Orbitally resolved charge sensitivity analysis: Basic concepts and relations

Publisher Website
Google Scholar
Abstract
Following the recent developments of the charge sensitivity analysis (CSA) in the atoms‐in‐molecules (AIM) resolution, the corresponding CSA quantities in the orbital (or shell) resolution (OR) are defined. The OR electron population variables, in the ordinary closed‐shell SCF problem, are the elements of the bond‐order matrix P, and their conjugates, “chemical potentials,” FT = ∂E/∂P, are the respective Fock matrix elements, appropriate for the representation in question; here E is the SCF energy. The second derivatives ∂2E/∂P∂P define the OR hardness tensor from which all related OR CSs, e.g., the hardness, softnesses, Fukui function (FF) indices, etc., can be determined. The rigid potentials and hardness tensor, corresponding to the “frozen” orbital approximation, are examined in more detail, and the decoupled representation of the normal orbitals (NoO) is introduced, in which the rigid hardness tensor becomes diagonal. Illustrative valence‐shell NoO contours for the water molecule are given and discussed. The new approximation for the OR FF indices, as the orbital occupation probabilities, is proposed on the basis of the density matrix functional development of Donnely and Parr for natural orbitals, and the relevant expressions for the molecular fragment (collection of orbitals) quantities are summarized.