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Register a new userPredicting the Right Mechanism for Hypervalent Iodine Reagents by Applying Two Types of Hypervalent Twist Models: Apical Twist and Equatorial Twist
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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.
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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.
We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the non-zero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, and which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over $N_mathrm{s}$ twist angles from $N_s$ CCD calculations to $N_s$ MP2 calculations plus one CCD calculation.
By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately $100$ base pairs (bp). We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape, that reproduces the exact loop energy up to the fourth significant digit, and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations. They perform a normal diffusive motion, whose origin is briefly discussed.
We present the calculation of the leading instanton contribution to the scaling dimensions of twist-two operators with arbitrary spin and to their structure constants in the OPE of two half-BPS operators in $mathcal N=4$ SYM. For spin-two operators we verify that, in agreement with $mathcal N=4$ superconformal Ward identities, the obtained expressions coincide with those for the Konishi operator. For operators with high spin we find that the leading instanton correction vanishes. This arises as the result of a rather involved calculation and requires a better understanding.
We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute the $SO(N)$ Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral $D_k$ symmetry of $SO(2n)_1$, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the $mathcal{C}/G$ twist liquids, where $G=mathbb{Z}_2$ for $mathcal{C}=U(1)_l$, $SU(n)_1$, and $G=mathbb{Z}_2$, $mathbb{Z}_k$, $D_k$ for $mathcal{C}=SO(2n)_1$. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in $SO(2n)_1/G$ by identifying the non-chiral components of the twist liquids with discrete gauge theories.
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