By Prof. Dr. Wolfram Koch, Dr. Max C. Holthausen(auth.)

"Chemists acquainted with traditional quantum mechanics will applaud and profit drastically from this rather instructive, thorough and obviously written exposition of density useful concept: its foundation, strategies, phrases, implementation, and function in assorted purposes. clients of DFT for constitution, power, and molecular estate computations, in addition to response mechanism experiences, are guided to the optimal offerings of the best equipment. good done!"

Paul von Ragu?chleyer

"A conspicuous gap within the computational chemist's library is properly stuffed by way of this ebook, which supplies a wide-ranging and pragmatic view of the subject.[...It] may still justifiably develop into the favourite textual content at the topic for practitioners who objective to take advantage of DFT to resolve chemical problems."

J. F. Stanton, J. Am. Chem. Soc.

"The authors' objective is to steer the chemist via easy theoretical and similar technical elements of DFT at an easy-to-understand theoretical point. They be triumphant admirably."

P. C. H. Mitchell, Appl. Organomet. Chem.

"The authors have performed a very good provider to the chemical neighborhood. [...] A Chemist's advisor to Density useful concept is precisely what the identify indicates. it may be a useful resource of perception and information for plenty of chemists utilizing DFT ways to resolve chemical problems."

M. Kaupp, Angew. Chem.

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**Extra resources for A Chemist's Guide to Density Functional Theory, Second Edition**

**Example text**

One of its important features is that at any posir tion of an atom, ρ( r ) exhibits a maximum with a finite value, due to the attractive force exerted by the positive charge of the nuclei. However, at these positions the gradient of the density has a discontinuity and a cusp results. This cusp is a consequence of the singularity Z in the − A part in the Hamiltonian as riA → 0. Actually, it has long been recognized that riA 19 2 Electron Density and Hole Functions O H H a) b) Figure 2-1. ). the properties of the cusp are intimately related to the nuclear charge Z of the nucleus according to ∂ r (2-4) lim + 2 ZA ρ( H ) = 0 r r where ρ( r ) is the spherical average of ρ( r ) .

It includes the correction for the self-interaction as well as all contributions of quantum-mechanical correlation effects. It should be obvious by now why the hole functions are so useful for discussing exchange and correlation effects. The more we know about the characteristics of hXC and the better the approximate hole functions we use in our calculations resemble the true ones, the more accurate results we can expect. r r The exchange-correlation hole can formally be split into the Fermi hole, h σX1 = σ2 ( r1 , r2 ) r r σ ,σ and the Coulomb hole h C1 2 ( r1 , r2 ) , r r r r r r D :+ ( H; r ) = D σ: =σ2 ( H; H ) + h σC1 ,σ2 (r1 , r2 ) (2-20) where the former is the hole in the probability density of electrons due to the Pauli principle, i.

The important point is that all parts are expressed as pure functionals of the density. Since, just like the original Thomas-Fermi model, the Thomas-Fermi-Dirac extension was also not very successful in chemical applications, we will not discuss it any further. 32 A Chemist’s Guide to Density Functional Theory. Second Edition Wolfram Koch, Max C. Holthausen Copyright © 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-30372-3 (Softcover); 3-527-60004-3 (Electronic) 4 The Hohenberg-Kohn Theorems Density functional theory as we know it today was born in 1964 when a landmark paper by Hohenberg and Kohn appeared in the Physical Review.