What is the minimum pH difference such that transfer of one H ion across the membrane would provide enough energy to make one molecule of ATP?

The minimum difference is already the value of 1

Explanation:

When the pH is not balanced between the extracellular and intracellular environment, the cell could go into shock, that is why in the face of the minimal differences in pH between the internal or external environment, the proton pump is activated, this is how the hydrogen ion or positively charged protons cross the membrane and indirectly generate ATP molecules.