H₂ — the covalent bond

The next rung: two hydrogen atoms, now bonding. Their 1s orbitals overlap and combine into two molecular orbitals — a σ bonding orbital that piles electron density between the nuclei, and a σ* antibonding orbital with a node there. Both electrons drop into σ; the pile-up screens the proton–proton repulsion and lowers the energy. That drop is the bond — 436 kJ/mol, released as the atoms settle to 74 pm apart. Slide them together and watch the well.

Bridge-Burners LLC · Fiddler · 1s + 1s → σ + σ* · bond order 1 · anchor: AKASHA

State

internuclear r160 pm
energy vs apart0 kJ/mol
bond order1
stateapproaching

Bare numbers (H₂)

bond lengthrₑ = 74 pm (0.74 Å)
bond energyD₀ = 436 kJ/mol (4.52 eV)
well depthDₑ ≈ 458 kJ/mol (zero-point sits above the floor)
MOsσ (bonding, 2 e⁻) · σ* (antibonding, empty)

Status discipline

Literal1s+1s → σ+σ*; both e⁻ in σ; bond order 1; rₑ=74 pm, D₀=436 kJ/mol. He₂ fills σ* too → bond order 0 → no molecule.
BridgeThe bond as the energy well; formation releases the bond energy; atom→molecule is shell-filling one level up.
SpeculativeThe density picture is LCAO (1s+1s), an approximation of the exact H₂ solution; the smooth Morse curve is a model of the real potential.