What to do with NPD atoms

In some of the examples in this book (e.g. 6.3.1 or 8.3.1), as well as most probably in your own practice as crystallographers, you have seen some atoms go NPD . NPD stands for non-positive definite and refers to a thermal ellipsoid with one or more of the three half-axes of the anisotropic displacement ellipsoid possessing a negative 

The answer to the question of how to treat NPD atoms depends largely on the reason why the atom is non-positive definite. Some people think that atoms that cannot be refined anisotropically should not be refined anisotropically, meaning that if an atom is listed as non-positive definite, it should be refined isotropically, as the data do not justify the anisotropic model. In some cases this is certainly trae, especially when the crystal was of poor quality and gave rise to a noisy dataset of only very low resolution (e.g. 1.1 A or worse). Usually in such a case, several or even most atoms are NPD and many others show pathologically shaped displacement ellipsoids. Sometimes, however, NPD atoms are observed with good high-resolution data and, frequently, something can be done to allow a full anisotropic model without NPD atoms. 

If an atom is NPD because of incorrectly assigned element type (carbon instead of sulfur or so) or due to an unresolved disorder, it usually suffices to correct the error to rectify the situation. In other, more difficult situations, constraints and restraints can help. 

If restraints do not help, it can be necessary to constrain two (or more) atoms to possess the same anisotropic displacement parameters, using the eadp constraint. This has been done in Examples 6.3.1 and 8.3.1 and, if there is a comprehensible reason for the atom to show NPD behaviour, can be quite adequate. If restraints or constraints were used to refine a sttucture, this should, however, always be mentioned in the publication. 

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