Conceptual DFT

Evaluation of p and rj faces a practical difficulty due to the discontinuity of the energy E with respect to the variation of N [3]. The implication of this discontinuity in conceptual DFT has also been pointed out recently [4]. One generally makes a finite difference approximation to calculate these quantities, and Scheme 12.1... 

Looking ahead, I am optimistic that we will see continued growth of our knowledge about this and other conceptual DFT-based reactivity and selectivity descriptors as well as broadening applications in understanding a diverse class of biophysicochemical properties and processes. 

SOLVENT EFFECT ON THE CONCEPTUAL DFT-BASED REACTIVITY DESCRIPTORS... 

As stated in the introduction, conceptual DFT is based on a series of reactivity descriptors mostly originating from a functional Taylor expansion of the E = E[N, v(r)] functional. These (<)nE/3NmSv(r)m ) quantities can be considered as response functions quantifying the response of a system for a given perturbation in N and/or v(r). In the case of molecular interactions (leading to a new constellation of covalent bonds or not), the perturbation is caused by the reaction partner. In Scheme 27.1 an overview of the interaction descriptors up to n 2 (for a more complex tabulation and discussion of descriptors up to n 3, see Refs. [11,12]) is given. 

As a further step currently under investigation, the relationship between local polarizability and local softness is studied with the aim to substitute atom-in-molecule polarizabilities by atom-condensed softness values. In this way, conceptual DFT could be exploited in a computational strategy, an ansatz rarely used until now, the best known example being the electronegativity equalization method [101]. 

The authors acknowledge many people for discussions and collaborations on many different aspects related to this chapter N. Sablon, A. Borgoo, Prof. P. Geerlings, Dr. A.M. Teale, M.J.G. Peach, Dr. M. Torrent-Sucarrat, and Prof. P.W. Ayers. F.D.P. also wishes to thank Professor Pratim Chattaraj, with whom he has had many interesting discussions on conceptual DFT and related aspects, for his kind invitation to contribute to this volume. 

Density functional theory thus offers precise definitions of previously poorly defined chemical quantities, enabling their first principles calculation. This part of DFT is termed by Parr as conceptual DFT [6]. 

Both aspects, calculational and conceptual DFT, can be elegantly linked, via the following scheme ... 

Another important trend already mentioned in previous sections is the increasing attention to angular momentum conservation and spin catalysis (Fig. 13). Attempts are now also made to find analogies between established semiempirical scales such as the spectrochemical and nephelauxetic series and local spin-philicity parameters included in calculations using spin-polarized conceptual DFT descriptors (168). 

Associated with these properties, important chemical reactivity principles have been rationalized within the framework of conceptual DFT the hard and soft acids and bases principle (F1SAB) [9], the Sanderson electronegativity equalization principle (EEP) [11], the maximum hardness principle (MF1P) [9,12,13], and the minimum polarizability principle (MPP) [14], The aim of this chapter is to revise the validity of the last two principles in nontotally symmetric vibrations. We start with a short section on the fundamental aspects of the MF1P and MPP (section 2). Section 3 focuses on the breakdown of these principles for nontotally symmetric vibrations, while section 4 analyses the relationship between the failure of the MF1P and the pseudo-Jahn-Teller (PJT) effect. A mathematical procedure that helps to determine the nontotally symmetric distortions of a given molecule that produce the maximum failures of the MPP or the... 

At a microscopic level, two kinds of functions can be derived from quantum mechanics. On the one hand are those corresponding to global properties such as the energy, expectation values of operators, chemical potential, or global hardness as defined within the conceptual DFT context [35] and on the other hand are local properties such as electron density distributions, the electron localization function ELF [24], local hardness [36,37], and the Fukui functions [38,39],... 

New, exciting developments can be expected from conceptual DFT, for example the extension of the theory to excited state Fukui functions , which may be of interest for an abiotic degradahon process of particular interest for agro-chemistry Photodegradation. 

P. Geerlings, A Computational and Conceptual DFT Study of the Reactivity of Anionic Compounds Implications for Enzymatic Catalysis,/. Phys. Chem. A, 2003, 107, 6828-6836. 

Geerlings P, De Proft F (2008) Conceptual DFT the chemical relevance of higher response functions. Phys Chem Chem Phys 10 3028... 

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