tl;dr

The hypothesis here is that early bacteria/archea basically worked a lot like a car battery, with a + and a - terminal and the the permeability of the cell membrane allowed H+ to flow through the cell turning the little ATPase crank to turn out ATP. The unspoken hypothesis here is that organisms like this probably lived on the rock surface of a geothermal vent when there aqueous phase was acidic and there was another 'layer' that was alkaline (probably on the rock face?).

Overtime a Na+/H+ exchanger was added to increase the movement of H+ across the membrane which made the ATPase crank turn 60% faster. Eventually in phase 3 ion pumps really supercharged the ion gradient and allowed these organisms to move into environments that didn't need a bi-phasic H+/OH- layer. It's likely that the ion pumps and non-permeable membranes formed as the little guys moved out of the geothermal vents and diverged into new environments, giving rise to the divergent archea and bacteria.