By Prof. Dr. Wolfram Koch, Dr. Max C. Holthausen(auth.)
"Chemists acquainted with traditional quantum mechanics will applaud and profit enormously from this fairly instructive, thorough and obviously written exposition of density sensible conception: its foundation, ideas, phrases, implementation, and function in varied 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 simplest tools. good done!"
Paul von Ragu?chleyer
"A conspicuous gap within the computational chemist's library is well stuffed by way of this publication, which gives a wide-ranging and pragmatic view of the subject.[...It] may still justifiably turn into the favourite textual content at the topic for practitioners who goal to take advantage of DFT to resolve chemical problems."
J. F. Stanton, J. Am. Chem. Soc.
"The authors' target is to steer the chemist via simple theoretical and comparable 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 an exceptional carrier to the chemical neighborhood. [...] A Chemist's advisor to Density practical thought is precisely what the name indicates. it's going to be a useful resource of perception and data for plenty of chemists utilizing DFT techniques to unravel chemical problems."
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Additional resources for A Chemist's Guide to Density Functional Theory, Second Edition
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.
We further assume that within the sphere the exchange hole density is constant, having H minus the value of ρ( r1 ) , while outside it is zero. Since the Fermi hole is known to contain exactly one elementary charge (cf. equation (2-21)), the radius of this sphere is then given by 3 rS = 4π 1/ 3 H ρ( r1 ) −1 / 3 . (3-4) The radius rS is sometimes called the Wigner-Seitz radius and can be interpreted to a first approximation as the average distance between two electrons in the particular system.
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 ) . Among the other properties of the density, we mention its asymptotic exponential decay for large distances from all nuclei riA → 0 ∂r r r ρ(r) ∝ exp[−2 2 I |r|] (2-5) where I is the exact first ionization energy of the system. As a typical example we illustrate in Figure 2-1 the electron density of the water molr ecule in two different representations.