Why does the computed energy of a set of semi-free atoms deviate from analytic/experimental values?

Just Got Here
If several atoms are pulled far apart the computed energy for such configuration should be a total of ionization energies of individual atoms.

The energy of such configuration of lithium atoms in the 3-21G basis:
Li -20.00000 -20.00000 -20.00000
Li -20.00000 -20.00000 20.00000
Li -20.00000 20.00000 -20.00000
Li -20.00000 20.00000 20.00000
Li 20.00000 -20.00000 -20.00000
Li 20.00000 -20.00000 20.00000
Li 20.00000 20.00000 -20.00000
Li 20.00000 20.00000 20.00000

is computed as -7.323 Hartree per lithium atom with a precision of 0.001.

However, based on https://en.wikipedia.org/wiki/Ionization_energies_of_the_elements_(data_page) the energy should be
-(5.39172+75.64018+122.45429) eV = -203.48619 eV = -7.478 Hartree

Similarly, for carbon NWChem computes the per-atom energy as -37.391 Hartree that deviates from the analytic value
-(11.26030 +24.38332 +47.8878 +64.4939 +392.087 +489.99334) eV = -1030.10566 eV = -37.856 Hartree

Similar deviations exist for other atoms.

Why do computation results deviate from the known experimental and analytical values?

Forum Regular
In short, your level of theory (method + basis set) is insufficient to achieve the level of agreement that you seek.

Also, one atom would be sufficient for what you are trying to do, unless you are also trying to test how far apart the atoms need to be in order for them to be (effectively) non-interacting.

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