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We define the Fourier transform of a basis function
by
The angular integral is performed by using the expansion of
into sphericalwaves
(A.3, appendix A) leaving the radial integral

(5.8) 
The radial integral can now be calculated using equations
A.4 and A.5 and the
boundary conditions (that the basis functions are finite at
and vanish at
) for the cases when
and
respectively. The final result for the
Fourier transform of a basis function is then

(5.9) 
Equation 5.9b is in fact a limiting case of
(5.9a) which can therefore always be substituted for
in an integral over
reciprocalspace.
Next: 5.4 Overlap matrix elements
Up: 5. Localised basisset
Previous: 5.2 Origin of the
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Peter Haynes