The vibrational (spectroscopic) theory of olfaction proposes that a receptor doesn't only sense an odorant's shape — it senses its vibrational spectrum, via inelastic electron tunneling (IET) from a bound donor site to an acceptor site across the molecule, the biological analogue of inelastic electron tunneling spectroscopy (IETS) used to fingerprint molecules in solid-state physics.
Γ(ω) ≈ Γ₀·exp(−2κd) + Γ₁·γ² / [(ħω − ΔE)² + γ²]
κ — decay constant of the electronic wavefunction in the barrier
d — donor–acceptor separation across the bound molecule
ħω — the odorant's vibrational quantum (from its IR-active stretch)
ΔE — the donor–acceptor electronic energy gap
γ — resonance linewidth (phonon-broadened)
The first term is plain elastic tunneling — it falls off exponentially with distance regardless of the molecule sitting in the gap. The second, inelastic term is the interesting one: it is a Lorentzian resonance that peaks when the vibrational energy ħω lines up with the electronic gap ΔE, because the tunneling electron can shed exactly one vibrational quantum into the molecule's stretch mode as it crosses (a phonon-assisted hop, via Fermi's golden rule).
- Isotope swap (C–H → C–D → C–T) — a harmonic C–X stretch has ω ∝ 1/√(reduced mass), so replacing hydrogen (mass 1) with deuterium (mass ≈2.0146) or tritium (mass ≈3.0160) lowers the vibrational quantum by √(1/2.0146) ≈ 0.705× and √(1/3.0160) ≈ 0.576× respectively, while the molecule's shape and binding barely change. Turin's proposal for why isotopomers can smell different despite being geometrically near-identical: the vibrational quantum moves off (or onto) resonance with ΔE, and the inelastic tunneling channel — the term the nose is proposed to be sensitive to — turns on or off.
- Stretch frequency slider — sweeps the light isotope's base ħω; every isotope's actual quantum is derived from it by the mass-scaling law above, so the resonance peak (in gap-space) visibly relocates when you switch isotope.
- Donor–acceptor gap / barrier width — set the receptor's own electronic structure: a wider barrier suppresses the elastic background exponentially, making the resonance spike easier to see against it.
This mechanism is proposed, not settled — most olfactory receptor biology is explained by lock-and-key shape recognition, and the IET hypothesis remains a minority, actively debated view. It is included here because it is one of the few mechanistically concrete, falsifiable proposals for a genuinely quantum effect in an everyday sense.