Density functional theory modem approaches

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

The novel approach for calculation of pore size distributions, which is reported in the current study is based on recent developments in the materials science and in the theory of inhomogeneous fluids. First, an application of experimental adsorption data for well-characterized MCM-41 silicas enabled proper calibration of the pore size analysis. Second, an application of a modem theory to describe the behavior of inhomogeneous fluids in confined spaces, that is the non-local density functional theory [6], allowed the numerical calculation of model isotherms for various pore sizes. In addition, a practical numerical deconvolution method that provides a "best fit" solution representing the pore distribution of the sample was implemented [7, 8]. In this paper we describe a deconvolution method for estimating mesopore size distribution that explicitly allows for unfilled large pores, and a method for creating composite, or hybrid, models that incorporate both theoretical calculations and experimental observations. Moreover, we showed the applicability of the new approach in characterization of MCM-41 and related materials. 

A suitable computational approach for the investigation of electronic and geometric structures of transactinide compounds is the fully relativistic Dirac-Slater discrete-variational method (DS-DVM), in a modem version called the density functional theory (DFT) method, which was originally developed in the 1970s (Rosdn and Ellis 1975). It offers a good compromise between accuracy and computational effort. A detailed description can be found in Chapter 4 of this book. 

Rosch, N., Kriiger, S., Mayer, M. andNasluzov.V. A. (1996) The Douglas-Kroll-Hess approach to relativistic density functional theory Methodological aspects and applications to metal complexes and clusters. In Recent Developments and Applications of Modem Density Functional Theory (ed. J. M. Seminario), pp. 497-566. Elsevier. 

Modem density functional theory has provided a very natural framework for molecular physics and quantum chemistry, especially since the formulation of the famous theorem of Hohenberg and Kohn [44, that gives the justification of many of the contemporary computational approaches in electron density modeling. 

Formalizes the atomic structure and reactivity, i.e., the chemical atom, by the algebra of quantum states, eventually continued with Thomas-Fermi realization as the density functional theory precursor, along the modem approach of the electronic localization problem in terms of electronic density combinations ... 

Modem solutions of the time independent Schroedinger eqimtion (equation 1) follow two very different theories wavefimction-based (ab initio Hartree-Fock and correlated methods) and electron density-based (density functional theory, DFT) (15). We will outline these approaches and then describe inq)lementations suitable for nanoscopic problems. 

Most of the ideas of molecular orbital theory are familiar to organic chemists, even if the details of modem computational methods remain somewhat obscure. A very different and often less familiar approach to calculating structure and properties known as density functional theory (DFT) has become prominent in recent years. DFT calculates an observable property, electron density, instead of a nonobservable entity, a molecular orbital. It is important to note that afunctional is not the same as a function. A function acts on a set of variables to produce a number, but a functional acts on another function to produce a number. For example, a wave function is a function, but the dependence of energy on a wave function is a functional. A function is denoted while a functional is denoted F[/]. ... 

Most quantitative calculations in modem quantum chemistry use either valence bond or molecular orbital theory as a starting point, although a third approach, density functional theory, has become increasingly popular in recent years. The impact of density functional theory over the last three decades has been amazing. Its... 

Gradually, the Thomas-Fermi method or its modem descendants, which are known as density functional theories, have become equally powerful compared to methods based on orbitals and wavefimctions and in many cases can outstrip the wavefunction approaches in terms of computational accuracy. The solution is expressed in terms of the variable Z, which represents atomic number, the crucial feature that distinguishes one kind of atom from any other element. One does not need to repeat the calculation separately for each atom, but this advantage applies only in principle, as discussed below. 

The spatial distribution of the electron cloud in a molecular system is investigated quantitatively through the single-particle electron density,which has served as a basic variable in the so-called density functional theory (DFT), an approach that bypasses the many-electron wavefunction, which is the usual vehicle in conventional quantum chemistry or electronic structure theory (for a review of modem developments in quantum chemistry, see reference 7). The theoretical framework of DFT is well known for the associated conceptual simplicity as well as for the computational economy it offers. Another equally important aspect of DFT is its ability to rationalize the existing concepts in chemistry as well as to give birth to newer concepts, which has led to the important field of conceptual DFT. ... 

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