Conceptual DFT: chemistry from the linear response function

Abstract

Within the context of reactivity descriptors known in conceptual DFT, the linear response function (χ(r,r')) remained nearly unexploited. Although well known, in its time dependent form, in the solid state physics and time-dependent DFT communities the study of the "chemistry" present in the kernel was, until recently, relatively unexplored. The evaluation of the linear response function as such and its study in the time independent form are highlighted in the present review. On the fundamental side, the focus is on the approaches of increasing complexity to compute and represent χ(r,r'), its visualisation going from plots of the unintegrated χ(r,r') to an atom condensed matrix. The study on atoms reveals its physical significance, retrieving atomic shell structure, while the results on molecules illustrate that a variety of chemical concepts are retrieved: inductive and mesomeric effects, electron delocalisation, aromaticity and anti-aromaticity, σ and π aromaticity,…. The applications show that the chemistry of aliphatic (saturated and unsaturated) chains, saturated and aromatic/anti-aromatic rings, organic, inorganic or metallic in nature, can be retrieved via the linear response function, including the variation of the electronic structure of the reagents along a reaction path. The connection of the linear response function with the concept of nearsightedness and the alchemical derivatives is also highlighted.

Nearsightedness-related indices of finite systems based on linear response function: one-dimensional cases

“…The original NEM scenario focuses on density changes at partial regions in infinite systems [2], i.e., (δρ(r)/δv(r )) μ . By contrast, a main interest of both our study and conceptual DFT lies in LRF at constant N, (δρ(r)/δv(r )) N , of finite systems [7,8,[16][17][18][19][20][21][22][23][24][25]. This is reasonable in the context of quantum chemistry calculations: the number of electrons is usually conserved.…”

“…Savin's group analysed LRFs of atoms along the adiabatic connection of density functional theory (DFT) and discussed the computational results from the viewpoints of electron correlation effects [15]. During the past decades, LRF of molecules has been mainly computed as a descriptor of chemical reactivities [14,[16][17][18][19][20][21][22][23][24][25]. In particular, there is an important relation called Berkowitz-Parr relation [16],…”

“…This type of theories is called conceptual DFT, which has been developed to link DFT and chemistry to investigate the intrinsic reactivities of molecules (see refs. [19,24] for comprehensive reviews). Here, we should emphasise that the LRF defined at the left side of Equation (1a) is for the cases that the number of electrons (N) is conserved.…”

“…Although the calculation of LRFs of density is not routine in either computational chemistry or computational physics, it has a long history [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. More than 50 years ago, LRFs of organic compounds were investigated on the basis of Hückel model by Coulson and LonguetHiggins [9] and Fukui's group [10], of which the theory was reformulated in terms of Green's function by Aono and Nishikawa [11].…”

The polarisability of atoms and molecules: a comparison between a conceptual density functional theory approach and time-dependent density functional theory

“…In our previous work (for a review see [36]), we have studied the uncondensed linear response kernel both at the independent particle level as well as the full coupled perturbed Kohn-Sham (CPKS) level on the basis of the equation,…”