GerritJan Linker

Hooke's law The value of the potential energy for a bond between two atoms A and B can be determined at an arbitrary point by taking a Taylor expansion about r_{eq}, the equilibrium bond length. U(r) = U(r_{eq}) + dU/drr=r_{eq]} + 1/2! d^{2}U/d^{2}rr=r_{eq} (rr_{eq})^{2}) + 1/3! d^{3}U/d^{3}rr=r_{eq} (rr_{eq})^{3}) + ... The first term U(r_{eq}) can be set to zero. By doing this we set the offset of the potential energy at U(r_{eq}) The second term dU/drr=r_{eq} is also zero as U is minimum at r_{eq} If we truncate after the first non zero term we have the simpelest possible expression for the vibrational potential energy: U(r) = 1/2! d^{2}U/d^{2}rr=r_{eq} (rr_{eq})^{2}) = 1/2 k_{AB} (r_{AB}  r_{AB,eq})^{2} We replaced the second derivative with the symbol k, the force constant for the spring. This equation is Hooke's law.
