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--- package:faq [2022/04/01 12:58] – pbloechl
+++ package:faq [2024/03/04 08:42] (current) – pbloechl
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 By providing the full wave functions and densities, the PAW method provides quantities such as electric field gradients
 or hyperfine parameters directly. In contrast the full density needs to be reconstructed in the pseudopotential approach.
 The PAW method uses extensively the numerical methodology developed for the pseudopotential approach and for the LMTO method. This results in fast algorithms, and a close similarity between those methods.
+==== I obtain negative occupations. Is that wrong? ====
+No. This occurs normally for the tetrahedron method using the corrections from  [[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.16223|Blöchl et al. Phys. Rev. B 49, 16223 (1994)]]. It reflects that the Brillouin-zone integration is not approximated by a sampling over a discrete k-point set, but energies and matrix elements are interpolated in between. What is printed as occupations are actually integration weights, which include the interpolation between the discrete k-points. Using these elaborate integration weights, the integral of the interpolated matrix elements and energies can still be expressed as weighted sum over the discrete k-point set. The interpolation is effectively "hidden" from the user at the price of complicated integration weights, which take on values that appear, at first sight, unphysical. When the interpolation between the discrete k-points is non-linear, which is the case with the "correction formula" from [[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.16223|Blöchl et al. Phys. Rev. B 49, 16223 (1994)]], the integration weights may also be negative or larger than one. See for example Eq.22 and Fig.7 of [[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.16223|Blöchl et al. Phys. Rev. B 49, 16223 (1994)]].