Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section B / 39 / e / Solution

When $|eV|$ reaches a vibrational quantum, a tunnelling electron can lose energy by exciting that vibration. Opening an inelastic channel changes $dI/dV$ at both voltage polarities. If the conductance increases in each direction, $d^{2}I/d{V}^2$ has a positive feature at positive threshold and a negative feature at the corresponding negative threshold. Approximate antisymmetry follows from approximate symmetry of the conductance; unequal tip and sample electronic structures can make amplitudes unequal.

The three energy scales are 8, 48 and 375 meV, corresponding to about 65, 387 and 3025 cm${}^{-1}$. A plausible assignment is a low-energy frustrated lateral translation or rotation, an adsorbate–metal stretch or hindered molecular mode at 48 meV, and a C–H stretching vibration at 375 meV. The terminal carbon of methyl isocyanide supplies a plausible adsorption contact, but exact mode assignment requires calculated normal modes or independent vibrational measurements. In particular the 48 meV band should not be labelled a C–N stretching vibration simply because the molecule contains that bond: its frequency is far too low for the usual internal stretching mode.