In 1929 London1 published a very approximate solution of the Schroedinger equation for a system of chemical interest: Hs. To the extent that chemistry can be regarded as existing separately from physics, this was a landmark in the history of chemistry, comparable in importance to the landmark in the history of physics marked by the appearance of the Heitler-London2 equation for H2. The expression for Hs, was, of necessity, even less accurate than that for H2, but chemists, like the habitual poor, were accustomed to this sort of misfortune. Together with the physicists they enjoyed the sensation of living in a renaissance. The physicists still could not calculate a great deal that was of interest to them, and the chemists could calculate less, but both could now dream.

The objective in this work has been one which I have shared with the two other 1986 Nobel lecturers in chemistry, D. R. Herschbach and Y. T. Lee, as well as with a wide group of colleagues and co-workers who have been responsible for bringing this field to its current state. That state is summarized in the title; we now have some concepts relevant to the motions of atoms and molecules in simple reactions, and some examples of the application of these concepts. We are, however, richer in vocabulary than in literature. The great epics of reaction dynamics remain to be written. I shall confine myself to some simple stories.

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The dynamics of exchange reactions A+BC→AB+C have been examined on two types of potential-energy hypersurfaces that differed in the location of the energy barrier along the reaction coordinate. On “surface I” the barrier was in the entry valley of the energy surface, along the approach coordinate. On “surface II” the barrier was in the exit valley of the energy surface, along the retreat coordinate. The classical barrier height was Ec = 7.0 kcal mole−1 on both surfaces, and was displaced from the corner of the energy surface by the same amount; on surface I, r1‡ = 1.20 Å, r2‡ = 0.80 Å; on surface II, r1‡ = 0.80 Å, r2‡ = 1.20 Å (r1 ≡ rAB, r2 ≡ rBC, and the superscript ‡ refers to the location of the crest of the barrier). Three-dimensional (3D) classical trajectory calculations were performed for the mass combination mA = mB = mC at several reagent energies. The reagent energy took the form of translation, vibration or an equilibrium distribution of the two. The main findings were that translation was markedly more effective than vibration in promoting reaction on surface I, and vibration markedly more effective than translation in promoting reaction on surface II. The total reactive cross section with the entire reagent energy vested in translation was symbolized ST, with the reagent energy (but for 1.5 kcal) in vibration, SV, and with an equilibrium distribution over reagent translation and vibration, Seq. On surface I ST ≫ SV: on surface II SV ≫ ST. Close to the threshold for ST on surface I, ST / Seq ∼ 10; close to the threshold for SV, on surface II, SV / Seq ∼ 10. At high reagent energies (2 × threshold) on surface I ST / Seq fell to 2, whereas on surface II SV / Seq increased to extremely large values. Product energy and angular distributions were recorded for two reagent energies. On surface I with low translational energy in the reagents a major part of the available energy appeared as vibration in the molecular product. At higher collision energy this fraction decreased. On surface II with low vibrational energy in the reagents only a small part of the available energy appeared as vibration in the product. At higher vibrational energy this fraction increased. The product angular distribution at low reagent translational energy on surfaces I and II corresponded to backward-peaked scattering of the molecular product. At increased reagent energy on both surfaces the distribution shifted forward (this is a novel phenomenon in the case of increased reagent vibration; surface II).

High-level ab initio calculations of the ground and several excited-state adiabatic potential surfaces of the NaFH system are reported. These calculations were performed by multireference configuration interaction on a large grid of geometries which allowed them to be used for constructing an accurate analytic representation of the NaFH potential surfaces. For the ground and first excited states, using a genetic algorithm, an analytic 2×2 matrix fit was obtained corresponding to a diabatic representation. The off-diagonal coupling was obtained by fitting the energy gap between the surfaces in the region of their avoided crossing, and the diagonal elements were then fit to reproduce the ab initio adiabatic energy at 1530 points. The full fit was used to locate the barrier and the van der Waals well on the ground-state potential surface, the exciplex on the first-excited-state potential surface, and the minimum energy path for the ground-state Na+HF→NaF+H reaction. Additional calculations on the van der Waals and saddle point regions were carried out by a variety of ab initio methods as a check on accuracy. Major topological features of the potential energy surfaces representing higher-than-first excited states were examined.