Final answer:
The proper name for the bond between phosphate groups in ATP is phosphoanhydride bond. These high-energy bonds are formed between the second and third phosphate groups and between the first and second phosphate groups in ATP.
Step-by-step explanation:
The proper name for the bond between phosphate groups in ATP is phosphoanhydride bond. ATP is composed of adenosine bound to three phosphate groups. The high-energy bonds are formed between the second and third (or beta and gamma) phosphate groups and between the first and second phosphate groups. These bonds are considered "high-energy" because the products of the bond breaking, adenosine diphosphate (ADP) and one inorganic phosphate group (P₁), have considerably lower free energy than the reactants: ATP and a water molecule.