First-principles calculations within periodic boundary conditions of the NMR shielding tensor for a transition metal nucleus in a solid state system: The example of 51V in AlVO4

We present the first density functional theory based calculations of NMR shielding parameters for a transition metal nucleus using periodic boundary conditions. These calculations employ the gauge-including projected augmented-wave pseudopotential approach. The quality of this method is discussed by comparing experimental and calculated chemical shift tensor eigenvalues for the quadrupolar 51V nucleus in the diamagnetic solid-state compound AlVO4. Furthermore, the combination of shielding tensor with fast and accurate projector augmented-wave electric field gradient tensor calculations allows us to determine the relative orientation of these two tensors.     

Application of group representation theory to derive Hermite interpolation polynomials on a triangle

Current methods used to devise sets of Hermite interpolation polynomials of minimal order that ensure C⁽ⁿ⁾ continuity across triangular element boundaries in two dimensions are not readily extensible to higher dimensions. The extension of such methods is especially difficult when the number of degrees of freedom afforded by data at points is different from the number of degrees of freedom determined by the coefficients of a complete polynomial basis to a particular order. This work introduces a formalism based on group representation theory that can accomplish this task in general. The method is introduced through the derivation of C⁽¹⁾ continuous Hermite polynomials that interpolate data at the three vertices of an equilateral triangular element. These interpolation polynomials are reported here for the first time. The polynomials derived here are compared to the standard polynomials defined in a right triangle by using the two sets of polynomials to solve the Laplace equation over finite elements. The methodology presented here is of use in higher dimensional elements when the complete polynomial degrees of freedom exceed the total C⁽ⁿ⁾ degrees of freedom at the nodes.     

Bioelectrocatalytic Synthesis: Concepts and Applications

Bioelectrocatalytic synthesis is the conversion of electrical energy into value-added products using biocatalysts. These methods merge the specificity and selectivity of biocatalysis and energy-related electrocatalysis to address challenges in the sustainable synthesis of pharmaceuticals, commodity chemicals, fuels, feedstocks and fertilizers. However, the specialized experimental setups and domain knowledge for bioelectrocatalysis pose a significant barrier to adoption. This review introduces key concepts of bioelectrosynthetic systems. We provide a tutorial on the methods of biocatalyst utilization, the setup of bioelectrosynthetic cells, and the analytical methods for assessing bioelectrocatalysts. Key applications of bioelectrosynthesis in ammonia production and small-molecule synthesis are outlined for both enzymatic and microbial systems. This review serves as a necessary introduction and resource for the non-specialist interested in bioelectrosynthetic research.