Investigations on the Pi Distortivity Problem and On the Use of Single Atom Thick Layers as Filters

Abstract

It has traditionally been believed that pi-electrons stabilize the D6h structure of benzene. However, this was questioned both using theoretical arguments, as well as circumstantial, experimental evidence. The theoretical arguments have all been based upon the partitioning of the total energy into the sigma- and pi- parts. This partitioning is not unique, the conclusions can be questioned.[1] We suggest an alternative approach based on the forces, calculated using the Hellmann-Feynman theorem. The partitioning of forces into their sigma and pi components is unique and can be used to analyze the behavior of and#960;- and and#963;- electrons. The procedure is exact and offers a rigorous solution to the problem of pi- distortivity.[2] We have successfully applied the method to benzene and have obtained an unambiguous proof for the pi- distortivity of benzene. Moreover, in all the conjugated and aromatic compounds we considered the pi-electrons are always distortive. We also applied our approach to understand the bent nature of the silicon conjugated compounds. In the second part, I consider the use of nano-porous graphene membranes as gas and isotope filters. Recent experiments demonstrate porous graphene can be used as a molecular sieve.[3] Synthetic chemists are successful to fabricate few nano-porous membranes viz. poly-phenylene, Graphdiyne, C2N-holey sheet. We investigated the separation of Helium and Hydrogen from an atmospheric gas mixture which consists of Helium, Hydrogen, Oxygen, Nitrogen, Carbo-di-oxide, Neon, and Argon using these membranes along with a few other theoretically proposed membranes. Further, we investigated the possibility of these membranes as helium isotope filters. As the quantum effects viz. tunneling, zero-point energy plays a vital role in the separation of the isotopes we did the three dimensional wave packet calculations using an analytical interaction potential. Our calculations showed that maximum He-4/He-3 separation for C2N-holey sheet, C2O-holey sheet, and graphenylene can be achieved...