I have been playing around between ab initio calculation of forces and their use in GULP fits for the establishment of potentials. I noticed in the GULP output that a constrained fit with force observables does not use force components of atom label 1 (the output table of observables starts with 2x, 2z, 2z labels). Does this mean that all forces are calculated with respect to this reference 1 atom ?
The reason that the forces of one atom are not used (which can be the first, last or any other atom you choose) is because of translational invariance. This means the sum of all the forces has to be zero & so the force on one atom is fixed once you know the forces of all the other atoms. When performing optimisation with second derivatives it’s necessary to fix an atom otherwise the Hessian matrix becomes singular, which is why one atom is excluded from the optimisation. For fitting, it means that there is no point fitting the force on all the atoms since there are only 3N-3 independent values (where N is the number of atoms).
Hope that helps,