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

Abstract

An overview is given of our recent work on the linear response function (LRF) χ r; r 0 ðÞ and its congener, the softness kernel s r; r 0 ðÞ , 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 EN; v ½ and Ω ¼ Ω μ; v ÂÃ functionals in v r ðÞresulting, 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 conditions 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 softness kernel for molecules are reported and scrutinized for their nearsightedness, reconciling 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 integralintegrand relationship between the atom-atom polarizability and the transmission probability 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.

Exploring chemical space with alchemical derivatives: alchemical transformations of H through Ar and their ions as a proof of concept

“…23,24 The most straightforward -first-order-case of a response function for a v  perturbation is the electron density   expansion involves the response function, commonly called the Linear Response Function (LRF). [23][24][25][26] At first sight tricky to evaluate and interpret, significant progress has been made in recent years in its evaluation and representation, in extracting chemical information (e.g. inductive and mesomeric effects, (anti)aromaticity) from it, 25,26 in exploring its analogies with macroscopic chemical thermodynamics 27 and its connection with molecular conductivity.…”

“…[23][24][25][26] At first sight tricky to evaluate and interpret, significant progress has been made in recent years in its evaluation and representation, in extracting chemical information (e.g. inductive and mesomeric effects, (anti)aromaticity) from it, 25,26 in exploring its analogies with macroscopic chemical thermodynamics 27 and its connection with molecular conductivity. 28,29 The link between LRF and the above-mentioned alchemical derivatives is easily seen.…”

Variational Principle for Eigenmodes of Reactivity in Conceptual Density Functional Theory

“…Apart from the explicit calculations of the eigenmodes for model functionals, the eigenmodes of the hardness kernel could be computed from the Kohn−Sham orbitals by following the method proposed by the Geerlings group for the numerical computation of the polarizability density kernel. 6,37 The main idea developed by the authors is to apply a set of perturbations to the system and to expand the response in a finite basis set. It is worth noting that this method allows a straightforward study of the polarization modes by diagonalizing the kernel χ 1 computed numerically in ref 6 For the numerical calculation of the hardness kernel, we can follow exactly similar lines than those in ref 6.…”

Parity symmetry in a number of problems of quantum and structural chemistry

“…Этот поход, развитый Парром и названный им Conceptual DFT, имеет много сторонников в современной квантовой химии, но мы на нем не будем останавливаться. Несколько иные акценты, идейно больше связанные со статьями Коулсона, даются в теории DFT-функций линейного отклика [55]. В цитируемом обзоре Геерлинга и сотр.…”