Dynamics on reactive potential energy surfaces: hyperspherical view and signatures of ‘quantum chaos’

Adiabatic energy levels for two prototypical reactions, F + H₂ → HF + H and He + H⁺ ₂ → HeH⁺ + H, are analysed by means of statistical tests. These levels result from quantum mechanical calculations of dynamics based on the hyperspherical approach, and are given as a function of the total inertia of the system measured by the hyperradius ρ The nearest neighbour level spacing distributions of Brody and of Berry and Robnik, the spectral rigidity δ₃ of Dyson and Mehta and the correlation coefficient are reported, together with other properties, such as variance, skewness and kurtosis of the distributions. Trends are studied as a function of ρ, proposed as a natural control variable. For low ρ, which correspond to the transition state, evidence is found of Wigner-like behaviour, which is interpreted as the signature of quantum chaos. On the passage of the systems through intermediate ρ a mixture of Wigner- and Poisson-like behaviour emerges. The situation for high ρ where reactants and products of the reactions are well separated, is characterized by a tendency towards regular Poisson-like behaviour. A comparison between the two investigated systems shows that the chaotic regime in the transition state region is more pronounced for the He reaction, which proceeds through a deep well and whose dynamics are characterized by a rich resonance pattern.     

Ab initio dynamics of the He + H+ 2 → HeH+ +H reaction: a new potential energy surface and quantum mechanical cross-sections

The reaction He + H⁺ ₂(v,j = 0) → HeH⁺(v′ = 0, j′) for v = 0, 1,2 and 3 and for scattering energies near the threshold (0.95–1.15 eV) has been studied by calculating ab initio points at MRCI level and ‘exact’ integral quantum reactive cross-sections. More than 1400 nuclear geometries have been chosen to cover the most important regions for the dynamics, an extended set of points being taken directly on a hyperspherical coordinate grid. A many-body expansion with a large number of terms permits an accurate analytical representation of the potential energy surface with a root-mean-square deviation <12meV. The hyperquantization algorithm has been extended to obtain quantum mechanical integral cross-sections which are compared with previous calculations and with experimental results.