Analytical Correlation in the H₂ Molecule from the Independent Atom Ansatz

The independent atom ansatz of density functional theory yields an accurate analytical expression for dynamic correlation energy in the H₂ molecule: Ec = 0.5(1 - √2)(ab|ba) for the atom-additive self-consistent density ρ = |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 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 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.