A prototypical system for a triatomic chemical reaction is the collision of atomic fluorine with molecular deuterium. Since the activation energy is very low (around 60 meV), the reaction rate is so high that the reaction products do not thermalize, and wavepacket effects play an important role. It turns out that the resulting DF is vibrationally highly excited (typically ν=4). The high reaction rate and efficient excitation make it possible to use this reaction for building a chemical laser, producing continuous output on the order of Megawatts. Here, we demonstrate the special case of a collinear reaction.
We use the Eckart bond coordinates with the bond lengths RD-F and RD-D for fixed bond angle (collinear collision geometry). This introduces cross-terms in the kinetic energy operator (see e.g. David Tannor's book on time-dependent Quantum mechanics, exercise 12.5).
Here, we visualize the collinear reaction of a Fluorine atom with a Deuterium molecule initially in its ground state. Note that the Deuterium atoms are indistinguishable. However, the Hamiltonian does not distinguish between both particles, so if we set up the initial wavefunction to be (anti-) symmetric under permutation of the particle numbers, it will stay this way.
The potential consists of a vertical trough that corresponds to bound D2 and free Fluorine, and a horizontal trough that describes bound DF and a free Deuterium atom. For low collision energies (around 25 meV), most of the Fluorine is deflected by the reaction barrier.
For higher collision energies (around 100 meV), most of the molecules undergo the reaction. The strong exothermicity is reflected in the nodal structure of the resulting DF, which suggests the formation of vibrationally excited molecules.
Last update: 26-Nov-2008