Energetics of Covalent Bonding from Wave Function Tiles

The mechanism of covalent bonding has been debated for a century, with proponents variously championing kinetic or potential energy as the driver. While detailed calculations have revealed the bonding mechanism for model systems such as H$_2^+$ and H$_2$, a consensus on larger systems exhibiting covalent C-C bonds has been elusive. Here, the bond energetics of the model system ethane are inspected by decomposing the 54-dimensional electronic wavefunction into repeating tiles related by permutation of like spin electrons, using our dynamic Voronoi Metropolis sampling algorithm. Within each tile, electrons are found to correspond to distinct chemical identities. The energies of the electrons are inspected as a function of C-C bond length, and the dominant contributors to the binding energy are found to be the pair of electrons in the C-C bonding region, as expected. A decomposition of the C-C bond energy into kinetic and potential terms shows that the bonding energetics mirror those of H$_2$, with an initial dip in kinetic energy upon methyl fragment interaction, followed by an increase in kinetic energy and decrease in potential energy as the bond is formed. The decrease in potential energy is accompanied by a marked contraction of C-C bonding electron density. These results show the similarity between the model C-C bond and that of H$_2$, and that wavefunction tiles are a convenient method to decompose the contributors to covalent bonding energetics in high dimensionalities, agnostic to the method used to calculate the wave function.