In the chemiosmosis/ electron transport, where does the energy come from to synthesize ATP from ADP and Pi ?

In aerobic cellular respiration, glucose undergoes glycolysis (in the cytosol) which gives an end product of pyruvate, 2 net ATP, and NADH + H+.  The pyruvate is converted to acetyl coenzyme A and enters Kreb's cycle (in the mitochondria). Here more  NADH + H+ and FADH2 are generated, along with CO2 and 2ATP.  The NADH + H+ and the FADH2 are used in the final stage, oxidative phosphorylation.  The NADH + H+ and FADH2 transfer the hydrogen electrons to the transport chain (leaving just the protons). Energy is captured from the electrons and used to pump hydrogen ions out of the inner mitochondrial matrix into the intermembrane space (between the 2 mitochondrion membranes). This pumping action sets up a hydrogen chemical gradient.  The hydrogen then flows back into the inner membrane matrix through a specialized structure that captures the energy from the influx of hydrogen and this energy is used to sythesize ATP.  Hydrogen then combines with oxygen to form water.