Application of the Characteristic Bisection Method for locating and computing periodic orbits in molecular systems

The Characteristic Bisection Method for finding the roots of non-linear alg ebraic and/or transcendental equations is applied to LiNC/LiCN molecular sy stem to locate periodic orbits and to construct the continuation/bifurcatio n diagram of the bend mode family. The algorithm is based on the Characteri stic Polyhedra which define a domain in phase space where the topological d egree is not zero. The results are compared with previous calculations obta ined by the Newton Multiple Shooting algorithm. The Characteristic Bisectio n Method not only reproduces the old results, but also, locates new symmetr ic and asymmetric families of periodic orbits of high multiplicity. (C) 200 1 Elsevier Science B.V. All rights reserved.