During a transition of a molecule from one state to another, it pass through a transition state. This transition state, mathematically speaking, is a saddle point. That means, the second derivative along all the coordinates, except one, is greater than zero. I have two questions:

1) Is it possible for a molecule to have a transition state at a maximum if there is no saddle point on the potential energy surface?

2) In the case of a diatomic molecule, there is no saddle point on the potential energy surface. So the transition state should be at a maximum right?

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    $\begingroup$ Do you have any particular situations in mind when you say "if there is no saddle point on the potential energy surface"? It seems unlikely such a situation might exist, since it ought to be possible for the configuration to avoid the maximum altogether by going around it. In the case of a diatomic molecule with only the vibrational degree of freedom being considered (moving in a Morse potential created by the electronic wavefunction), the notion of transition state is sort of meaningless, as there is only one stable product: the diatomic itself. The only other possibility is dissociation. $\endgroup$ – DumpsterDoofus Apr 5 '14 at 20:52
  • $\begingroup$ Now I realize such a situation is unlikely to exist. That was my wrong and illogical imagination. OK, but, I didn't clearly understand why in the case of diatomic molecule the transition state is meaningless. For example, if the excited potential energy surface overlap the ground potential energy surface, there can be another minima at a higher energy. The molecule can possibly excited to this stable configuration which is of higher energy. In this case, the molecule will pass through a transition state, right? Here the transition state, I mean, the point of overlap of two PE surface. $\endgroup$ – albedo Apr 6 '14 at 7:23
  • $\begingroup$ When you excite a molecule from one state to another, it does not follow the potential energy surface. Instead, it jumps to another surface with that extra energy that it received from a photon. $\endgroup$ – gigacyan Apr 7 '14 at 14:59

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