On 14 September 2012 13:05, Tim Gruene <[log in to unmask]> wrote:
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> Dear Niu,
>
> as far as I can tell, all your parameters are correct and the
> scattering term for f(s) you use is also correct. f(s) furthermore
> matches very closely those tabulated in the Intl. Tables C Tab. 6.1.1.1.
>
> My reproduction of the mentioned formula with r=2.0 using MAXIMA also
> shows quite a different graph.
>
> The graph does not make much sense:
> as d_max -> 0 1/d_max -> infinity and the integrand goes to infinity,
d_min surely, i.e. minimum d-spacing?
> because f(s) contains a constant positive term. Hence the integral
> should oscilatingly approach infinity and not stabilise as the upper
> integral limit approaches infinity.
Tim, exactly so, in fact like this:
http://journals.iucr.org/d/issues/2012/04/00/dz5235/dz5235.pdf
See eqn 2 and Fig 11(b). Note that although rho(r) itself does indeed
tend to zero as d_min -> 0 as expected, the volume integral of rho(r)
(i.e. the calculated number of electrons) does not (unless d_min -> 0)
!
Cheers
-- Ian
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