By Carlos Fiolhais, Fernando Nogueira, Miguel A.L. Marques

ISBN-10: 3540030832

ISBN-13: 9783540030836

Density practical thought (DFT) is by way of now a well-established process for tackling the quantum mechanics of many-body structures. initially utilized to compute homes of atoms and straightforward molecules, DFT has fast turn into a piece horse for extra complicated functions within the chemical and fabrics sciences. the current set of lectures, spanning the total variety from simple ideas to relativistic and time-dependent extensions of the speculation, is the precise creation for graduate scholars or nonspecialist researchers wishing to familiarize themselves with either the elemental and so much complicated concepts during this box.

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**Additional info for A Primer in Density Functional Theory**

**Sample text**

176) is δGLSD ∂ = [(n↑ + n↓ )g(n↑ , n↓ )] . 177) By construction, LSD is exact for a uniform density, or more generally for a density that varies slowly over space [6]. More precisely, LSD should be valid when the length scale of the density variation is large in comparison with length scales set by the local density, such as the Fermi wavelength 2π/kF or the screening length 1/ks . This condition is rarely satisﬁed in real electronic systems, so we must look elsewhere to understand why LSD works.

In 1986, Perdew and Wang [13] simpliﬁed this GGA in two ways: (1) They replaced nGEA (r, r+u), which depends upon both ﬁrst and second derivatives x (r, r+u), an equivalent expression found through integration of n(r), by n ˜ GEA x by parts, which depends only upon ∇n(r). 106). The function Fx (s) was plotted and ﬁtted by an analytic form. 127) was used to generate a spin-density generalization. Perdew and Wang [13] also coined the term “generalized gradient approximation”. A parallel but more empirical line of GGA development arose in quantum chemistry around 1986.

4). LSD provides a surprisingly good account of the linear response of the spin-unpolarized uniform electron gas (Sect. 4). 179) a constant independent of q, which must be the exact q → 0 or slowlyvarying limit of γxc (q). Figure 1 of [20] shows that the “exact” γxc (q) from a Quantum Monte Carlo calculation [62] for rs = 4 is remarkably close to the LSD prediction for q ≤ 2kF . The same is true over the whole valence-electron density range 2 ≤ rs ≤ 5, and results from a strong cancellation between the nonlocalities of exchange and correlation.

### A Primer in Density Functional Theory by Carlos Fiolhais, Fernando Nogueira, Miguel A.L. Marques

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