Application of efficient composite methods for computing with certainty periodic orbits in molecular systems

Recently, we have proposed a technique for the computation of periodic orbits in molecular systems, based on the characteristic bisection method [Vrahatis et al., Comput. Phys. Commun. 138 (2001) 53]. The main advantage of the characteristic bisection method is that it converges with certainty within a given starting rectangular region. In this paper we further improve this technique by applying, on a surface of section of a Poincaré map, an iterative scheme based on the composition of the characteristic bisection method with other more rapid root-finding methods such as Newton’s or Broyden’s methods. Thus, the composite schemes compute rapidly with certainty periodic orbits of molecular systems. By applying these methods to the LiNC/LiCN molecular system we obtain promising results. We have reproduced previous results using considerable less CPU time. Also, we have located and computed new asymmetric families of periodic orbits.  2002 Elsevier Science B.V. All rights reserved. PACS: 39.30; 31.15.-p; 02.70.-c; 05.45.+b