Energy Decomposition Analysis with a Stable Charge-Transfer Term for Interpreting Intermolecular Interactions

Many schemes for decomposing quantum-chemical calculations of intermolecular interaction energies into physically meaningful components can be found in the literature, but the definition of the charge-transfer (CT) contribution has proven particularly vexing to define in a satisfactory way and typically depends strongly on the choice of basis set. This is problematic, especially in cases of dative bonding and for open-shell complexes involving cation radicals, for which one might expect significant CT. Here, we analyze CT interactions predicted by several popular energy decomposition analyses and ultimately recommend the definition afforded by constrained density functional theory (cDFT), as it is scarcely dependent on basis set and provides results that are in accord with chemical intuition in simple cases, and in quantitative agreement with experimental estimates of the CT energy, where available. For open-shell complexes, the cDFT approach affords CT energies that are in line with trends expected based on ionization potentials and electron affinities whereas some other definitions afford unreasonably large CT energies in large-gap systems, which are sometimes artificially offset by underestimation of van der Waals interactions by density functional theory. Our recommended energy decomposition analysis is a composite approach, in which cDFT is used to define the CT component of the interaction energy and symmetry-adapted perturbation theory (SAPT) defines the electrostatic, polarization, Pauli repulsion, and van der Waals contributions. SAPT/cDFT provides a stable and physically motivated energy decomposition that, when combined with a new implementation of open-shell SAPT, can be applied to supramolecular complexes involving molecules, ions, and/or radicals.