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?