# Mixing pseudopotentials with gaussian and plane wave basis

I am somewhat of a novice in computational chemistry of materials, and have been tasked to replicate simulations from a relevant paper. The paper is a bit scant on details so I am trying to recreate its exact input, as closely as possible from their description. I have fundamental understanding of pseudo potentials and basis sets, but I could not figure out what the following line implies:

... Goedecker pseudopotentials used in all simulations. Kohn-Sham orbitals expanded in triple-zeta plus polarization Gaussian-type basis and the charge density expanded in plane waves with a 300 Ry cut-off.

What is meant by "gaussian basis for KS" and "plane-wave for charge density"? Is charge density not derived from the KS orbitals? How and why mix two different kind of basis?

I apologize in advance if what I asked is too naïve, most of my quantum chemistry knowledge is text book level, not research paper level!

Just as I posted this, this showed up in the side bar, which gave me a thread to start exploring (GAPW). That answers one of my three questions I believe.

• CP2K uses such a scheme. You could have a look at their latest paper: J. Chem. Phys. 152, 194103 (2020); doi: 10.1063/5.0007045 Commented Oct 29, 2022 at 13:20

## 1 Answer

This is the hybrid Gaussian and plane wave method described in Mol. Phys. 92, 477 (1997), in which you expand the orbitals $$\psi_{i\sigma}$$ in a Gaussian basis set, but compute the Coulomb interaction of the charge density with itself with a plane-wave expansion employing Fast Fourier Transforms. The benefit of this approach is that you have simultaneously a compact orbital basis in which you can use dense diagonalization to find the orbitals from the Fock matrix, and a faster way to compute the Madelung sums. The pseudopotential is necessary to eliminate the core orbitals, which can't be represented in the plane wave basis; it also allows for the use of a smaller Gaussian basis set as tight exponents are not needed in the basis set.

• As a "rule-of-thumb" are there any kind of systems this basis provides an advantage for? I mean why is it not more widely used? For some reason, above link is not working correctly (looks like T and F issue), this link works : tandfonline.com/doi/abs/10.1080/002689797170220. Commented Nov 2, 2022 at 15:33