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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.

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    $\begingroup$ This question appears to be off-topic because it is about physics mathematics. $\endgroup$ – user467 Aug 6 '14 at 18:10
  • $\begingroup$ where could i ask it? $\endgroup$ – freude Aug 6 '14 at 18:56
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    $\begingroup$ You could try the Physics Stackexchange $\endgroup$ – user467 Aug 6 '14 at 20:16
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    $\begingroup$ you might be interested in helping us start a brand new stack exchange just for this type of question: area51.stackexchange.com/proposals/122958/materials-modeling $\endgroup$ – user1271772 Sep 17 '19 at 20:42
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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.

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