A problematic issue for atoms in molecules: Impact of (quasi-)degenerate states on Quantum Theory Atoms in Molecules and Hirshfeld-I properties

We examine the dependence of atomic properties derived from the Quantum Theory of Atoms in Molecules and the Hirshfeld-I method on the existence of (quasi-)degenerate states. As atomic charges are mostly used to quickly assess chemical reactivity using the molecular electrostatic potential, we computed the correct zeroth order density matrices using degenerate perturbation theory for a perturbing point charge of given magnitude, sign and position. This density matrix is then used as input for Atoms in Molecules (AIM) analysis and the dependence of atomic charges on the nature of the perturbation examined for two molecules. It is shown that in simple cases, the atomic charges are deceptively robust due to symmetry reasons whereas in a less symmetrical case the atomic charges vary significantly. This establishes that for the prediction of reactivity, for every kind of perturbation, a specific perturbation matrix needs to be diagonalised and the resulting density matrix used for AIM analysis.