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

"Chemists accustomed to traditional quantum mechanics will applaud and gain significantly from this rather instructive, thorough and obviously written exposition of density practical concept: its foundation, innovations, phrases, implementation, and function in diversified functions. clients of DFT for constitution, strength, and molecular estate computations, in addition to response mechanism experiences, are guided to the optimal offerings of the best tools. good done!"

Paul von Ragu?chleyer

"A conspicuous gap within the computational chemist's library is well stuffed by means of this booklet, 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 target 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 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 great carrier to the chemical group. [...] A Chemist's advisor to Density sensible conception is precisely what the name indicates. it's going to be a useful resource of perception and information for plenty of chemists utilizing DFT ways to unravel chemical problems."

M. Kaupp, Angew. Chem.

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

**Sample text**

2 (see also Baerends and Gritsenko, 1997). 2 The Coulomb Hole From equations (2-17) and (2-21) it is obvious that the Coulomb hole must be normalized to zero, i. e. the integral over all space contains no charge: r r r ∫ h C ( r1; r2 ) dr2 = 0. (2-25) This makes good physical sense since for electrons of unlike spin the probability of finding an electron of spin σ anywhere in space is of course the total number of electrons of this spin, i. , Nσ. This result is independent of the positions of electrons with spin σ’ ≠ σ.

Nσ. This result is independent of the positions of electrons with spin σ’ ≠ σ. Also, there is no need for a self-interaction correction. The Coulomb hole will be negative and largest at the position of the reference electron since it originates from the 1/r12 electrostatic interaction which keeps electrons apart. Since there is a finite probability that two electrons of different spin (and approximated r r as volume-less point charges) can be found within the same volume element h C ( r1; r1 ) has no predetermined value at vanishing r r r interelectronic distance, unlike the Fermi hole which for r2 → r1 approaches −ρ( r1 ) .

If we want to make the distinction from the Fermi correlation, the electrostatic effects are known under the label Coulomb correlation. It can easily be shown that the HF approximation discussed in Chapter 1 does include the Fermi-correlation, but completely neglects the Coulomb part. To demonstrate this, we analyze the Hartree-Fock pair density for a two-electron system with the two spatial orbitals φ1 and φ2 and spin functions σ1 and σ2 2 r r r r ρHF 2 (x1 , x 2 ) = det {φ1 (r1 )σ1 (s1 ) φ2 (r2 )σ2 (s2 )} (2-11) which after squaring the expanded determinants becomes r 2 r 2 r r 2 2 ρHF 2 (x1 , x2 ) = φ1 (r1 ) φ2 (r2 ) σ1 (s1 ) σ2 (s2 ) r r +φ1 (r2 )2 φ2 (r1 )2 σ1 (s2 )2 σ2 (s1 )2 r r r r −2 φ1 (r1 ) φ2 (r1 ) φ1 (r2 ) φ2 (r2 ) σ1 (s1 ) σ2 (s1 ) σ1 (s2 ) σ2 (s2 ) (2-12) r The spin-independent probability of finding one electron at r1 and the other simulr taneously at r2 is obtained by integrating over the spins.