# A Primer in Density Functional Theory by John P. Perdew, Stefan Kurth (auth.), Carlos Fiolhais,

By John P. Perdew, Stefan Kurth (auth.), Carlos Fiolhais, Fernando Nogueira, Miguel A. L. Marques (eds.)

Density practical concept (DFT) is by means of now a well-established procedure for tackling the quantum mechanics of many-body platforms. initially utilized to compute homes of atoms and easy molecules, DFT has quick develop into a piece horse for extra advanced functions within the chemical and fabrics sciences. the current set of lectures, spanning the entire variety from uncomplicated ideas to relativistic and time-dependent extensions of the idea, is the perfect creation for graduate scholars or nonspecialist researchers wishing to familiarize themselves with either the elemental and such a lot complex concepts during this field.

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We begin by evaluating the non-interacting kinetic energy (this section) and exchange energy (next section) per electron for a spin-unpolarized electron gas of uniform density n. 127). By symmetry, the Kohn-Sham potential vs (r) must be uniform or constant, and we take it to be zero. , we require that the orbitals repeat from one face of the cube to its opposite face. ) The Kohn-Sham orbitals are √ then plane waves exp(ik · r)/ V, with momenta or wavevectors k and energies k 2 /2. The number of orbitals of both spins in a volume d3 k of wavevector space is 2[V/(2π)3 ]d3 k, by an elementary geometrical argument [53].

194) to write s → 0 : Fx (s) = 1 + µs2 . 215) Then the gradient coeﬃcients for exchange and correlation will cancel for all rs and ζ, apart from small ∇ζ contributions to ExGGA , as discussed in the next section. 196), the proper gradient coeﬃcient for exchange in the slowly-varying limit. But this choice can be justiﬁed in two other ways as well: (a) It provides a decent ﬁt to the results of the real-space cutoﬀ construction [79] of the PW91 exchange energy, which does not recover µAK in the slowly-varying limit.

804. 804 gives a GGA which is virtually identical to PW91 over the range of densities and reduced density gradients important in most real systems. We shall complete the discussion of this paragraph in the next section. 217) where c = (3/4π)(9π/4)1/3 and −c/rs = ex (rs , ζ = 0) is the exchange energy per electron of a spin-unpolarized uniform electron gas. The enhancement factor Fxc (rs , ζ, s) shows the eﬀects of correlation (through its rs dependence), 1 Density Functionals for Non-relativistic Coulomb Systems 45 spin polarization (ζ), and inhomogeneity or nonlocality (s).