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What is the PAW Method?

The Projector Augmented Wave (PAW) method is a simulation algorithm to obtain the total energy, electron distribution and atomic structure and dynamics. The term PAW is often also used as short hand for the CP-PAW code developed originally by Peter Blöchl.

Where can I find a description of the PAW method?

The original reference is P.E. Blöchl, Phys. Rev. B 50, 17953 (1994). Some of the ideas have been shaped during earlier pseudopotential work described in P.E. Blöchl, Phys. Rev. B 41, 5414 (1989). There is also a publication targeting beginners to PAW: P.E. Blöchl, C.J. Först and J.Schimpl, Bull. of Mater. Sci. 26, 33 (2003) (Arxiv Version).

Are there other implementations of the PAW method

The PAW method is used by a number of electronic structure codes. (The list is probably not complete)

Besides complete implementations of the PAW method, there is another branch of methods using the reconstruction of wave functions from the PAW method for property calculations, but not during the self-consistency cycle. This approach could be termed “post-pseudopotential PAW”. This development began with the evaluation for hyperfine parameters from a pseudopotential calculation using the PAW reconstruction operator (C.G. Van de Walle and P.E. Blöchl, Phys. Rev. B 47, 4244 (1993)) and is now used in the pseudopotential approach to calculate properties that require the correct wave functions.

What is the relation between PAW and the pseudopotential approach?

The PAW method is an all-electron method, that is the full wave functions including their nodal structure are properly defined, whereas the pseudopotential method deals with nodeless wave functions. The PAW method is more rigorous, and can be made exact by converging series expansions. (The current implementation in CP-PAW still uses the frozen core approximation.) The pseudopotential approach can be derived from the PAW method by a well-defined approximation. This approximation discriminates the pseudopotential approach from all-electron methods. They can cause transferability problems of the pseudopotentials if the density deviates strongly from that of the reference atom. In practice the errors are larger for high-spin configurations. 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 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 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 Blöchl et al. Phys. Rev. B 49, 16223 (1994).

package/faq.txt · Last modified: 2024/03/04 08:42 by pbloechl

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