The gamma subunit is slightly off center and is more associated with one alpha-beta pair than with the other two. This results in slightly different three dimensional structures for each alpha-beta pair. This is born out by what is bound to each pair.
The one pair that is most associated with the gamma subunit binds ADP and PO4= most well and that is what is observed in the active site.
The pair next to it binds ATP best and going in the same direction the next pair does not bind either ADP OR ATP very well
and it is found with an empty binding site.
These differences in binding are determined by the slight changes in structure of the alpha-beta pair as the gamma subunit comes in contact with it.
The H+ gradient "flowing" through the F0 subunit
causes rotation of the of the gamma subunit (represented by the yellow circle in the figure below)
which in turn performs work in the form of slightly altering the structure of proteins which it contacts.
The work of the structural change is used to synthesize an ATP.
There are three different structural conformations in the alpha-beta pairs. One represented by blue, another magenta and the last red. The rotation of the gamma subunit "causes" a structural change in the alpha-beta pairs (There is no physical rotation of the three alpha-beta pairs)