(a) Consider the stationary point structures A and B for this reaction noting that the reaction coordinate, X, principally describes the motion of just one hydrogen atom. Structure B is found to have the following vibrational wavenumbers: 387, (i) 759, 1248, 1718, 3147 and 3219 cm. What do these tell us about the topology of the PES? (ii) Using the data given overleaf, sketch (or plot) the potential energy curve along the reaction coordinate X. If the reaction from A to B is endothermic, what values of the reaction coordinate correspond to A and B? (iii) For a third structure, C, the derivative of the PE with respect to the change in any of the coordinates describing the structure of the molecule is found to be zero. A harmonic vibrational analysis of this structure is found to have vibrational wavenumbers of 947i, 576, 922, 1864, 2500 and 3392 cm . Give reasons why this structure corresponds to X=0. Data: x /(au) -4.0 -3.0 -2.0 -1.0 -0.5 0 0.5 1.0 2.0 3.0 V(X)/(kJ mol-) 0 10 62 145 185 200 194 188 178 173 (12 marks) (b) Briefly discuss the validity of each of the following statements: (i) In combination with a geometry optimisation method, molecular mechanics (MM) can be used to find the activation energy of a Diels-Alder chemical reaction. (ii) A canonical ensemble is a group of molecules which when averaged gives us an equilibrium structure at room temperature. (iii) A single trajectory of a low temperature molecular dynamics simulation can be used to search for conformers of large molecules.