## Derivatives

Solid-state derivatives with respect to geometry are handled differently from molecule derivatives. If the Cartesian coordinate derivatives are printed, using DEBUG and DCART, then for a molecule with an optimized geometry all the derivatives will be zero. This is not the case for an infinite system.

An infinite system is represented by cell supplied by the user, called the Central Unit Cell, or the CUC, and the cells surrounding this CUC. When DCART, LARGE, and DEBUG are used in an infinite system calculation for which the geometry has been optimized, the Cartesian derivatives for all unit cells are output. Many of these will be quite large, up to about 60 kcal/mol/Å. This is not an error, rather it is a peculiarity of the way solid-state derivatives are stored.

The Cartesian derivatives of the CUC represent the sum of all forces acting on the atoms of the CUC due to all the atoms in the CUC. Thus, if the atoms in the CUC are the set (a,b,c,d,e,f), then the Cartesian derivatives for atom a represent the forces on a due to the set (b,c,d,e,f). The Cartesian derivatives of atom a do NOT include terms from the surrounding unit cells. Because of this, those atoms in the CUC which are at the cell boundaries are likely to have large derivatives.

The Cartesian derivatives of the surrounding unit cells represent the forces acting on the atoms in those cells arising from the atoms of the CUC. Again, this is an unbalanced set of forces, and those atoms near to the cell boundaries are likely to have large resultant forces.

It is possible to evaluate the total, balanced, forces acting on the atoms of the CUC. This is done by simply adding the forces acting on the atoms of the three unit cells. When the keywords given above are used, the last part of the derivative output consists of the forces acting on the CUC itself.

Only by representing the forces in this unusual manner can the information necessary for calculating the derivative of the translation vector be generated.