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Hello Ian,

your article describes f(s) as sum of four Gaussians, which is not the
same f(s) from Cromer's and Mann's paper and the one used both by Niu
and me. Here, f(s) contains a constant, as I pointed out to in my
response, which makes the integral oscillate between plus and minus
infinity as the upper integral border (called 1/dmax in the article
Niu refers to) goes to infinity).

Maybe you can shed some light on why your article uses a different
f(s) than Cromer/Mann. This explanation might be the answer to Nius
question, I reckon, and feed my curiosity, too.

Cheers,
Tim

On 09/14/2012 02:39 PM, Ian Tickle wrote:
> 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
> 

- -- 
- --
Dr Tim Gruene
Institut fuer anorganische Chemie
Tammannstr. 4
D-37077 Goettingen

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