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

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.

• +1, would be good to know but this definitely gave some confusion as I thought this referred to GPAW at first. Dec 16 '20 at 22:25
• @TristanMaxson That was my fault since I added the GPAW tag. There's space for 2 more tags, which would help the user's question get seen by more people, and in more chat rooms, such as this one: chat.stackexchange.com/rooms/112878/gpaw. Does the question have to be about GPAW to have that tag? AW and PAW and APW questions that weren't specifically about GPAW, have used that tag before, and other software tags have been used when it was believed that members of those programs' communities might be able to help. Maybe we can discuss here chat.stackexchange.com/rooms/107328/tags? Dec 16 '20 at 23:28

## 1 Answer

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.

• That's a nice answer. +1. I was thinking that even if GAPW's purpose is just to speed up calculations, they might "by coincidence" help with BSSE, but I doubt someone has done a systematic enough study to observe this. Dec 18 '20 at 3:26
• No; basis set superposition error and basis set incompleteness error arise from the orbital basis. Dec 18 '20 at 17:06
• Good point actually! Dec 26 '20 at 20:04