Density functional theory theoretical background

This presentation is structured in the following way. The first section outlines the procedure for the quantum mechanics and classical mechanics approach. The following two sections contain an overview of how to establish a density functional theory and molecular mechanics method along with the theoretical background for... 

It has been discussed in Section 2 that concepts such as electronegativity and hardness could explain important aspects of chemical reactions and could be related to different physico-chemical properties. Density functional theory has been found to provide a rigorous theoretical background for electronegativity, hardness, and related concepts. 

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. 

This chapter is devoted to the presentation of the computational methods used for the determination of the thermodynamic and the kinetic data of the compound considered in this work. We give in a first part a theoretical background of the methods used in the present work Electronic Structure Theory (ah initio, and Density Functional Theory), Statistical Mechanics theory. Group Additivity method, and multifrequency Quantum Rice-Ramsperger-Kassel theory (QRRK). 

Density Functional Theory (DFT) aims at the description of the physico-ehemical properties of a system using its electron density, in contrast to traditional quantum chemistry which focuses the attention on the molecular wavefunction. DFT originated in the sixties from a fundamental idea by J.C. Slater and received a solid theoretical background in the papers by P. Hohenberg, W. Kohn and L.J. Sham. 

By its size, this chapter fails to address the entire background of MQS and for more information, the reader is referred to several reviews that have been published on the topic. Also it could not address many related approaches, such as the density matrix similarity ideas of Ciosloswki and Fleischmann [79,80], the work of Leherte et al. [81-83] describing simplified alignment algorithms based on quantum similarity or the empirical procedure of Popelier et al. on using only a reduced number of points of the density function to express similarity [84-88]. It is worth noting that MQS is not restricted to the most commonly used electron density in position space. Many concepts and theoretical developments in the theory can be extended to momentum space where one deals with the three components of linear momentum... 

In the final part the application of concepts from information theory is reviewed. After covering the necessary theoretical background a particular form of the Kullback-Liebler information measure is adopted and employed to define a functional for the investigation of density functions throughout Mendeleev s Table. The evaluation of the constructed functional reveals clear periodic patterns, which are even further improved when the shape function is employed instead of the density functions. These results clearly demonstrate that it is possible to retrieve chemically interesting information from the density function. Moreover the results indicate that the shape function further simplifies the density function without loosing essential information. The latter point of view is extensively treated in [64], where the authors elaborately discuss information carriers such as the wave function, the reduced density matrix, the electron density function and the shape function. 

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