Late-Stage Alkylation of Heterocycles Using N-(Acyloxy)phthalimides

Synthetic methods enabling late-stage modification of heterocycles hold tremendous importance in the pharmaceutical and agrochemical industry and drug discovery. Accordingly, efficient, functional group tolerant and selective late-stage alkylation of valuable molecular entities is of enormous significance and well-acknowledged in medicinal chemistry. Radical alkylation of heteroarenes employing carboxylic acids as the alkyl radical precursor represents one of the most direct ways of C−H functionalizations of heterocycles. Recently, the field has undergone a revolutionary development especially with regard to the generation of alkyl radicals under much milder conditions. In this regard N-(acyloxy)phthalimides (NHPI esters) have emerged as a suitable precursor of a diverse set of alkyl radicals allowing formal C−H alkylation of not only N-heteroarenes but a diverse set of non-aromatic heterocycles under visible light photocatalysis or electrochemical conditions. This review delineates all these discoveries and provides readers a comprehensive overview of this rapidly expanding field.     

Defining the Determinant-like Function for m by n Matrices Using the Exterior Algebra

In this paper, we present a function called the Determinant-Like Function that generalises the determinant function to m by n matrices using the Clifford algebra C?(V, 0). By definition, this generalisation satisfies the property that the exterior product of its column vectors has a magnitude that equals its determinant-like function if it has more rows than columns. For matrices which have more columns than rows, we make use of another property that the exterior product of its rows has a magnitude that equals the absolute value of its determinant-like function if it has more columns than rows. Defining the sign of this determinant-like function remains an open question.     

Synthesis of spirocyclic azacycles from the cyclization of furan tethered N-acyliminium ions

The protic and Lewis acid promoted cyclization reactions of tethered furan-4,5-dihydroxypiperid-2-ones, furan-4,5-diacetoxypiperid-2-ones and furan-3,4-diacetoxypyrrolid-2-ones, via their corresponding N-acyliminium ion intermediates, have been studied. In the case of the furan-4,5-dihydroxypiperid-2-one 2a and its diacetate derivative 2b, macrocyclic products were formed from an initial intermolecular reaction between 2a or 2b, via the nucleophilic C5 furan carbon, and their corresponding N-acyliminium ion intermediates. When the furan C5 position of 2b was blocked by substitution with bromine then TFA or Sc(OTf)₃ catalysed cyclization reactions gave a spirotricyclic product (a 5-6-6-tricycle) in a highly diastereoselective manner. Cyclization of the analogous C5-Br-furan-pyrrolidone 29 with TFA resulted in a related spirotricyclic (a 5-6-5 tricycle) product. Attempts to prepare an analogous azepine system, a 5-7-5 tricycle, were not successful. Cyclization reactions of the C5-PhS-furan- or C5-phenylsulfonyl-pyrrolidone analogues of 29 with TFA were also not successful.     

Regio-selective synthesis of 1,2-aminoalcohols from epoxides and chlorohydrins

A simple and efficient procedure for the regio-selective synthesis of 1,2-aminoalcohols from terminal epoxides and chlorohydrins by using NaHMDS as the source of amine is reported. The wider scope and utility of this method is demonstrated.     

Cascade intermolecular Michael addition-intramolecular azide/internal alkyne 1,3-dipolar cycloaddition reaction in one pot

A rapid one-pot protocol for the synthesis of indole-based polyheterocycles via a sequential Lewis acid catalyzed intermolecular Michael addition and an intramolecular azide/internal alkyne 1,3-dipolar cycloaddition reaction has been described. The generality of the method has been demonstrated by treating a series of aromatic/aliphatic 2-alkynyl indoles with substituted (E)-1-azido-2-(2-nitrovinyl)benzenes to furnish annulated tetracyclic indolo[2,3-c][1,2,3]triazolo[1,5-a][1]benzazepines in good yields.     

Kac’s ring: Entropy and Poincaré recurrence

We study the entropy of an N$N$-site Kac ring in a non-equilibrium state. As the system dynamically evolves towards equilibrium and eventually to the initial state exhibiting Poincaré recurrence, we see that the entropy saturates over a period of time which is large for large N$N$. At about the time of order N$N$, the system starts to return to its initial state. We show that there is indeed a perfect “recurrence of statistical fluctuations”, which we are able to explore, as Kac’s ring possesses a finite recurrence time. Entropy is shown here to be a periodic function of the Poincaré recurrence time.     

Three-dimensional QSAR using the k-nearest neighbor method and its interpretation

In this paper we report a novel three-dimensional QSAR approach, kNN-MFA, developed based on principles of the k-nearest neighbor method combined with various variable selection procedures. The kNN-MFA approach was used to generate models for three different data sets and predict the activity of test molecules through each of these models. The three data sets used were the standard steroid benchmark, an antiinflammatory and an anticancerous data set. The study resulted in kNN-MFA models having better statistical parameters than the reported CoMFA models for all the three data sets. It was also found that stochastic methods generate better models resulting in more accurate predictions as compared to stepwise forward selection procedures. Thus, kNN-MFA method represents a good alternative to CoMFA-like methods.