The origin of electron density accumulation within CH,HC contacts in biphenyl : a theoretical study

Abstract

The primary focus of this work is the investigation into the nature and origin of the electron density between the ortho-hydrogens in the higher energy, planar transition state of biphenyl. This interaction has been the subject of debate within the scientific community for almost three decades with no clear consensus being made. Since the distance between these hydrogens is smaller than their summed van der Waals radii (2.4 Å), classically one can assume that they partake in a steric clash, however the Quantum Theory of Atoms in Molecules (QTAIM) depicts a bond path for this H,H contact. This presence of a bond path caused the rift in the scientific community. To investigate the problem, we made use of cross-section decomposition analysis whereby the electron density at any given coordinate is decomposed into the components that contribute to its presence. In this dissertation, three methods using this analysis were made, namely (i) MO-ED, (ii) FALDI-ED, and (iii) NBO-ED. These represent the decomposition products that the density is decomposed into; the MO-ED method decomposed the density between the ortho-hydrogens into its molecular orbital (MO) contributions, the FALDI-ED method decomposed the density into fragment and diatomic contributions, and the NBO-ED method decomposed the density into its natural bond orbital (NBO) contributions. With all three methods, when decomposing the density along eigenvector-2 from the bond critical point (BCP) between the ortho-hydrogens in the planar conformer, it was found that the total electron density is concentrating, shown by the directional second partial derivative. This means that the electron density is purposefully accumulated in the H,H contact rather than dissipated as one would expect from a classical steric clash. Furthermore, this density decomposition analysis revealed that this density is due to a large molecular-wide delocalisation, rather than a classical 2-centred approach, with the largest contributions (in both conformers) being from the two covalent ortho C-H bonds. This delocalisation forms a density channel between two hydrogens, of an overwhelmingly concentrating/bonding nature, forming a weak covalent bond. Due to these findings, it is clear that the classical idea of a steric clash cannot be the case for this system, and that QTAIM correctly predicts the bond path between these ortho-hydrogens.