A dicationic ferrocene derivative has previously been shown to bind cucurbit[7]uril (CB[7]) in water with ultra-high affinity (ΔGo= −21 kcal/mol). Here, we describe new compounds that bind aqueous CB[7] equally well, validating our prior suggestion that they, too, would be ultra-high affinity CB[7] guests. The present guests, which are based upon either a bicyclo[2.2.2]octane or adamantane core, have no metal atoms, so these results also confirm that the remarkably high affinities of the ferrocene-based guest need not be attributed to metal-specific interactions. Because we used the M2 method to compute the affinities of several of the new host-guest systems prior to synthesizing them, the present results also provide for the first blinded evaluation of this computational method. The blinded calculations agree reasonably well with experiment and successfully reproduce the observation that the new adamantane-based guests achieve extremely high affinities, despite the fact that they position a cationic substituent at only one electronegative portal of the CB[7] host. However, there are also significant deviations from experiment, and these lead to the correction of a procedural error and an instructive evaluation of the sensitivity of the calculations to physically reasonable variations in molecular energy parameters. The new experimental and computational results presented here bear on the physical mechanisms of molecular recognition, the accuracy of the M2 method, and the usefulness of host-guest systems as test-beds for computational methods.
Over the past decade, major progress in supramolecular polymerization has had a substantial effect on the design of functional soft materials. However, despite recent advances, most studies are still based on a preconceived notion that supramolecular polymerization follows a step-growth mechanism, which precludes control over chain length, sequence, and stereochemical structure. Here we report the realization of chain-growth polymerization by designing metastable monomers with a shape-promoted intramolecular hydrogen-bonding network. The monomers are conformationally restricted from spontaneous polymerization at ambient temperatures but begin to polymerize with characteristics typical of a living mechanism upon mixing with tailored initiators. The chain growth occurs stereoselectively and therefore enables optical resolution of a racemic monomer.
The chiroptical properties of a series of carbo[n]helicenes (n = 4-10) were investigated by the state-of-the-art approximate coupled cluster and density functional theory calculations. The theoretical calculation at the RI-CC2/TZVPP//DFT-D2-B97-D/TZVP level nicely reproduced the experimental CD spectra in both excitation energy and rotational strength without any shift or scaling. These calculations afforded the electric and the magnetic transition dipole moment vectors in [n]helicenes, allowing us to discuss the observed rotational strengths as a function of the number of benzene rings. Although the observed CD intensity was not immediately correlated to any of the calculated parameters, the anisotropy (g) factor of the (1)B(b) band and the specific rotation were found inversely proportional to n and nicely correlated with the helical pitch, but discontinuous at n = 6, where the aromatic rings start to overlap. In contrast, the g factor at the (1)B(a) band was rather insensitive to n. It was also revealed that the excitation energies of the (1)B(b) and (1)B(a) bands are inversely proportional to n over the entire range of n examined. The theoretical predictions also enabled us to rectify the erroneous experimental CD spectra of [5]- and [6]helicenes reported earlier, by using the enantiopure samples resolved by chiral HPLC.
This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update systems. The formula indicates that the stationary distribution of the AoI is given in terms of the stationary distributions of the system delay and the peak AoI. To demonstrate its applicability and usefulness, we analyze the AoI in single-server queues with four different service disciplines: first-come first-served (FCFS), preemptive last-come first-served (LCFS), and two variants of non-preemptive LCFS service disciplines. For the FCFS and the preemptive LCFS service disciplines, the GI/GI/1, M/GI/1, and GI/M/1 queues are considered, and for the non-preemptive LCFS service disciplines, the M/GI/1 and GI/M/1 queues are considered. With these results, we further show comparison results for the mean AoI's in the M/GI/1 and GI/M/1 queues under those service disciplines.where η t (t ≥ 0) denotes the time-stamp of information being displayed on the monitor at time t. The mean AoI E[A] is defined asand under a fairly general setting, E[A] is given by [2]where E[G † ] and E[(G † ) 2 ] denote the mean and the second moment of interarrival times and E[G † n D n ] denotes the mean product of the interarrival time G † n of the (n − 1)st and the nth packets and the system delay D n of the nth packet. This formula has been the starting point in most previous work on the analysis of the AoI. As stated in [1, Page 170], however, the calculation of the mean AoI based on (2) is cumbersome because G † n and D n are dependent in general and their joint distribution can take a complicated form.The purpose of this paper is twofold. The first one is the derivation of a general formula for the stationary distribution A(x) (x ≥ 0) of the AoI in ergodic information update systems, which is defined as the long-run fraction of time in which the AoI is not greater than an arbitrarily fixed value x:where 1 {·} denotes an indicator function. Although the mean AoI E[A] is a primary performance metric, it alone is not sufficient to characterize the long-run behavior of the AoI and its related processes. First of all, if the stationary distribution A(x) of the AoI is available, we can evaluate the deviation of the AoI from its mean value. To support our claim further, we provide two examples, which show that the stationary distribution of the AoI plays a central role in the analysis of AoI-related processes. P-LCFS GI/GI/1/0 LST and E[A] (Theorem 26); Decomposition formula (Corollary 27) P-LCFS M/GI/1/0 LST, E[A], and E[A 2 ] (Corollary 28 (i)); ordering of E[A] (Corollary 31 (i)) P-LCFS GI/M/1/0 LST, E[A], and E[A 2 ] (Corollary 28 (ii)); ordering of dist. function (Corollary 31 (ii)) P-LCFS M/M/1/0 LST, dist. function, E[A] and E[A 2 ] (Appendix A.2) P-LCFS M/D/1/0 E[A] and E[A 2 ] (Appendix A.2) P-LCFS D/M/1/0 E[A] and E[A 2 ] (Appendix A.2)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.