Synthesis of Elusive Chloropnictenium Ions

This work describes the synthesis and full characterization of elusive chloropnictenium ion salts of the type [^RAr*N(SiMe)ECl][A] (^RAr*=2,6‐(CHPh₂)‐4‐R‐C₆H₂, R=Me, tBu; E=Sb, Bi; A^?=GaCl₄, Al(OCH(CF₃)₂)₄). In these species the cation is significantly stabilized by weak arene interactions to flanking phenyl groups of the ^RAr* moiety. In this context the bonding situation has been studied by computational means and the reactivity towards the Lewis base 4‐dimethylaminopyridine (dmap) was investigated.     

Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n\times n$ spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\epsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n\log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which outperforms traditional approaches with $O(n^3\log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n\log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3\times n^3$ matrices and vectors in ${?}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n.     

Selective Benzylic CH-Borylations by Tandem Cobalt Catalysis

Metal-catalyzed C?H activations are environmentally and economically attractive synthetic strategies for the construction of functional molecules as they obviate the need for pre-functionalized substrates and minimize waste generation. Great challenges reside in the control of selectivities, the utilization of unbiased hydrocarbons, and the operation of atom-economical dehydrocoupling mechanisms. An especially mild borylation of benzylic CH bonds was developed with the ligand-free pre-catalyst Co[N(SiMe₃)₂]₂ and the bench-stable and inexpensive borylation reagent B₂pin₂ that produces H₂ as the only by-product. A full set of kinetic, spectroscopic, and preparative mechanistic studies are indicative of a tandem catalysis mechanism of CH-borylation and dehydrocoupling via molecular Co^I catalysts.