How does the corresponding diagram for cyclohexene look like?
I found the answer in the book: "Practical Aspects of Computational Chemistry" . In chapter 19: Unusual Properties of Usual Molecules. Conformational Analysis of Cyclohexene, Its Derivatives and Heterocyclic Analogues.
The value for ring inversion of cyclohexene is smaller than the one of cyclohexane (which is near 10 kcal/mol):
Value of ring inversion barrier is within 4.2– 7.9 kcal/mol for molecular mechanics and 5.2–6.6 kcal/mol for quantum chemical methods.
The inversion proceeds as follows:
The ring inversion process in cyclohexene includes three stage. The first stage involves the transition from an equilibrium half-chair conformation to a twist-boat conformation with a significant increase in energy. The second stage may be described as a very easy transformation of one twist-boat conformation to another via boat almost without any changes in energy. The third stage includes the transition from a twist-boat conformation to a half-chair conformation accompanied by a significant decrease in energy. The difference in energy between the twist-boat and the boat conformation is less than 0.01 kcal/mol. The boat conformation is just central point of this plateau and it is only the most convenient point for a description of the saddle point for the ring inversion .