Now the electronic system is self-consistent it is possible to evaluate the forces on the atoms in order to optimise the structure.

The forces are determined from the gradient of the free energy, *F*
determined above, with respect to displacement,

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These forces can be determined analytically by considering the change in each term in the total energy for a displacement of . Thus

where

These are rearranged and substitutions made to eliminate and , leaving terms in only and . contains terms in and which can be determined from
Equations 3.2.23 and 3.2.27. Although *T*_{ij} and *S*_{ij}
only depend on *R*_{la} through the basis functions, , the pseudopotential term is also dependent on *R*_{la}
due to ; this is determined by
integrating by parts to replace with terms in :

The forces are relatively quick to evaluate compared to determination of the self-consistent energy.