Or, in other words: why is the sum of atomic energies for a single atom different from its total energy?

As an exercise, I carried out the calculation of the binding energy for the H2 molecule as the total energy of the H2 molecule minus twice that of a single H atom, and compared my result with the one thrown automatically by DMol3.

I found a 2.56 % deviation from DMol3 result, which still acceptable, I certainly expected it to be zero!

It could be a matter of numerical precision and I should be happy with my result.

However, by using the "sum of atomic energies" (SOAE) from the outmol file of the H2 run, -0.9969616 Ha, it can be calculated the total energy for a single hydrogen atom as half of the above value, giving -0.4984808 Ha which is exactly the SOAE value reported in the outmol file for the single H atom's run.

That is, the H2 binding-energy 2.56 % deviation might not be solely due to a numerical precision.

The outmol file of the single H atom also reports its total energy (Et), -0.4963433 Ha, which is just the one I used for calculating the binding energy of H2. Surprisingly, this single-atom total energy does not match its SOAE, and therefore the difference Et - SOAE, i.e., the "binding energy" (as in fact is indeed labeled in the outmol file despite having only one atom), instead zero gives +0.0021375 Ha! Nevertheless, this non-zero binding energy could be considered spurious because of its small size, 0.4 % relative to the SOAE.

I would like to know either why SOAE and Et are not exactly the same for a single atom, or how DMol3 internally calculate the SOAE.