Past exam of the chemistry A course of the University of Cambridge / 2025 / Paper 2 / A8 / b

The quantities $f_A$ and $f_B$ are molecular partition functions per unit volume for the two reactants, with their internal rotational, vibrational and electronic factors included. Thus their translational factors are $(2\pi m_{j}kT/h^2{)}^{3/2}$, rather than those factors multiplied by $V$. Their energy zeros must match the separately displayed barrier convention.

The primed $f_{\mathrm{TS}}^{\prime }$ is the corresponding transition state partition function per unit volume with the unstable reaction-coordinate degree of freedom omitted. Its replacement by the crossing-frequency factor $kT/h$ is already outside the partition-function ratio. For a diatomic atom-pair transition state, the omitted coordinate is the bond stretch, leaving translation and rotation.

The barrier $\Delta {\epsilon }_0^{‡}$ is the energy difference between the transition-state reference level and the separated reactant reference levels. Consistent zero-point energies of stable transverse modes belong in this reference-level difference. It is an energy per reacting pair; a molar activation energy uses $R$ instead of $k$ in the exponential.