Hydrogen-hydrogen interaction in planar biphenyl: a theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods.

The nature of H-H interaction between ortho-hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial-based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H-H bonding, partitioning the atomic energy into intra-atomic and interatomic terms reveals that there is a net attractive interaction between the ortho-hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho-hydrogens remains almost constant when they participate in the H-H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H-H bond, it is almost compensated by the destabilizing effects of the intra-atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra-atomic and interatomic energy terms of ortho-hydrogens during H-H bond formation are very similar to those observed for the H2 molecule.