Softness from density functional theory

As we have seen, an atom under pressure changes its electron structure drastically and consequently, its chemical reactivity is also modified. In this direction we can use the significant chemical concepts such as the electronegativity and hardness, which have foundations in the density functional theory [9]. The intuition tells us that the polarizability of an atom must be reduced when it is confined, because the electron density has less possibility to be extended. Furthermore, it is known that the polarizability is related directly with the softness of a system [14], Thus, we expect atoms to be harder than usual when they are confined by rigid walls. Estimates of the electronegativity, x and die hardness, tj, can be obtained from [9]... 

DFT-based descriptors are those derived from the Density Functional Theory [Parr and Yang, 1989 Geerlings et al, 1996a Geerlings et al, 1996b], The most important are hardness and softness indices. 

Popular qualitative chemical concepts such as electronegativity [1] and hardness [2] have been widely used in understanding various aspects of chemical reactivity. A rigorous theoretical basis for these concepts has been provided by density functional theory (DFT). These reactivity indices are better appreciated in terms of the associated electronic structure principles such as electronegativity equalization principle (EEP), hard-soft acid-base principle, maximum hardness principle, minimum polarizability principle (MPP), etc. Local reactivity descriptors such as density, Fukui function, local softness, etc., have been used successfully in the studies of site selectivity in a molecule. Local variants of the structure principles have also been proposed. The importance of these structure principles in the study of different facets of medicinal chemistry has been highlighted. Because chemical reactions are actually dynamic processes, time-dependent profiles of these reactivity descriptors and the dynamic counterparts of the structure principles have been made use of in order to follow a chemical reaction from start to finish. 

In order to understand the importance of frontier orbitals in chemical reactivity, Berkowitz [213] studied the frontier-controlled reactions within the purview of density functional theory. It is evident that the directional characteristics of frontier orbitals determine the extent of charge transfer, and soft-soft interactions are frontier-con-trolled. A somewhat similar analysis showed that charge transfer would be facilitated at a place where the difference in local softness of two partners is large [87], It may be noted that Fukui function is obtainable from local softness but the reverse is not true. On the other hand, local hardness suffers from the drawback of ambiguity [87], which allows one to even consider it to be equal to global hardness without disturbing their... 

The purpose of this work is to start from the basic equations of density functional theory to describe the changes in the energy associated with the transition from one ground-state to another, in terms of different sets of variables. In this process one will find the natural definitions of the hardness and softness kernels, the local hardness, the local softness, the global hardness and the global softness [23]. Then, we will proceed to establish their relation with ionization potentials and electron affinities, in order to confirm their behavior as a measure of chemical hardness or softness [14, 24]. Finally, this theoretical framework will be used to analyze the maximum hardness and the HSAB principles. 

The beauty of the Density Functional theory and a source of its remarkable successes relies on the electron density function p(r), as a basic variable of the theory. Electron density is of necessity a local value that does not distinguish between parts of a molecule, and decomposition of p(r) into contributions from individual atoms has not been pursued. Instead, properties of the molecule are inspected through the local parameter of hardness, q(r) and softness s(r), introduced by Parr and Berkowitz [35, 36, 37], as opposed to the global quantities resulting in integration over the volume of the molecule. They turned their attention to the fact, that determining all properties of the system, i.e. both the dependence on the number of electrons N and the local field K(r) is possible by even more subtle parameters hardness (or softness) kernels q(r, r ). Nalewajski explored this device in analysis of the protonation reaction path [28, 38]. 

Reviews the main pictures for electronegativity, from Pauling and Mulliken to the author s analytical density functionals within the softness density functional theory with proper illustration of atomic periodicity ... 

Of course the absolute softness is the reciprocal of the absolute hardness. The apparent success of the density-functional theory is to provide two parameters from which we ean calculate the number of electrons transferred, resulting mainly from the eharge transfer between two molecules, i.e., from electrons flow until chemical potential reaehes an equilibrium. As a first approximation, the number of electron transferred is given by ... 

From a more theoretical point of view, the chemical potential, and hardness (and softness) concepts can be rigorously defined in the framework of density functional theory (DFT), allowing their non-empirical evaluation and accurate calculation (see for instance ref.[12] and [13]). DFT is an ab initio approach... 

A number of new results obtained with the "direct" ab initio methods include phonon frequencies, anharmonicities, predictions of displacement patterns, soft-mode phase transitions, effective charges, dielectric constant, local field variations, elements of inverse dielectric matrix, etc. they were all obtained from the same fundamental equations. The Density Functional method opens a way to unified description of ground state properties of solids static, dynamic and dielectric ones. Though all the partial results above are interesting by themselves, they are even more important by providing further tests of and support for the validity of the Density Functional theory. 

WuJZ Density functional theory for chemical engineering from capillarity to soft materials, AIChEJ 52 3) ii69-ii93, 2006. 

Pearson has described S how the concepts of hardness and softness can be understood through application of density functional theory (DFT) to chemical systems and, further, how the results correlate with molecular orbital theory. A firm theoretical basis for the HSAB principle is evolving from these studies that links chemical hardness to absolute electronegativity which, in this sense, refers to the electronic chemical potential of a system rather than the electronegativity of a single atom within a molecule. 

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