On the Metric of Charge Transfer Molecular Excitations: A Simple Chemical Descriptor

A new index is defined with the aim of further exploring the metric of excited electronic states in the framework of the time-dependent density functional theory. This descriptor, called Δr, is based on the charge centroids of the orbitals involved in the excitations and can be interpreted in term of the hole–electron distance. The tests carried out on a set of molecules characterized by a significant number of charge-transfer excitations well illustrate its ability in discriminating between short (Δr ≤ 1.5 Å) and long-range (Δr ≥ 2.0 Å) excitations. On the basis of the well-known pitfalls of TD-DFT, its values can be then associated to the functional performances in reproducing different type of transitions and allow for the definition of a "trust radius" for GGA and hybrid functionals. The study of other systems, including some well-known difficult cases for other metric descriptors, gives further evidence of the high discrimination power of the proposed index. The combined use with other density or orbital-based descriptors is finally suggested to have a reliable diagnostic test of TD-DFT transitions.