Manifold

Highly position selective alkylations of N-alkylindoles at C7-positions have been enabled by cationic zirconium complexes. The strategy provides a straightforward access to install alkyl groups at C7-positions of indoles without a complex directing group. Mechanistic studies provided support for the importance of Brønsted acids in the catalytic manifold.     

On universal subsets of Banach spaces

We prove that to most of the known hypercyclic operators A on separable Banach spaces there exist compact (compact convex, compact connected) subsets K of E such that each compact (compact convex, compact connected) subset of E can be approximated with respect to Hausdorff's distance by for suitable . Received July 8, 1997, in final form October 17, 1997     

Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus

Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid. Received: 12 April 1995 / In revised form: 7 March 1996     

Congruence criteria for finite subsets of complex projective and complex hyperbolic spaces

We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP ⁿ . For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP ⁿ and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by congruence classes or if distances π/2 are allowed. Finally we do the same kind of investigation also for the complex hyperbolic space ℂH ⁿ . Most of the results are completely analogous, however, there are also some interesting differences. Received: 15 January 1996