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You are correct that the 4s orbital in calcium is indeed less energetic than the 3d orbital. However, when it comes to the radial distribution functions (RDFs), the situation is slightly different.

The RDF represents the probability density of finding an electron at a particular distance from the nucleus. It does not directly correlate to the energy levels of the orbitals. The RDFs provide information about the spatial distribution of the electron density.

In the case of calcium, the 4s orbital has a larger radial extent compared to the 3d orbital. This means that the probability of finding an electron in the 4s orbital is higher at larger distances from the nucleus than in the 3d orbital. The maximum of the 4s RDF is indeed at a larger radius than the maximum of the 3d RDF.

Here is the corrected link you mentioned for reference: Calcium 4s and 3d RDFs

Thank you for pointing out the discrepancy, and I apologize for any confusion caused by my previous response.

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