The integrated number of vibrational states in acetylene ((C2H2)-C-12, (C2H2)-C-13, (C2D2)-C-12)

A calculated exhaustive set of vibrational state energies in (C2H2)-C-12, (C2H2)-C-13 and (C2D2)-C-12 has been used to analyse the evolution of the integrated number of states with increasing vibrational energy N(E) up to 15 000 cm(-1), 12 000 cm(-1) and 10 000 cm(-1) in each isotopomer, respectively. The regular contribution to N(E) was modelled analytically and numerical parameters were fitted. The other expected contribution to N(E), which is of oscillatory nature, was quantified and is discussed using energy- and time-dependent theories. Related periods of oscillation and temporal recurrences are interpreted consistently in terms of the constant of the motion N-r = 5v(1) = 3v(2) = 5v(3) = v(4) = v(5) and of an average vibrational quantum. More pragmatically, the vibrational dynamics appear to be dominated by the bending vibrations, i.e., by the slowest oscillators.