Density-functional theory foundations

Engel, E. Keller, S. Dreizler, R. M. Phys. Rev. A 1996, 53, 1367-1374 Engel, E. Relativistic density functional theory foundations and basic formalism. In Relativistic Electronic Structure... 

RELATIVISTIC DENSITY FUNCTIONAL THEORY FOUNDATIONS AND BASIC FORMALISM... 

Engel, E. Relativistic density functional theory Foundations and basic formalism. In Schwerdtfeger, P. (ed.) Relativistic Electronic Structure Theory, Part I, pp. 523-621. Elsevier, Amsterdam (2002)... 

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. 

FORMAL FOUNDATIONS OF DENSITY FUNCTIONAL THEORY FOR TIME-DEPENDENT ELECTRIC AND MAGNETIC FIELDS... 

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]... 

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... 

The methods of structure determination of supported nanoclusters are essentially the same as those mentioned previously for supported metal complexes. EXAFS spectroscopy plays a more dominant role for the metal clusters than for the complexes because it provides good evidence of metal-metal bonds. Combined with density functional theory, EXAFS spectroscopy has provided much of the structural foundation for investigation of supported metal clusters. EXAFS spectroscopy provides accurate determinations of metal-metal distances ( 1-2%), but it gives only average structural information and relatively imprecise values of coordination numbers. EXAFS spectroscopy provides structure data that are most precise when the clusters are extremely small (containing about six or fewer atoms) and nearly uniform (Alexeev and Gates, 2000). 

Quantum chemical simulations based on density functional theory (DFT) are widely regarded as reaching the appropriate compromise between chemical accuracy and the need to study structurally complex extended materials in order to tackle problems associate with heterogeneous catalysis involving alloys. A review of DFT and heterogeneous catalysis can be found in the previous SPR and that review also listed several general reviews of applications and foundations of DFT. Experimental and theoretical studies of monolayer bimetallic surfaces were recently reviewed. In... 

The theory of catalysis has been notably advanced through the work in density functional theory (DFT) of Jens Norskov. He and coworkers have formulated scaling models of catalytic rates dependent upon an element s position in the periodic table and surface structural factors linked to low coordinate and highly active catalytic sites on the surface of that element. This work provides a quantitative foundation... 

In this section we provide a unified point of view of the different theoretical methods used in the study of electronic structure. This includes two rather different families of methods that nevertheless arise from the principles of quantum mechanics. On the one hand, one has the ab initio methods of computation of electronic wave functions and, on the other hand, one has the methods based in the modern density functional theory. In the forthcoming discussion we attempt to focus mainly on the physical significance rather than on mathematical foundation and technical aspects of computer implementation. Details of the methods outlined in this section can be found in specialized references, monographs [70], and textbooks [71]. 

At the present time, by far the most useful non-empirical alternatives to Cl are the methods based on density functional theory (DFT) . The development of DFT can be traced from its pre-quantum-mechanical roots in Drude s treatment of the electron gas" in metals and Sommerfeld s quantum-statistical version of this, through the Thomas-Fermi-Dirac model of the atom. Slater s Xa method, the laying of the formal foundations by... 

---