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Register a new userRevisiting the Effect of f-Functions in Predicting the Right Reaction Mechanism for Hypervalent Iodine Reagents
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To understand the effect of f-functions in predicting the right reaction mechanism for hypervalent iodine reagents, we adopt the Ahlrichs basis set family def2-SVP and def2-TZVP to revisit the potential energy surfaces of IBX-mediated oxidation and Togni Is isomerisation. Our results further prove that f-functions (in either Pople, Dunning, or Ahlrichs basis set series) are indispensable to predict the correct rate-determining step of hypervalent iodine reagents. The f-functions have a significant impact on the predicted reaction barriers for processes involving the I-X (X = O, OH, CF$_3$, etc.) bond cleavage and formation, e.g. in the reductive elimination step or the hypervalent twist step. We furthermore explore two hypervalent twist modes that account for the different influences of f-functions for IBX and Togni I. Our findings may be helpful for theoretical chemists to appropriately study the reaction mechanism of hypervalent iodine reagents.
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Since the hypervalent twist followed by reductive elimination is a general reaction pattern for hypervalent iodine reagents, mechanistic studies about the hypervalent twist step provide significant guidance for experiments. Our previous work showed there are two types of hypervalent twist models, i.e. apical twist and equatorial twist. We applied both hypervalent twist models to explain the isomerization mechanism of two important electrophilic trifluoromethylating reagents, Togni I and Togni II. To the best of our knowledge, there are less detailed studies about the different twist modes between both reagents, which are important to predict the right reaction mechanism and especially, understand well the differences of reactivity and stability. Here, we successfully identified Togni IIs isomerization pathway via equatorial twist, and suggested different hypervalent twist models should be considered to predict the right mechanisms of reactions with hypervalent iodine reagents.
We reexamine the screening mechanism in $f(R)$ gravity using N-body simulations. By explicitly examining the relation between the extra scalar field $delta f_R$ and the gravitational potential $phi$ in the perturbed Universe, we find that the relation between these two fields plays an important role in understanding the screening mechanism. We show that the screening mechanism in $f(R)$ gravity depends mainly on the depth of the potential well, and find a useful condition for identifying unscreened halos in simulations. We also discuss the potential application of our results to real galaxy surveys.
In 1961, Renyi discovered a rich family of non-classical Lyapunov functions for kinetics of the Markov chains, or, what is the same, for the linear kinetic equations. This family was parameterised by convex functions on the positive semi-axis. After works of Csiszar and Morimoto, these functions became widely known as $f$-divergences or the Csiszar--Morimoto divergences. These Lyapunov functions are universal in the following sense: they depend only on the state of equilibrium, not on the kinetic parameters themselves. Despite many years of research, no such wide family of universal Lyapunov functions has been found for nonlinear reaction networks. For general non-linear networks with detailed or complex balance, the classical thermodynamics potentials remain the only universal Lyapunov functions. We constructed a rich family of new universal Lyapunov functions for {em any non-linear reaction network} with detailed or complex balance. These functions are parameterised by compact subsets of the projective space. They are universal in the same sense: they depend only on the state of equilibrium and on the network structure, but not on the kinetic parameters themselves. The main elements and operations in the construction of the new Lyapunov functions are partial equilibria of reactions and convex envelopes of families of functions.
Metallization and dissociation are key transformations in diatomic molecules at high densities particularly significant for modeling giant planets. Using X-ray absorption spectroscopy and atomistic modeling, we demonstrate that in halogens, the formation of a textit{connected} molecular structure takes place at pressures well below metallization. Here we show that the iodine diatomic molecule first elongates of $sim$0.007 AA~up to a critical pressure of $P_c$ $backsim$7~GPa developing bonds between molecules. Then its length continuously decreases with pressure up to 15-20~GPa. Universal trends in halogens are shown and allow to predict for chlorine a pressure of 42$pm$8~GPa for molecular bond-length reversal. Our findings tackle the molecule invariability paradigm in diatomic molecular phases at high pressures and may be generalized to other abundant diatomic molecules in the universe, including hydrogen.
Porous electrodes are found in energy storage devices such as supercapacitors and pseudo-capacitors. However, the effect of electrode-pore-size distribution over their energy storage properties remains unclear. Here, we develop a model for the charging of electrical double layers inside a cylindrical pore for arbitrary pore size. We assume small applied potentials and perform a regular perturbation analysis to predict the evolution of electrical potential and ion concentrations in both the radial and axial directions. We validate our perturbation model with direct numerical simulations of the Poisson-Nernst-Planck equations, and obtain quantitative agreement between the two approaches for small and moderate potentials. Our analysis yields two main characteristic features of arbitrary pore size: i) a monotonic decrease of the charging timescale with an increase in relative pore size (pore size relative to Debye length); ii) a region of large potential gradients at the mouth of the pore due to charge conservation. We develop a modified transmission circuit model that captures the effect of arbitrary pore sizes and demonstrate that a time-dependent interfacial capacitance needs to be included in the circuit. We also derive expressions for effective capacitance and charging timescale as a function of pore-size distribution, and show that the capacitance and charging timescale increase for narrower and less polydisperse distributions, resulting in a gain of energy density at a constant power density. Overall, our results advance the fundamental understanding of electrical-double-layer charging and will be useful for the electrode design of energy storage devices.
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