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DENSITY-FUNCTIONAL THEORY OF THE ELECTRONIC STRUCTURE OF MOLECULES'
Recent fundamental advances in the density-functional theory of elec tronic structure are summarized. Emphasis is given to four aspects of the subject: (a) tests of functionals, (b) new methods for determining accurate exchange-correlation functionals, (c) linear scaling methods, and (d) devel opments in the description of chemical reactivity.
Density functional theory: An introduction
American Journal of Physics, 2000
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often considered too lengthy to be included in various curricula. An alternative introduction to DFT is presented here, drawing on ideas which are well-known from thermodynamics, especially the idea of switching between different independent variables. The central theme of DFT, i.e. the notion that it is possible and beneficial to replace the dependence on the external potential v(r) by a dependence on the density distribution n(r), is presented as a straightforward generalization of the familiar Legendre transform from the chemical potential µ to the number of particles N. This approach is used here to introduce the Hohenberg-Kohn energy functional and to obtain the corresponding theorems, using classical nonuniform fluids as simple examples. The energy functional for electronic systems is considered next, and the Kohn-Sham equations are derived. The exchange-correlation part of this functional is discussed, including both the local density approximation to it, and its formally exact expression in terms of the exchange-correlation hole. A very brief survey of various applications and extensions is included.
Improving Results by Improving Densities: Density-Corrected Density Functional Theory
Journal of the American Chemical Society
DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This article explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.
A quantum chemical view of density functional theory
The Journal of Physical Chemistry …, 1997
A comparison is made between traditional quantum chemical approaches to the electron correlation problem and the one taken in density functional theory (DFT). Well-known concepts of DFT, such as the exchangecorrelation energy E xc ) ∫F(r) xc (r) dr and the exchange-correlation potential V xc (r) are related to electron correlation as described in terms of density matrices and the conditional amplitude (Fermi and Coulomb holes). The Kohn-Sham one-electron or orbital model of DFT is contrasted with Hartree-Fock, and the definitions of exchange and correlation in DFT are compared with the traditional ones. The exchangecorrelation energy density xc (r) is decomposed into kinetic and electron-electron potential energy components, and a practical way of calculating these from accurate wave functions is discussed, which offers a route to systematic improvement. V xc (r) is likewise decomposed, and special features (bond midpoint peak, various types of step behavior) are identified and related to electronic correlation. X Figure 4. Correlation energy density in He compared to a number of model correlation energy densities: PW, Perdew-Wang; 11 WL, Wilson-Levy; 127 LYP, Lee-Yang-Parr; 8 LW, local Wigner. 126 (a) -F(r) c(r) from r ) 0.0-0.5 bohr. (b) -4π r 2 F(r) c(r) from r ) 0.0-2.0 bohr. Feature Article
2013
Se presentan los fundamentos matematicos de la teoria funcional de la densidad DFT en este trabajo. Empezamos con el inicio de la mecanica cuantica de esta teoria, es decir, el modelo de Thomas-Fermi (TF), que utiliza la densidad de electrones n (R), una funcion de solo 3 coordenadas, como la unica variable fisica. A continuacion mostramos la fundacion formal de DFT, los teoremas de Hohenberg y Kohn, expresados en una teoria bien establecida representada por pruebas twoexcited. Le mostramos al final del articulo como Kohn y Sham (KS) idearon una aplicacion practica y trajeron DFT en los calculos de la corriente principal de la estructura electronica.
An Introduction to Density Functional Theory
For the past 30 years density functional theory has been the dominant method for the quantum mechanical simulation of periodic systems. In recent years it has also been adopted by quantum chemists and is now very widely used for the simulation of energy surfaces in molecules. In this lecture we introduce the basic concepts underlying density functional theory and outline the features that have lead to its wide spread adoption. Recent developments in exchange correlation functionals are introduced and the performance of families of functionals reviewed. The lecture is intended for a researcher with little or no experience of quantum mechanical simulations but with a basic (undergraduate) knowledge of quantum mechanics. We hope to provide sufficient background to enable informed judgements on the applicability of a particular implementation of density functional theory to a specific problem in materials simulation. For those who wish to go more deeply into the formalism of density functional theory there are a number of reviews and books aimed at intermediate and advanced levels available in the literature [1,2,3]. Where appropriate source articles are referred to in the text.
4. QUANTUM CHEMISTRY METHODS: II DENSITY FUNCTIONAL THEORY
The Density Functional Theory (DFT)(Parr, 1989) represents an alternative to the conventional ab initio methods of introducing the effects of electron correlation into the solution to the electronic Schrödinger equation. According to the DFT, the energy of the ground state of a many-electron system can be expressed through the electron density, and in fact, the use of the electron density in place of the wave function to calculate the energy is the foundation of the DFT.
A new density functional method for electronic structure calculation of atoms and molecules
arXiv: Chemical Physics, 2019
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradi...
A well-tempered density functional theory of electrons in molecules
Physical chemistry chemical physics : PCCP, 2007
This Invited Article reports extensions of a recently developed approach to density functional theory with correct long-range behavior (R. Baer and D. Neuhauser, Phys. Rev. Lett., 2005, 94, 043002). The central quantities are a splitting functional gamma[n] and a complementary exchange-correlation functional E[n]. We give a practical method for determining the value of gamma in molecules, assuming an approximation for E is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond lengths of the molecules in the G2(1) database. The optimized val...