The criterion for choosing is that it be close to, but larger than, the machine precision . I have found that pushing too close to (or smaller) does affect the quality of the returned eigenvector from the recipe in the previous section. One simple measure of this is the difference , which should be zero. For I found while for it drops to . It is unknown how the contamination by other (error) eigenvectors varies with . However I believe that since the errors mainly occur in the evaluation of small eigenvalue/eigenvector pairs of , any contamination is mainly by harmless (null-space) vectors.
On the other hand, also provides an approximate lower bound for the tension that can be reported. Therefore, in order to preserve the full depth of the tension minima, as small an as possible should be used. In practice, tension minima rarely are smaller than using RPWs, but with better basis sets they can reach typical values of in systems under investigation.
A choice of has proved optimal for calculations in this and the next chapter.