Perdew, Burke, Ernzerhof method

A common feature of all pseudopotential methods is that the parameters depend on the employed method, i.e. the potential derived for e.g. the Local Spin Density Approximation (LSDA) functional (Section 6.5.1) is different from that derived from a generalized gradient functional such as Perdew-Burke-Ernzerhof (PBE) (Section 6.5.2). In practice, the difference is relatively small and pseudopotentials optimized for one functional are often used for other functionals without re-optimization. 

The quantity 2Ec(2)[n] is particularly important because it is the initial slope in the adiabatic connection method (coupling-constant formula) for Ec[n] [10,14-18]. In fact, quite good use of the evaluation of 2Ec(2)[n] has recently been made by Ernzerhof [19] and by Perdew, Burke, and Ernzerhof [20-23] in their modeling of... 

To illustrate the use of real-space methods, we again chose to study methane (CH4). For all calculations, we used the program octopus [90] (see also http //www.tddft.org/programs/octopus), which was written by some of the authors, and is freely available under an open source license. Furthermore, we employed the Troullier-Martins pseudo-potentials which are distributed with the code, and the GGA in the parameterization of Perdew, Burke and Ernzerhof. 

M. Ernzerhof, J.P. Perdew and K. Burke, Density Functional methods in Chemistry, eds. B.B. laird, R. Ross and T. Ziegler, American Chemical Society Symposium Series (1996). 

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