The density functional theory framework

Density functional theory provides an alternative approach to the description of the electronic structure of atoms and molecules, in principle more simple than conventional wavefunction theory, because the total energy is determined directly from the electronic density distribution p(r), through the expression 

The electronic density of the ground state is determined fi om the Euler-Lagrange equation that results from the variation of Eq. (1) with respect to p(r), subject to the condition that the integral of the latter over the whole space must be equal to the total number of electrons N, 

The problem of a pure density functional theory lies in the fact that the exact forms of T[p] and Exc[p] in terms of p(r) are unknown at the moment [18,19], and the approximations, which are generally based on the generalized gradient expansion, do not provide the accuracy required for chemical properties, such as the bond energies, mainly 

On the other hand, the pure density functional theory provides a conceptual framework that has proven to be very useful to establish expressions that are closely related with chemical concepts, and to rationalize, through the values associated with them, the behavior of a wide variety of chemical species under different circumstances [20]. In order to calculate the values of these quantities, it has become common practice to make use of conventional molecular orbital theory [21-26]. Thus, this procedure allows one to transform the relevant information contained in the wavefunction, into chemically meaningful results, through the bridge provided by pure density functional theory. 

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The overall analysis presented in this work shows that through the use of the density functional theory framework one may establish a simple unified approach to bond energies, activation energies, and reaction energies, in terms of hardness differences. 

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