Diamagnetism in RealQM — the induced counter-current

A closed-shell atom carries no current at rest. Switch on a field B (out of the screen) and the whole charge cloud takes up a real Larmor circulation — an induced current that opposes B (Lenz), giving a small moment against the field. Its strength grows with the atom's size: μdia ∝ −⟨r²⟩ B, the Langevin law. Because RealQM supplies ⟨r²⟩=∫r²ρ directly, this is a magnetic number it can compute and check against experiment.
Top-down view along B. Dots = electrons, placed at the RealQM per-shell ⟨r⟩; when B≠0 they circulate rigidly (Larmor, ω∝B) in the sense that opposes B.
∑⟨r²⟩ (RealQM, a₀²) 2.38
Larmor ωL = eB/2me 0.25
induced μdia ∝ −⟨r²⟩B 0
χcalc = −0.79×10⁻⁶⟨r²⟩ -1.88
χexp (measured) -1.90
ratio calc/exp 0.99
χ in 10⁻⁶ cm³/mol. Every atom is diamagnetic (χ<0): the induced current always opposes B. He is essentially exact; Ne, Ar come out too diamagnetic because the radial mean field lets the valence spread (no exchange/non-overlap contraction).
χcalc (filled) vs χexp (outline) for the three atoms. Diamagnetism grows steeply with size, ∝⟨r²⟩.