Basic density-functional theory

Basically, density functional theory (DFT) is similar to the ab initio method, but it is not based on a wavefunction. Instead, the energy is computed as a functional of the electron density (16). The DFT methods were developed that are much faster than Gaussian-style programs. Currently, many functional approximations are in use. 

Basic density-functional theory in the Hohenberg-Kohn and Kohn-Sham formulations " " is a time-independent, i.e. a static, approach. To remind the reader, the two Hohenberg-Kohn theorems state and prove (i) that there is a one-to-one mapping between the real system of interest and the artificial system of non-interacting particles that is described, and (ii) that the variational principle holds for this system. These two theorems and the Kohn-Sham equations that are used to perform the actual calculation need to be derived for time-dependent processes as well. 

In this section we introduce the basic ingredients of a field-theoretic approach to electrified interfaces and compare it with both the standard method of statistical mechanics and the density functional theory. 

Gross, E. K. U., Oliveira, L. N., Kohn, W., 1988b, Density-Functional Theory for Ensembles of Fractionally Occupied States. I. Basic Formalism , Phys. Rev. A, 37, 2809. 

There are many varieties of density functional theories depending on the choice of ideal systems and approximations for the excess free energy functional. In the study of non-uniform polymers, density functional theories have been more popular than integral equations for a variety of reasons. A survey of various theories can be found in the proceedings of a symposium on chemical applications of density functional methods [102]. This section reviews the basic concepts and tools in these theoretical methods including techniques for numerical implementation. 

During the last decade, density-functional theory (DFT)-based approaches [1, 2] have advanced to prominent first-principles quantum chemical methods. As computationally affordable tools apt to treat fairly extended systems at the correlated level, they are also of special interest for applications in medicinal chemistry (as demonstrated in the chapters by Rovira, Raber et al. and Cavalli et al. in this book). Several excellent text books [3-5] and reviews [6] are available as introduction to the basic theory and to the various flavors of its practical realization (in terms of different approximations for the exchange-correlation functional). The actual performance of these different approximations for diverse chemical [7] and biological systems [8] has been evaluated in a number of contributions. 

It is however possible to obtain a physically meaningful representation of 0(r) for cations, in the context of density functional theory. The basic expression here is the fundamental stationary principle of DFT, which relates the electronic chemical potential ju, with the electrostatic potential and the functional derivatives of the kinetic and exchange-correlation contributions [20] ... 

Local density functional theory may be introduced within the RF model of solvent effects thorugh the induced electron density. The basic quantity for such a development is the linear density response function [39] ... 

In the last three decades, density functional theory (DFT) has been extensively used to generate what may be considered as a general approach to the description of chemical reactivity [1-5]. The concepts that emerge from this theory are response functions expressed basically in terms of derivatives of the total energy and of the electronic density with respect to the number of electrons and to the external potential. As such, they correspond to conceptually simple, but at the same time, chemically meaningful quantities. 

Although one could consider the electron density as just one of the many quantum chemical descriptors available, it deserves special attention. In QSM, it is the only descriptor used for a number of reasons. The idea of using the electron density as the ultimate molecular descriptor is founded on the basic elements of quantum mechanics. First of all, it is the all-determinmg quantity in density functional theory (DFT) [11] and also holds a very close relation to the wave function. Convincing arguments were given by Handy and are attributed to Wilson [12], although initial ideas can also be traced back to Bom [13] and von... 

Density functional theory (DFT) uses the electron density p(r) as the basic source of information of an atomic or molecular system instead of the many-electron wave function T [1-7]. The theory is based on the Hohenberg-Kohn theorems, which establish the one-to-one correspondence between the ground state electron density of the system and the external potential v(r) (for an isolated system, this is the potential due to the nuclei) [6]. The electron density uniquely determines the number of electrons N of the system [6]. These theorems also provide a variational principle, stating that the exact ground state electron density minimizes the exact energy functional F[p(r)]. 

The basic variable in density functional theory (DFT)22 is the electron density n(r). In the usual implementation of DFT, the density is calculated from the occupied single-particle wave functions (r) of an auxiliary system of noninteracting electrons... 

Hypercube, Inc. at http //www.hyper.com offers molecular modeling packages under the HyperChem name. HyperChem s newest version, Hyper-Chem Release 7.5, is a full 32-bit application, developed for the Windows 95, 98, NT, ME, 2000, and XP operating systems. Density Functional Theory (DFT) has been added as a basic computational engine to complement Molecular Mechanics, Semiempirical Quantum Mechanics and ab initio Quantum Mechanics. The DFT engine includes four combination or hybrid functions, such as the popular B3-LYP or Becke-97 methods. The Bio+ force field in HyperChem represents a version of the Chemistry at HARvard using Molecular Mechanics (CHARMM) force field. Release 7.5 of HyperChem updates... 

The basic quantity in density functional theory is the energy functional which within constrained search [24, 25] is defined as... 

In variational treatments of many-particle systems in the context of conventional quantum mechanics, these symmetry conditions are explicitly introduced, either in a direct constructive fashion or by resorting to projection operators. In the usual versions of density functional theory, however, little attention has b n payed to this problem. In our opinion, the basic question has to do with how to incorporate these symmetry conditions - which must be fulfilled by either an exact or approximate wavefunction - into the energy density functional. 

For completeness, we need to point out that the name density functional theory is not solely applied to the type of quantum mechanics calculations we have described in this chapter. The idea of casting problems using functionals of density has also been used in the classical theory of fluid thermodynamics. In this case, the density of interest is the fluid density not the electron density, and the basic equation of interest is not the Schrodinger equation. Realizing that these two distinct scientific communities use the same name for their methods may save you some confusion if you find yourself in a seminar by a researcher from the other community. 

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