An effective Hamiltonian for the short-time dynamics at a conical intersection

The construction of an effective Hamiltonian which accurately accounts for the short-time dynamics at a conical intersection in high-dimensional systems [Phys. Rev. Lett. 94, 113003 ( 2005)] is discussed and extended to include topological considerations. A set of three topology-adapted, orthogonal coordinates is introduced, two of which span the branching space at the conical intersection. The new coordinates are at the same time characteristic dynamical and topological coordinates. This description is compared with the characteristic (g, h, s) vectors of the adiabatic representation. The dynamics induced by the effective Hamiltonian is discussed for a 22-dimensional model system related to the D-1-D-0 conical intersection in the butatriene cation.