  The independent atom ansatz of density functional theory yields an accurate
analytical expression for dynamic correlation energy in the H$_{2}$ molecule:
$E_{c} = 0.5(1 - \sqrt{2})(ab|ba)$ for the atom-additive self-consistent
density $\rho = |a|^{2} + |b|^{2}$. Combined with exact atomic self-exchange,
it recovers more than 99.5 % of nearly exact SCAN exchange-correlation energy
at R > 0.5 $\r{A}$, differing by less than 0.12 eV. The total energy functional
correctly dissociates the H-H bond and yields absolute errors of 0.002 $\r{A}$,
0.19 eV, and 13 cm$^{-1}$ relative to experiment at the tight binding
computational cost. The chemical bond formation is attributed to the asymptotic
Heitler-London resonance of quasi-orthogonal atomic states ($- (ab|ba)$) with
no contributions from kinetic energy or charge accumulation in the bond.
