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========= Dummy centers vs Ghost centers ========== ==== The Characters Originally dummy centers (named "x") were a mathematical trick to specify zmatrices for tricky molecules. E.g. benzene, or linear molecules. Because of their role it is alright to delete dummy centers. This was introduced at some point to clean up zmatrices. After deleting the dummies the autoz function would be used to regenerate a zmatrix. Ghost centers (named "bq" after the ghost Banquo from William Shakespeare's Macbeth) were introduced to calculate BSSE free energies. These centers have basis sets, but no charge and no electrons. ==== The conflict The way the deletion is implemented means that different things happen depending on how dummy centers are named. Due to a different choice of internal coordinates this could lead to a different optimization path. ==== The resolution To fix this all centers starting with "x" but not "xe" are deleted and a new zmatrix generated. Bq centers by their nature should not be deleted, and they now won't be. ==== The dénouement Not clear to me at present is what happens if the original input zmatrix contains constraints. I don't see how these can be handled so that they would always survive the elimination of the dummy centers. Of course one could replace the dummy centers by ghost centers without a basis set to deal with such a case. The dft_bsse test case has been updated to match the new approach.