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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 104, 2006 - Issue 5-7: A Special Issue in Honour of Professor Michael Albert Robb
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Original Articles

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

, &
Pages 1081-1093 | Received 15 Jun 2005, Accepted 28 Jul 2005, Published online: 21 Feb 2007

References

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  • Note that, in the case of glancing, or Renner–Teller intersections 1, 3, the quadratic term would correspond to the lowest order in the expansion around the intersection
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  • As discussed further in 38, an additional transformation can be introduced for H eff such as to diagonalize the quadratic potential form in the three-mode subspace i.e. for this choice, the dij (i,j =1,…, 3, j>i) vanish
  • Note further that the residual modes do not couple among each other. This is a result of a certain freedom in determining the remaining elements of the transformation yielding equations (9–11) 29
  • The cumulant expansion represents a resummation with respect to the moment expansion equation (12), such that , with the cumulants , , , etc. 48. Cumulant expansions avoid an exponential scaling with time, such that truncation of the series gives results valid beyond short times
  • Another interesting choice for an additional rotation leads to branching plane vectors that have the same frequency. This is achieved by a rotation with the parameter . With this choice, one recovers a Jahn–Teller 1 type problem in the branching plane
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  • van Kampen , NG . 1992 . Stochastic Processes in Physics and Chemistry , North-Holland : Amsterdam .

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