Potential energy surfaces spherically symmetric molecules

In order to calculate the maximum rate of the bimolecular reaction, the assumption is made that every time two molecules collide, a chemical reaction occurs. Consider the diffusion of a system of A molecules into stationary B molecules. If every time A collides with B a reaction occurs, the concentration of A at the surface of B must equal zero, while the concentration at a large distance from B is equal to the bulk concentration C o In order to simplify the problem mathematically, the molecules are assumed to be spherical, so that the diffusion process is spherically symmetric, and the potential energy U is assumed to be a function of r only. This model is depicted in Fig. 2-13. A general solution of Eq. (2-85) is still not possible, but if a steady state is assumed (that is, dCJdt = 0), the total flux through the surface of a sphere of radius r around B is constant for all values of r and is... 

Unfortunately there is as yet no known way to obtain the repulsion energy from properties of the separate molecules. An attempt has been made to characterise the repulsive surface of a molecule by performing IMPT calculations between the molecule and a suitable test particle, such as a helium atom. Because the helium atom has only one molecular orbital and is spherically symmetrical, such calculations can be done much more easily than calculations involving two ordinary molecules. From the data for the repulsion between molecule A and the test particle, and between B and the test particle, it may be possible to construct a repulsive potential between A and B. Some limited progress has been made with this idea. An alternative approach has been based on the suggestion that the repulsion energy is closely correlated with the overlap between the molecular wavefunctions, but this seems likely to be more useful as a guide to the form of analytic models than as a direct route to accurate potential functions. 

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