New Insights and Horizons from the Linear Response Function in Conceptual DFT

An overview is given of our recent work on the linear response function (LRF) χ r ; r 0 ð Þ and its congener, the softness kernel s r ; r 0 ð Þ , the second functional derivatives of the energy E and the grand potential Ω with respect to the external potential at constant N and μ , respectively. In a first section on new insights into the LRF in the context of conceptual DFT, the mathematical and physical properties of these kernels are scrutinized through the concavity of the E ¼ E N ; v ½ (cid:2) and Ω ¼ Ω μ ; v (cid:1) (cid:3) functionals in v r ð Þ resulting, for example, in the negative semidefiniteness of χ . As an example of the analogy between the CDFT functionals and thermodynamic state functions, the analogy between the stability condi- tions of the macroscopic Gibbs free energy function and the concavity conditions for Ω is established, yielding a relationship between the global and local softness and the softness kernel. The role of LRF and especially the softness kernel in Kohn ’ s nearsightedness of electronic matter (NEM) principle is highlighted. The first numerical results on the soft- ness kernel for molecules are reported and scrutinized for their nearsightedness, reconcil-ing the physicists ’ NEM view and the chemists ’ transferability paradigm. The extension of LRF in the context of spin polarized conceptual DFT is presented. Finally, two sections are devoted to ‘ new horizons ’ for the LRF. The role of LRF in (evaluating) alchemical derivatives is stressed, the latter playing a promising role in exploring the chemical compound space. Examples for the transmutation of N 2 and the CC ! BN substitution pattern in 2D and 3D carbocyclic systems illustrate the computational efficiency of the use of alchemical derivatives in exploring nearest neighbours in the chemical compound space. As a second perspective, the role of LRF in evaluating and interpreting molecular conductivity is described. Returning to its forerunner, Coulson ’ s atom-atom polarizability, it is shown how in conjugated π systems (and within certain approximations) a remarkable integral-integrand relationship between the atom-atom polarizability and the transmission proba- bility between the atoms/contacts exists, leading to similar trends in both properties. A simple selection rule for transmission probability in alternating hydrocarbons is derived based on the sign of the atom-atom polarizability.