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A Chemist's Guide to Density Functional Theory by Wolfram Koch

By Wolfram Koch

"Chemists accustomed to traditional quantum mechanics will applaud and gain tremendously from this fairly instructive, thorough and obviously written exposition of density practical concept: its foundation, suggestions, phrases, implementation, and function in assorted functions. clients of DFT for constitution, power, and molecular estate computations, in addition to response mechanism reports, are guided to the optimal offerings of the best tools. good done!"Paul von Ragu? Schleyer"A conspicuous gap within the computational chemist's library is properly crammed via this booklet, which supplies a wide-ranging and pragmatic view of the subject.[...It] should still justifiably turn into the favourite textual content at the topic for practitioners who goal to exploit DFT to unravel chemical problems."J. F. Stanton, J. Am. Chem. Soc."The authors' target is to steer the chemist via simple theoretical and similar technical points of DFT at an easy-to-understand theoretical point. They be successful admirably."P. C. H. Mitchell, Appl. Organomet. Chem."The authors have performed a good carrier to the chemical neighborhood. [...] A Chemist's advisor to Density useful concept is strictly what the identify indicates. it may be a useful resource of perception and data for lots of chemists utilizing DFT methods to unravel chemical problems."M. Kaupp, Angew. Chem.

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2 The Second Hohenberg-Kohn Theorem: Variational Principle Up to this point we have established that the ground state density is in principle sufficient to obtain all properties of interest. But, how can we be sure that a certain density is really the ground state density that we are looking for? A formal prescription for how this problem should be tackled has been given through the second theorem proven by Hohenberg and Kohn in their 1964 contribution. In plain words, this theorem states that FHK[ρ], the functional that delivers the ground state energy of the system, delivers the lowest energy if and only if the input density is the true ground state density, ρ0.

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. The theorems proven in this report represent the major theoretical pillars on which all modern day density functional theories are erected. This chapter introduces these Hohenberg-Kohn theorems and discusses their obvious and maybe not so obvious consequences.

It applies equally well to neutral fermions and – also this is very important to keep in mind – does not hold if the two electrons have different spin. This effect is known as exchange or Fermi correlation. As we will show below, this kind of correlation is included in the Hartree-Fock approach due to the antisymmetry of a Slater determinant and therefore has nothing to do with the correlation energy E HF C discussed in the previous chapter. Next, let us explore the consequences of the charge of the electrons on the pair density.

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