By Holtje, Hans-Dieter
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Extra info for A Chemists Guide to Density Functional Theory
6 Electron correlation can most economically be accounted for through second order perturbation theory due to Møller and Plesset. This frequently used level is abbreviated MP2. MP4, i. , Møller-Plesset perturbation theory to fourth order is also often used. This technique is more accurate but also significantly more costly than MP2: while MP2 formally scales with the fifth power of the system size, MP4 scales as O(m7); m being a measure of the molecular size. 7 Other popular methods are based on configuration interaction (CI), quadratic CI (QCI) and coupled cluster approaches (CC).
6 A Figure 2-2. Fermi, Coulomb and the resulting total exchange-correlation holes for H2 at three different internuclear distances; the position of the probe electron is marked with an arrow (adapted from Baerends and Gritsenko, J. Phys. Chem. A, 101, 5390 (1997), with permission by the American Chemical Society). 28 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) 3 The Electron Density as the Basic Variable: Early Attempts In this section we will approach the question which is at the very heart of density functional theory: can we possibly replace the complicated N-electron wave function with its dependence on 3N spatial plus N spin variables by a simpler quantity, such as the electron density?
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.
A Chemists Guide to Density Functional Theory by Holtje, Hans-Dieter