# Two-electron Integrals over Gaussian Plane Waves [closed]

Is there an efficient method to compute the two-electron integrals over the basis set represented by a product of a Gaussian function $g(r)$ and plane wave:

$\psi(r)=g(r)e^{ikr}$

where $\lambda=1/k$ is approximately one fifth of the width of gaussians.

## closed as off-topic by Philipp, LDC3, ron, Martin - マーチン♦, Klaus-Dieter WarzechaAug 15 '14 at 5:26

• This question does not appear to be about chemistry within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• This question appears to be off-topic because it is about physics mathematics. – user467 Aug 6 '14 at 18:10
• where could i ask it? – freude Aug 6 '14 at 18:56
• You could try the Physics Stackexchange – user467 Aug 6 '14 at 20:16

I'm not sure if anyone has done it, but the closest I can think of is the GPW (mixed Gaussian Plane Wave) method. I think that involves a mapping between Gaussian and PW basis. It's DFT, but just look for the Coulomb integrals.

General idea:

Lippert, Gerald, et al. "A hybrid Gaussian and plane wave density functional scheme." Molecular Physics 92.3 (1997): 477-488.

The implementation can be found here:

VandeVondele, Joost, et al. "Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach." Computer Physics Communications 167.2 (2005): 103-128.