Quantum-mechanical wavepacket dynamics of the CH group in symmetric top X3CH compounds using effective Hamiltonians from high-resolution spectroscopy

Abstract

The recently established ‘universal’ effective Hamiltonian for the coupled CH stretching and bending vibrations in alkyl X₃CH compounds has been used to calculate the dynamics of this system at high excitation energies. We discuss the nature of the basis functions and eigenfunctions of the effective Hamiltonian and the time-dependent populations and probability densities in coordinate space. It is found that most regions of coordinate space are probed with high probability within time scales of < 1 ps after pure CH stretching excitation. With an excitation energy of ca. 200 kJ mol^–1 in the N= 6 polyad for a typical member of the series of X₃CH compounds, a microcanonical probability density distribution for stretching and bending motions is approached but not completely attained. It is found that such a widespread distribution applies at most times, apart from certain recurrence phenomena. The dynamics are thus highly non-classical and the wavepacket does not remain localized in a semi-classical manner for appreciable times. Some of the eigenfunctions show an interesting specific mode structure, which is further evidence that a fully statistical, global vibrational state is not attained in this case. It is shown that the main conclusions for the short time behaviour of the CH motions are rather insensitive with respect to the way in which the multidimensional vibrational problem is reduced to an effectively two-dimensional problem.