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The discussion in How does density functional theory scale with system size? already tells, how DFT scales with the number of electrons. I want to simulate some clusters, so the simulation cell contains much vacuum and its size can be changed without affecting the number of electrons.

I know that with a larger cell less k-points are needed in my plane-wave-code, but I am wondering which further scaling effects there are.

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In planewave calculations, we use a regularly spaced grid that fills the entire unit cell to perform calculations. The number of planewaves is proportional to the number of grid points used (as well as other system dependent parameters). Thus, when you add vacuum to your unit cell, you increase the number of planewave basis functions.

With this in mind, you can use the link you posted to figure out the scaling. In the link, he has four parameters: $n_a$, $n_e$, $n_p$, and $n_v$. $n_v$ is the size of the basis, so when adding vacuum, only the value of $n_v$ will change.

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