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

"Chemists conversant in traditional quantum mechanics will applaud and gain drastically from this quite instructive, thorough and obviously written exposition of density useful thought: its foundation, recommendations, phrases, implementation, and function in various purposes. clients of DFT for constitution, strength, and molecular estate computations, in addition to response mechanism stories, 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 properly stuffed by means of this ebook, which supplies 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 objective to exploit DFT to unravel chemical problems."

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

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M. Kaupp, Angew. Chem.

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

**Example text**

The common denominator in our discussion is the primacy of the applicationoriented understanding over the puristic theoretical point of view. Readers who have also an affinity towards the latter and want to learn more about the many theoretical intricacies of the Hohenberg-Kohn theorems are recommended to consult the comprehensive and theoretically sound discussions contained in Parr and Yang, 1989, Kryachko and Ludeña, 1990, Dreizler and Gross, 1995 and Eschrig, 1996. 1 The First Hohenberg-Kohn Theorem: Proof of Existence The first Hohenberg-Kohn theorem provides the proof that our plausibility arguments given at the beginning of the previous chapter are indeed physically justified.

15 1 Elementary Quantum Chemistry in the HF picture let us recall from basic quantum mechanics that the HF ground state wave function of the H2 molecule is the Slater determinant where the bonding σ orbital is doubly occupied Φ GS = 1 2 r r det{σg (r1 ) α(s1 ) σg (r2 ) β(s2 )} . (1-31) Using the simplest picture (and neglecting the effect of overlap on the normalization), this doubly occupied σg spatial molecular orbital can be thought of as being the symmetric linear combination of the two 1s atomic orbitals on the ‘left’ and ‘right’ hydrogens, HL and HR σg = 1 2 {1sL + 1sR } .

On the other hand, in the UHF scheme we are always dealing with single-determinantal wave functions. However, the major disadvantage of the UHF technique is that unlike the true and also the ROHF wave function, a UHF Slater determinant is no longer an eigenfunction of the total spin operator, Sˆ 2 . The more the 〈Sˆ 2 〉 expectation value of a Slater determinant deviates from the correct value – i. , S(S+1) where S is the spin quantum number representing the total spin of the system – the more this unrestricted determinant is contaminated by functions corresponding to states of higher spin multiplicity and the less physically meaningful it obviously gets.