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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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