Interaction at pre-bonding distances and bond formation for open p-shell atoms: quantum and classical methods

We employ the ΔSCF framework to build and optimize, via the Maximum Overlap Method (MOM), non-Aufbau Hartree–Fock determinants for molecular systems containing atoms with open p-shells. We use these determinants in the coupled-cluster (CC) Ansatz to calculate interaction energies at pre-bonding distances and to study bond formation pathways for the ground and excited states of the molecules. We propose that the MOM-CC combination presents a straightforward and general way to study interatomic forces between open-shell atoms with arbitrarily populated orbitals. As a practical application of the MOM combined with CC with singles, doubles, and perturbative triples, we demonstrate that fixed multipole Coulomb interactions between open p-shell atoms play an important role at pre-bonding distances and can lead to an overall repulsive interaction between two neutral atoms. Using three diatomic molecules, B2, Al2, and AlB, as examples, we illustrate how the mutual orientation of atomic p-orbitals at large separations determines the type of the established chemical bond. Implementation of the proposed method for atoms with other configurations of unfilled shells is straightforward. We also demonstrate that a previously proposed classical small dielectric spheres model, which has been shown to be highly accurate for interactions between closed-shell atoms, remains more accurate than density-functional theory calculations also for atoms with open shells. This suggests that rigorous classical electrostatics is capable of capturing a significant part of electron correlation and polarization effects and potentially can be used for accurate yet low-cost calculations of pre-bonding interactions between larger molecules, for which high-level quantum chemical methods would be computationally impractical.