A regular isomerization path among chaotic vibrational states of CH 2 ð~ a 1 A 1 Þ Stavros C. Farantos a,b, * , Shi Ying Lin c , Hua Guo c a Department of Chemistry, University of Crete, Iraklion, Crete 71110, Greece b Institute of Electronic Structure and Laser, FORTH, Iraklion 71110, Greece c Department of Chemistry, University of New Mexico, Albuquerque, NM 87131, USA Received 21 September 2004; in final form 5 October 2004 Available online 28 October 2004 Abstract The nearest neighbor level spacing and D 3 distributions indicate that the vibrational spectrum of CH 2 ð~ a 1 A 1 Þ is largely chaotic. Nevertheless, regular localized states coexist with the chaotic ones and they are related to overtone states of the principal vibrational modes. Periodic orbits accompanied by a stability analysis identify these states and explain their topologies and localization in con- figuration space. Particularly, the bending vibrational mode which is associated to the isomerization pathway which connects two equivalent minima separated by a linear symmetric saddle point, shows the dip in energy level spacings at the region of the saddle point. The corresponding wave functions are identified by periodic orbits emanated from saddle-node bifurcations below and above the barrier of isomerization. Ó 2004 Elsevier B.V. All rights reserved. 1. Introduction Vibrational molecular spectroscopy has seen signifi- cant advances in the last decades [1]. Methods such as Stimulated Emission Pumping, Laser Induced Fluores- cence and Overtone Spectroscopy are among those used to excite molecules at high vibrational levels and record spectra close and above the isomerization or dissocia- tion thresholds. Parallel to the experimental work new theories and algorithms have been developed to calcu- late hundreds of vibrational quantum energy levels and wave functions using accurate potential energy sur- faces (PES). The importance of this work stems from our efforts in understanding the dynamics of the mole- cule close to the reaction threshold. The PES, even for a triatomic molecule, is a complex non-linear multi-dimensional function with a landscape that has several minima and saddle points. In elemen- tary chemical reactions specific bonds break and/or form requiring the localization of energy to specific regions of the PES. How such processes can be traced in the vibra- tional spectra? To answer this question usually a global molecular potential produced by ab initio electronic structure calculations is employed. Given the PES the eigenenergies and the eigenfunctions of the molecule are calculated by solving the nuclear Schro ¨ dinger equa- tion. Although for small molecules it is feasible to exam- ine every state separately, generally some statistical measures related to the energy difference of adjacent lev- els are used to distinguish regular from chaotic behav- iors. Nevertheless, at high excitation energies the knowledge of the eigenenergies and eigenfunctions alone is not enough to extract the mechanisms of energy local- ization, and thus, the breaking/forming of a bond. Such mechanisms are better investigated in the limit of classi- cal mechanics. Classical mechanics provide the means for a detailed analysis of the motions of non-linear sys- tems. In Hamiltonian systems stationary phase space 0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.10.018 * Corresponding author. Fax: +30 2810 391305. E-mail address: farantos@iesl.forth.gr (S.C. Farantos). www.elsevier.com/locate/cplett Chemical Physics Letters 399 (2004) 260–265