Foundations of the 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]... 

In this work we have given on overview of the mathematical foundations of stationary density functional theory. We discussed in great detail the question of differentiability of the functionals and showed that the Kohn-Sham theory can be put on a solid basis for all practical purposes, since the set of noninteracting E-V-densities is dense in the set of interacting E-V-densities. The question whether these two sets are in fact identical is still an open question. We further discussed two systematic approaches for the construction of the exchange-correlation functional and potential. What can we say about future developments within density functional theory There have been many extensions of density functional theory involving... 

An overview of relativistic density functional theory (RDFT) is presented with special emphasis on its field theoretical foundations and the construction of relativistic density functionals. A summary of quantum electrodynamics (QED) for bound states provides the background for the discussion of the relativistic generalization of the Hohenberg-Kohn theorem and the effective single-particle equations of RDFT. In particular, the renormalization procedure of bound state QED is reviewed in some detail. Knowledge of this renormalization scheme is pertinent for a careful derivation of the RDFT concept which necessarily has to reflect all the features of QED, such as transverse and vacuum corrections. This aspect not only shows up in the existence proof of RDFT, but also leads to an extended form of the single-particle equations which includes radiative corrections. The need for renormalization is also evident in the construction of explicit functionals. 

A more rigorous foundation of a density-based theory was provided by the Hohen-berg and Kohn treatment [17,18], where they stated that the ground-state properties of an inhomogeneous many-body system can be expressed as a unique functional of its particle density. 

The reaction mechanism of VC is not yet determined. From the density functional theory (DFT) calculations of supermolecules, (EC) Li (VC), the possibility that EC is cleaved through intermolecular electron transfer from VC to EC was proposed. " Among the cyclic carbonates, VC is most susceptible to a two-electron reduction, possibly one of the characteristics as an additive for SEI film formation, although polymerization of the one-electron reduction product is likely to proceed in parallel for building a foundation for SEI film. ... 

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... 

It is a truism that in the past decade density functional theory has made its way from a peripheral position in quantum chemistry to center stage. Of course the often excellent accuracy of the DFT based methods has provided the primary driving force of this development. When one adds to this the computational economy of the calculations, the choice for DFT appears natural and practical. So DFT has conquered the rational minds of the quantum chemists and computational chemists, but has it also won their hearts To many, the success of DFT appeared somewhat miraculous, and maybe even unjust and unjustified. Unjust in view of the easy achievement of accuracy that was so hard to come by in the wave function based methods. And unjustified it appeared to those who doubted the soundness of the theoretical foundations. There has been misunderstanding concerning the status of the one-determinantal approach of Kohn and Sham, which superficially appeared to preclude the incorporation of correlation effects. There has been uneasiness about the molecular orbitals of the Kohn-Sham model, which chemists used qualitatively as they always have used orbitals but which in the physics literature were sometimes denoted as mathematical constructs devoid of physical (let alone chemical) meaning. 

Acknowledgment The author is indebted to the US National Science Foundation for support of this workunder Grant CHE-0716718. This article is dedicated to the memory of Prof. loan Silaghi-Dumitrescu (1950-2009) in recognition of the pivotal role that he played in density functional theory studies on bare post-transition element clusters. 

As the wave function is not known analytically for systems larger than a hydrogen-like atom, suitable approximate wave functions have to be found and the accuracy of Eq. (1) depends of course on the level of approximation. A survey of the various quantum chemical methods to generate approximated wave functions can be found in Refs. (22,23). Here, we shall only present the foundations of Hartree-Fock and density functional theory (DFT) needed in later sections. 

Cortright and Dumesic present an update of progress in reaction kinetics, showing how it is providing a broader and sturdier foundation for heterogeneous catalysis. The chapter illustrates how the power of computers and modern theoretical methods, exemplified by density functional theory, allow the incorporation of numerous elementary steps and realistic models of... 

---