Microsolvated transition state models for improved insight into chemical properties and reaction mechanisms

Over the years, several methods have been developed to effectively represent the chemical behavior of solutes in solvents. The environmental effects arising due to solvation can generally be achieved either through inclusion of discrete solvent molecules or by inscribing into a cavity in a homogeneous and continuum dielectric medium. In both these approaches of computational origin, the perturbations on the solute induced by the surrounding solvent are at the focus of the problem. While the rigor and method of inclusion of solvent effects vary, such solvation models have found widespread applications, as evident from modern chemical literature. A hybrid method, commonly referred to as cluster-continuum model (CCM), brings together the key advantages of discrete and continuum models. In this perspective, we intend to highlight the latent potential of CCM toward obtaining accurate estimates on a number of properties as well as reactions of contemporary significance. The objective has generally been achieved by choosing illustrative examples from the literature, besides expending efforts to bring out the complementary advantages of CCM as compared to continuum or discrete solvation models. The majority of examples emanate from the prevalent applications of CCM to organic reactions, although a handful of interesting organometallic reactions have also been discussed. In addition, increasingly accurate computations of properties like pK(a) and solvation of ions obtained using the CCM protocol are also presented.     

Origin of stereoselectivity in a chiral N-heterocyclic carbene-catalyzed desymmetrization of substituted cyclohexyl 1,3-diketones

The mechanism and stereoselectivity in a chiral N-heterocyclic carbene-catalyzed desymmetrization of a 1,3-diketone is established by using density functional theory computations. The Breslow intermediate formation is identified to involve Hunig's base-assisted proton transfer. The relative energies of stereoselectivity-determining intramolecular aldol cyclization transition states reveal that in the most preferred mode the re-face of enolate adds to the si-face of carbonyl leading to a tricyclic lactone with a configuration (2aS,4aS,8'S) in excellent agreement with previous experimental reports.     

Stereoselective synthesis of the macrolactone core of (+)-neopeltolide

A stereoselective synthesis of the macrolactone core of the potent anticancer agent neopeltolide is disclosed. The key steps of the synthesis include asymmetric allylation using Krische' protocol, conjugate reduction using MacMillan's methodology, and an asymmetric hetero-Diels-Alder reaction using Jacobsen's catalyst. Substrate controlled diastereoselective 1,3-anti reduction of a keto alcohol, Luche reduction followed by Ireland-Claisen rearrangement, oxymercuration, and reductive lithiation are other key steps.     

Microwave- and Ultrasound-Assisted Extraction of Cannabinoids and Terpenes from Cannabis Using Response Surface Methodology

Limited studies have explored different extraction techniques that improve cannabis extraction with scale-up potential. Ultrasound-assisted and microwave-assisted extraction were evaluated to maximize the yield and concentration of cannabinoids and terpenes. A central composite rotatable design was used to optimize independent factors (sample-to-solvent ratio, extraction time, extraction temperature, and duty cycle). The optimal conditions for ultrasound- and microwave-assisted extraction were the sample-to-solvent ratios of 1:15 and 1:14.4, respectively, for 30 min at 60 °C. Ultrasound-assisted extraction yielded 14.4% and 14.2% more oil and terpenes, respectively, compared with microwave-assisted extracts. Ultrasound-assisted extraction increased cannabinoid concentration from 13.2–39.2%. Considering reference ground samples, tetrahydrocannabinolic acid increased from 17.9 (g 100 g dry matter⁻¹) to 28.5 and 20 with extraction efficiencies of 159.2% and 111.4% for ultrasound-assisted and microwave-assisted extraction, respectively. Principal component analyses indicate that the first two principal components accounted for 96.6% of the total variance (PC1 = 93.2% and PC2 = 3.4%) for ultrasound-assisted extraction and 92.4% of the total variance (PC1 = 85.4% and PC2 = 7%) for microwave-assisted extraction. Sample-to-solvent ratios significantly (p < 0.05) influenced the secondary metabolite profiles and yields for ultrasound-assisted extracts, but not microwave-assisted extracts.     

Cold Ethanol Extraction of Cannabinoids and Terpenes from Cannabis Using Response Surface Methodology: Optimization and Comparative Study

Efficient cannabis biomass extraction can increase yield while reducing costs and minimizing waste. Cold ethanol extraction was evaluated to maximize yield and concentrations of cannabinoids and terpenes at different temperatures. Central composite rotatable design was used to optimize two independent factors: sample-to-solvent ratio (1:2.9 to 1:17.1) and extraction time (5.7 min–34.1 min). With response surface methodology, predicted optimal conditions at different extraction temperatures were a cannabis-to-ethanol ratio of 1:15 and a 10 min extraction time. With these conditions, yields (g 100 g dry matter⁻¹) were 18.2, 19.7, and 18.5 for −20 °C, −40 °C and room temperature, respectively. Compared to the reference ground sample, tetrahydrocannabinolic acid changed from 17.9 (g 100 g dry matter⁻¹) to 15, 17.5, and 18.3 with an extraction efficiency of 83.6%, 97.7%, 102.1% for −20 °C, −40 °C, and room temperature, respectively. Terpene content decreased by 54.1% and 32.2% for extraction at −20 °C and room temperature, respectively, compared to extraction at −40 °C. Principal component analysis showed that principal component 1 and principal component 2 account for 88% and 7.31% of total variance, respectively, although no significant differences in cold ethanol extraction at different temperatures were observed.     

Orbits of euclidean frames under discrete linear groups

We obtain certain sufficient conditions for the orbit of a (euclidean)p-frame over a vector spaceV,p<dimV, under the action of a discrete subgroup of GL(V), to be dense in the corresponding orbit of a Lie subgroup of GL(V). Using the result we classify thep-frames whose orbits under SL (n,Z) are dense in the space ofp-frames and deduce, in turn, a classification of dense orbits of certain horospherical flows. A similar result is obtained for Sp (2n,Z) forp≦n.     

Monotonicity and dummy free property for multi-choice cooperative games

Given a coalition of ann-person cooperative game in characteristic function form, we can associate a zero-one vector whose non-zero coordinates identify the players in the given coalition. The cooperative game with this identification is just a map on such vectors. By allowing each coordinate to take finitely many values we can define multi-choice cooperative games. In such multi-choice games we can also define Shapley value axiomatically. We show that this multi-choice Shapley value is dummy free of actions, dummy free of players, non-decreasing for non-decreasing multi-choice games, and strictly increasing for strictly increasing cooperative games. Some of these properties are closely related to some properties of independent exponentially distributed random variables. An advantage of multi-choice formulation is that it allows to model strategic behavior of players within the context of cooperation.Partially funded by the NSF grant DMS-9024408