Vibrational motions making allowed

CHECKPOINT In Eq. 8.2, our color-coding emphasizes that we can now draw on the solved energy eigenvalues E iec from Chapter 6 to replace the electronic part of the Hamiltonian in this chapter. The Born-Oppenheimer approximation not only makes the electronic part of the Schrodinger equation problem easier to solve, it allows us to address the vibrational motions now without worrying about the motions of all the electrons. 

The study of dynamics allows us to raise additional questions, questions that do not quite make sense when we study the net change, at or near equilibrium, in the bulk. For example, we can wonder if exciting vibrational motion in either or both reactant diatomic molecules will make the CI2 + Br2 four-center reaction proceed more rapidly. In bulk chemical kinetics, when the reactants are intentionally arranged to be in thermal equilibrium, a particular mode cannot be energized preferentially. To learn about a selective role of internal energy in promoting a reaction it is necessary to work under non-equilibrium conditions. ... 

Equation (1-13) or its body-fixed equivalent is of little use for Van der Waals complexes, as it discriminates one nuclear coordinate, e.g. y = 1. Specific mathematical forms of Hamiltonians describing the nuclear motions in Van der Waals dimers have been developed (7). This point will be discussed in more details in Section 12.4. Here we only want to stress that whatever the mathematical form of the Hamiltonian is used to solve the problem of nuclear motions, the results will be the same, if the Schrodinger equation is solved exactly. However, in weakly bound complexes there is a hierarchy of motions due to the strong intramolecular forces which determine the internal vibrations of the molecules, and to much weaker intermolecular forces which determine their relative translations and rotations. This hierarchy allows to make a separation between the intramolecular vibrations with high frequencies and the intermolecular modes with much lower frequencies. Such a separation of the fast intramolecular vibrations and slow rotation-vibration-tunneling motions can be performed if a suitable form of the Hamiltonian for the nuclear motions in Van der Waals molecules is used. 

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