I want to ask a question about the exchange integral $\ce{H_{AB}}$ -
If I consider an exchange integral $\ce{H_{AB}}$ the following exchange integral can be evaluated:
so $\ce{S_{AB}}$ is $0$ at $\ce{R = \infty}$
but in this presentation I was shown today, at large values of R, $\ce{H_{AB}}$ is preportional to the overap integral $\ce{S_{AB}}$.
Surely at large distances and towards infinity, as $\ce{S_{AB}}$ goes to zero, $\ce{H_{AB}}$ also goes to zero too.
Where does the preportionality
$$H_{AB} \propto S_{AB}$$
come from then using these approimations when R is large?