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

Abstract

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 D₁–D₀ conical intersection in the butatriene cation.

Keywords:

• Conical intersection
• Effective Hamiltonian
• Short-time dynamics

Acknowledgements

It is a great pleasure to dedicate this work to Professor Mike Robb on the occasion of his 60th birthday. This work was supported in part by a CNRS/DFG collaboration project and by an Alexander-von-Humboldt post-doctoral fellowship for one of us (E.G.). We thank Horst Köppel for valuable discussions.