The force on ion i is given by
where 
is the energy of interaction between the ions.
The Hellmann-Feynman theorem states that if 
is an eigenstate of
H, then
and hence applying this to Equation 2.8 gives
Thus if the electron configuration has been relaxed sufficiently, so that the orbitals are approximate eigenstates, the forces on the ions may be efficiently calculated. The use of a non-local basis set removes the need for an additional term due to the derivative of the basis set with respect to atomic position, called the Pulay Force.
