The dynamics of the molecular transition state, in a reaction or photodissociation process, may be analyzed by semiclassical methods. We investigate the classical dynamics of the transition state in the dissociation HgI2(X (1) Sigma(g)(+))-->(HgI)-Hg-hv(X (2) Sigma(+))+I, and apply the semiclassical quantization methods based on periodic-orbit theory. A series of resonances is characterized in a low-energy regime, where the classical dynamics is regular, and at high energies, after a transition to chaos has occurred. In a complementary fashion, we analyze the quantum-mechanical propagation of wave packets. The spectrum which is derived from the quantum-mechanical autocorrelation function is compared with the semiclassical results.