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The results in equations
(19,20,22,
23) have been
written in a form which shows that in general each term can be
represented by a real numerical prefactor, integers which are the
powers of
and one further integer
to signify the presence of one of the terms
. When these terms are combined and differentiated by the
, the general term also needs integers to represent powers
of
. Therefore a general term in the
expressions for
and
could be
represented by a data structure consisting of one real variable
and ten integer variables as follows:

(36) 
with the following correspondence between and :
A recursive function can be written to manipulate these encoded terms
and perform the differentiation by the
, which can
themselves be generated using the recursion rules for the associated
Legendre polynomials. Thus it is straightforward to write a code which
starts from equation (14) and generates the results up to
arbitrary values of for
and
for the cases when
. The
results for
are simple enough to be coded
within the program which uses this basis.
We have successfully implemented this basis set in a totalenergy
pseudopotential code and are currently performing preliminary
calculations. For a given ionic configuration the matrix elements
between the basis states can be calculated initially and stored on
disk for use during the calculation.
Next: 8. Conclusions
Up: Localised sphericalwave basis set
Previous: 6. Nonlocal pseudopotential
Peter Haynes