Derivatives in parameters

For optimisation on lattice observables we need partial derivatives of each type of observable with respect to potential energy function parameters. So far, we have two types of observables conformation. Including lattice constants, and lattice energy. 

Optimisation on molecular conformation Is done in all details as for free molecules. Technically we treat lattice constants as up to six extra conformational observables the partial derivatives are gotten exactly as for derivatives in cartesian coordinates, see section 7 3 1  

The lattice energy is made up of lattice sums S. In S we have terms of the form 

When convergence acceleration is used we have also terms which depend on( qj(u)) and on Y q Cu). The contributions of these to 3S /Qq(w) are  

In the methods of Williams and of Hagler and Lifson it is necessary to be able to write the lattice sums in this way, as they, and therefore the functions f(r j), are calculated only once, namely at the experimental geometry. 

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