Is basis set superposition error reduced when using the GAPW method?

Question

CP2K implements the Gaussian and Augmented Planewaves (GAPW) approach for all-electron calculations. My understanding is that the GAPW method involves using atom-centered Gaussian type orbitals to represent rapidly varying electron density around nuclei, and planewaves for the electron density in the slowly varying interstitial regions.

My question is: does use of the GAPW method mostly eliminate basis set superposition error effects, for example bond length contraction during optimization? I would think so, since the core regions probably will not overlap in most systems, but I may be misunderstanding how GAPW works.

Answer 1

Short answer: no.

The idea of the GAPW method described in Theor. Chem. Acc. 103, 124 (1999) is simply to speed up the evaluation of the Coulomb and exchange-correlation contributions. Quoting from the conclusions:

Starting from the GPW approach we substituted the PW auxiliary basis for the electron density by an APW auxiliary basis which besides plane waves relies on Gaussians. Therefore, the electron density, the XC potential, and the Coulomb potential can be separated into a smooth nonlocal contribution expanded in PW and local contributions that can be described in Gaussians and which can thus be treated analytically.

Füsti-Molnar and coworkers have pursued similar approaches also for molecules, see e.g. J. Chem. Phys. 116, 7795 (2002), J. Chem. Phys. 122, 074108 (2005), J. Chem. Phys. 117, 7827 (2002), andn J. Chem. Phys. 119, 11080 (2003)

I would also like to point out here that if one is pursuing periodic calculations with Gaussian basis sets, the basis functions are not really Gaussian anymore since one is actually using Bloch functions $\chi_\mu ({\bf k};{\bf r}) = \sum_{\bf g} \chi_\mu ({\bf r}-{\bf g}) \exp(i {\bf k} \cdot {\bf r})$, see e.g. the book by Pisani, Dovesi, and Roetti, doi:10.1007/978-3-642-93385-1.