Dispersion energy −C₆/R⁶ from atomic polarizabilities

Deterministic dispersion: instead of postulating quantum fluctuations, use the static polarizability α (response of the ground-state charge density to a dipole field) and the ionization potential I of each atom. Compute the C₆ coefficient via the Slater–Kirkwood / London formula:
C₆^{AB} ≈ (3/2) · α_A · α_B · I_A · I_B / (I_A + I_B)
This is the static-polarizability limit of the Casimir–Polder integral C₆ = (3/π) ∫₀^∞ α_A(iω)·α_B(iω) dω. Then the dispersion energy E_disp(R) = −C₆/R⁶ emerges from coupled-oscillator algebra alone — no Born rule, no fluctuations, no full TDSE.

Atomic data (atomic units)

α: experimental polarizabilities · I: ionization energies (Ha)

Atomα (a.u.)I (Ha)
H4.500.500
He1.380.904
Li164.0.198
Be37.70.342
Ne2.670.793
Na163.0.189
Ar11.10.579
Kr16.80.515
Xe27.30.446

Pair selector

Atom A  Atom B

Reference C₆ values (a.u.)

PairLondon (this calc)Reference
H–H6.50
He–He1.46
Ne–Ne6.38
Ar–Ar64.3
Kr–Kr130
Xe–Xe286
The London formula is the leading approximation; it captures C₆ within ~30% of full Casimir–Polder values for noble gases. With α(iω) instead of static α, accuracy < 5%.