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When we read about orbitals, I'm sure we are all used to seeing illustrations of them by drawing some contour "along" the probability density function so that the electron's position is equiprobable on the contour and so that, for example, within the shape shown, the electron has a 99% chance of being present.

However, how does one make calculations of these shapes? I've read that the Hartree-Fock method allows one to approximate radial density functions for each electron in a multi-electron atom, but how does this lead to radially-asymmetric images of orbitals and their wonderful shapes?

If anyone knows about the theory that predicts these shapes and has some resource on its computation, this would be much appreciated.

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