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

Adiabatic energy levels for two prototypical reactions, F + H(2) --> 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 rho. The nearest neighbour level spacing distributions of Brody and of Berry and Robnik, the spectral rigidity Delta (3) 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 rho, proposed as a natural control variable. For low rho, 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 rho, a mixture of Wigner-and Poisson-like behaviour emerges. The situation for high rho, 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.