Density Functional Theory HSAB principle

The HSAB principle can be considered as a condensed statement of a very large amount of experimental information, but cannot be labelled a law, since a quantitative definition of the intuitive concepts of chemical hardness (T ) and softness (S) was lacking. This problem was solved when the hardness found an exact, and also an operational, definition in the framework of the Density Functional Theory (DFT) by Parr and co-workers [2], In this context, the hardness is defined as the second order derivative of energy with respect to the number of electrons and has the meaning of resistance to change in the number of electrons. The softness is the inverse of the hardness [3]. Moreover, these quantities are defined in their local version [4, 5] as response functions [6] and have found a wide application in the chemical reactivity theory [7],... 

Density functional theory suggests that the HSAB principle, which was initially formulated to study global changes in a reaction, can also be applied to local inter-... 

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 energy gap between HOMO and LUMO has been equated to the absolute hardness of the HSAB principle. This principle describes some basic rules about kinetics and equilibrium of the acid-base interactions in solutions. The HSAB principle will be described as it has evolved in recent years on the basis of the density-functional theory. "For organic interactions, the following statements were proposed ... 

It is shown that Density Functional Theory offers both a conceptual and a computational tool for chemists in relating electronic structure of atoms and molecules to their properties both as isolated systems and upon interaction. The computational performance of DFT in the calculation of typical DFT quantities such as electronegativity and hardness and in the ev uation of atomic electronic affinities and molecular dipole and quadrupole momCTits is assessed. DFT concepts are discussed as such (a non finite difference evaluation of the electronic Fukui function, local softness and its use in similarity analysis of peptideisosteres and the nuclear Fukui function as a indicator of nuclear rearrangemCTits upon reaction) and in the context of principles (EEM, MHP, HSAB) for a variety of reactions involving the influence of solvent on the acidity of alcohols and the addition of HNC to dipolarophiles. 

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. 

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

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