Density functional theories unified framework

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. 

Unified Framework of Multiscale Density Functional Theories and Its Recent Applications... 

In this chapter, a unified framework of multiscale density functional theories (DFTs) is introduced, and we demonstrate that this framework is capable of supplying a versatile tool to address mesoscale phenomena. DFTs are modem statistical mechanics methods, and historically, the foundations of DFTs were first laid in 1964 by Hohenberg and Kohn (FIK) (Hohenberg and Kohn, 1964) who proved that the ground state energy of any QM system could be expressed as a functional of the one-body density only. Basing... 

Figure 4 Schematic graph for the unified framework of density functional theories.

In chapter 2, Profs. Contreras, Perez and Aizman present the density functional (DF) theory in the framework of the reaction field (RF) approach to solvent effects. In spite of the fact that the electrostatic potentials for cations and anions display quite a different functional dependence with the radial variable, they show that it is possible in both cases to build up an unified procedure consistent with the Bom model of ion solvation. The proposed procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy. Especially interesting is the introduction of local indices in the solvation energy expression, the effect of the polarizable medium is directly expressed in terms of the natural reactivity indices of DF theory. The paper provides the theoretical basis for the treatment of chemical reactivity in solution. 

In a recent progress in the QM/MM-ER method we formulated a simple and rigorous functional [24] to evaluate the free energy 8fx arising from the electron density fluctuation of a QM solute in solution. Importantly, this formulation provides a versatile tool which allows various extensions useful for several important applications. For instance, the effect of the electronic polarization of the solvent molecules on the solvation free energy can be treated within a unified framework. Further, the approach can also be applied to the free energy calculation for a QM/MM system where the electron density fluctuation of the QM subsystem is described with the second-order perturbation theory (PT2) [26]. 

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