Memorias de investigación
Quantum and classical correspondence in vibrational molecular systems

Research Areas
  • Electronic

The advent of modern experimental techniques greatly broadened the horizons of classical molecular spectroscopy. Some of these methods, for example stimulated emission pumping, electron photodetachment, or femtochemistry, have the additional advantage of providing a direct link between spectroscopy and the underlying nuclear dynamics. At the same time, di erent variational approaches were developed to eciently compute the corresponding vibrational levels. As the excitation energy increases the correspondence principle starts to work, while simultaneously the vibrational dynamics become chaotic, due to the destruction of regular motions (taking place on invariant tori) dictated by the KAM theorem. The dynamical structure of phase space can be revealed by the construction of composite Poincar`e surface of section. Unfortunately, this method is only feasible for two degrees of freedom (dof) Hamiltonian systems. Therefore as soon as a third mode is considered a new way of visualizing the dynamics is required. A good method for the characterization of invariant tori should provide accurate descriptions of invariant tori, and at the same time measure local di usion strength, in order to distinguish regular from chaotic regions. For this purpose we use the frequency analysis(FA) method. The corresponding spectra can become very complex, but they usually show simple low resolution features related to the above mentioned classical structures. The associated nonlinear dynamical e ects, driven by anharmonicities and mode couplings, control chemically interesting processes, such as intramolecular vibrational relaxation or chemical reactivity. This is especially true of floppy molecules, in which large amplitude motions allow the exploration of potential energy surface regions far from the equilibrium configuration. We have constructed a quantum levels correlation diagram for LiNC/LiCN and HCN/HNC floppy molecular systems , taking as a parameter ¯h. Special attention is paid to the avoided crossing at the edge of the chaotic region, where scar formation takes place. It has been found that the wave functions of the two interacting states appear clearly scarred by the stable and unstable POs corresponding to the same resonance 1:8 for LiCN and 1:10 for HCN. Moreover, the two POs are conjugate, in the sense of the Poincar?e¿Birkho theorem, that is, they correspond to an unstable¿stable pair originated at the same bifurcation. Furthermore we have found that these resonances have also a profound influences in the classical dynamics of chaotic trajectories of these systems, as can be seen in the corresponding frequency maps shown in the figures for 2 and 3 dof LiCN system.
Universidades Politécnica y Autónoma de Madrid
Entity Nationality
Madrid (España)

Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Grupo de Sistemas Complejos
  • Departamento: Física y Mecánica Fundamentales y Aplicada a la Ingeniería Agroforestal
  • Departamento: Ingeniería Rural
  • Departamento: Física Aplicada a la Ingeniería Industrial
  • Departamento: Tecnología de la Edificación