Quantifying the Role of Orbital Contraction in Chemical Bonding

This work reports an approach to variationally quantify orbital contraction in chemical bonds by an extension of an energy decomposition analysis (EDA). The orbital contraction energy is defined as the energy lowering due to optimization of the isolated fragments (that combine to form the bond) with a specially constructed virtual set of contraction/expansion functions. This set contains one function per occupied orbital, obtained as the linear response to scaling the nuclear charges. EDA results for a variety of single bonds show substantial changes in the importance of orbital contraction; it plays a critical role for bonds to H but only a very minor role in the bonds between heavier elements. Additionally, energetic stabilization due to rehybridization is separated from inductive polarization by the fact that no mixing with virtual orbitals is involved and is shown to be significant in fragments such as NH2, OH, and F.