Optimal control of a Cope rearrangement by coupling the reaction path to a dissipative bath or a second active mode

We compare the strategy found by the optimal control theory in a complex molecular system according to the active subspace coupled to the field. The model is the isomerization during a Cope rearrangement of Thiele's ester that is the most stable dimer obtained by the dimerization of methyl-cyclopentadienenylcarboxylate. The crudest partitioning consists in retaining in the active space only the reaction coordinate, coupled to a dissipative bath of harmonic oscillators which are not coupled to the field. The control then fights against dissipation by accelerating the passage across the transition region which is very wide and flat in a Cope reaction. This mechanism has been observed in our previous simulations [Chenel et al., J. Phys. Chem. A 116, 11273 (2012)]. We compare here, the response of the control field when the reaction path is coupled to a second active mode. Constraints on the integrated intensity and on the maximum amplitude of the fields are imposed limiting the control landscape. Then, optimum field from one-dimensional simulation cannot provide a very high yield. Better guess fields based on the two-dimensional model allow the control to exploit different mechanisms providing a high control yield. By coupling the reaction surface to a bath, we confirm the link between the robustness of the field against dissipation and the time spent in the delocalized states above the transition barrier.