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Quantum vs point-particle proton
Nuclear wavefunctions and the geometric isotope effect
Geometric isotope effect
—
⟨x⟩H − ⟨x⟩D. The two isotopes sit in the same potential
and still have different average positions — the heavier one hugs the
classical minimum more closely.
Barrier and well separation are tied to R by an illustrative relation,
Vb = 140 (R − 2.35 Å)² kJ/mol and 2a = R − 2.00 Å.
Not fitted to a specific hydrogen bond. The real geometric isotope effect in
hydrogen bonds also involves the heavy-atom donor–acceptor coordinate
itself responding to isotopic substitution — a relaxation this 1D
proton model cannot represent. What is shown here is the proton's own shift
in an asymmetric well: a legitimate 1D analogue, but not the same observable.