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. T hese levels result from quantum mechanical calculations of dynamics based o n the hyperspherical approach, and are given as a function of the total ine rtia of the system measured by the hyperradius rho. The nearest neighbour l evel spacing distributions of Brody and of Berry and Robnik, the spectral r igidity Delta (3) of Dyson and Mehta and the correlation coefficient are re ported, together with other properties, such as variance, skewness and kurt osis of the distributions. Trends are studied as a function of rho, propose d as a natural control variable. For low rho, which correspond to the trans ition state, evidence is found of Wigner-like behaviour, which is interpret ed 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 a re well separated, is characterized by a tendency towards regular Poisson-l ike behaviour. A comparison between the two investigated systems shows that the chaotic regime in the transition state region is more pronounced for t he He reaction, which proceeds through a deep well and whose dynamics are c haracterized by a rich resonance pattern.