A direct influence of porphyrin's ring current on the sigma-hole potential of halogen atoms at the axial position of metalloporphyrins during halogen bonded self-assembly is determined in this study.
Let A be a lattice in R3 of determinant 1. Define the homogeneous minimum of A as m/,(A) = inf |uiU2U3| extended over all points (ui,1*2,113) of A other than the origin. It is shown that for any given (ci, 02,03) in R3 there exists a point (ui,1*2,113) of A for which
To 80 th birthday of Paul ErdSsHilbert's irreducibility theorem and its validity for fields other than the field of rational numbers (such fields are called Hilbertian) is central in trying to realize some speciM finite groups as Galois groups. These Hilbertian fields are now being studied extensively.The property of approximation couples of rings arose out of Artin [1] on algebraic approximations. Recently, Robba [5] and Schoutens [6] gave examples of such couples.In this note we show that if A C .4 is a pair of domains having the property of approximation, then Hilbertianity of .~ implies Hilbertianity of A. To make this note self-contained, we recall the necessary definitions of pairs of rings with approximation property and Hilbertian rings and fields. We also give some known examples. In the last section, the main result is proved.
w 1. Approximation CouplesLet A C -4 be a pair of commutative rings with the same identity and A be provided with a linear topology r which stems from a filtration {P2~} of ideals such that (i) N92n = 0 and (ii) A is dense in A.
<p>We demonstrate herein a
computational study probing the influence of metalloporphyrin ring current directionality
on intermolecular halogen bonding (XB) during supramolecular self-assembly. The
results demonstrate that porphyrin ring current can activate or deactivate
halogen bonding interactions, an essential superamolecular driving force.</p>
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.