Density functional theory quantum chemistry

In this chapter we have largely relied on computational chemistry, in particular on density-functional theory. Quantum mechanical calculations of a macroscopic piece of metal with various species adsorbed on it are as yet impossible, but it is possible to obtain realistic results on simplified systems. One approach is to simulate the metal by a cluster of 3-30 atoms on which the molecule adsorbs and then describe all the involved orbitals. Many calculations have been performed on this basis with many useful results. Obviously, the cluster must be sufficiently large that the results do not represent an artefact of the particular cluster size chosen, which can be verified by varying the cluster size. 

Abstract. The paper by Johnson and Smith is representative of the Xa -scattered wave (SW) effort of the 1970s. Despite the severe approximations that were necessary at the time, the paper shows that a first-principles Xa calculation yields a compelling account of the electronic structure and spectrum of permanganate. Contemporaneous semiempirical and ab initio calculations were not up to the task. The quality of the results and the prospect of treating really large systems were sufficient to attract the attention of many quantum chemists (as well as the disdain of some and the ire of others). The Xa-SW work was an important link in the chain of contributions that would bring density functional theory into chemistry. 

The next block of chapters (by T.Helgaker, K.Ruud and P.R.Taylor, by W.Quapp, O.Imig, and D.Heidrich, and by G.Seifert and K.Kruger) is dedicated to the mathematical and quantum chemical techniques of calculating points on the RP. The last of these chapters includes a review of applications of the density functional theory in chemistry. 

Ira N. Levine, Quantum Chemistry, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 1991. (Source for density functional theory.)... 

A comprehensive treatment of density functional theory, an idea that is currently very popular in quantum chemistry. 

Density functional theory-based methods ultimately derive from quantum mechanics research from the 1920 s, especially the Thomas-Fermi-Dirac model, and from Slater s fundamental work in quantum chemistry in the 1950 s. The DFT approach is based upon a strategy of modeling electron correlation via general functionals of the electron density. 

Parr, R.G. Aspects of Density Functional Theory . In Local Density Approximations in Quantum Chemistry and Solid State Physics , Dahl, J.P. and Avery, J., Eds. Plenum Press New York, 1984, pp. 21-31. 

Suzumura, T., Nakajima, T. and Hirao, K. (1999) Ground-state properties of MH, MCI, and M2 (M—Cu, Ag, and Au) calculated by a scalar relativistic density functional theory International Journal of Quantum Chemistry, 75, lVJ-1. ... 

The usual way chemistry handles electrons is through a quantum-mechanical treatment in the frozen-nuclei approximation, often incorrectly referred to as the Born-Oppenheimer approximation. A description of the electrons involves either a wavefunction ( traditional quantum chemistry) or an electron density representation (density functional theory, DFT). Relativistic quantum chemistry has remained a specialist field and in most calculations of practical... 

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. 

Dunlap, B. I., 1987, Symmetry and Degeneracy in Xa and Density Functional Theory in Ab Initio Methods in Quantum Chemistry - II, Lawley, K. P. (ed.), Wiley, Chichester. 

Handy, N. C., 1994, Density Functional Theory in Lecture Notes in Quantum Chemistry II, Roos, B. O. (ed.), Springer, Heidelberg. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

In recent years, density-functional theory has emerged as the computational quantum chemistry method of choice for biological problems of medium size range (up to a few hundreds of atoms) in applications that do not require extensive conformational sampling. The field continues to advance in the accuracy of new functionals, the improvement of algorithms and the functionality and computational performance of software [81]. 

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. 

These few remarks highlight that quantum-chemical methods have adapted an important role in medicinal chemistry. It is the intention of the present volume to document this role in adequate detail. Accordingly, the book is divided into three main sections. The first section is dedicated to density functional theory. 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

Vargas, R., Cedillo, A., Garza, J., and Galvan, M. 2002. Reactivity criteria in spin-polarized density functional theory. In Reviews of Modem Quantum Chemistry, ed. 

The advent of density functional theory (DFT) [1,2] has had a profound impact on quantum and computational chemistry. The ingenious proof, given in 1964 by Hohenberg and Kohn [1], that the wave function of a many-electron system... 

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