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Dear Ian,
provided that f(s) is given by the formula in the Cromer/Mann article,
which I believe we have agreed on, the inset of Fig.1 of the Science
article we are talking about is claimed to be the graph of the
function g, which I added as pdf to this email for better readability.
Irrespective of what has been plotted in any other article meantioned
throughout this thread, this claim is incorrect, given a_i, b_i, c > 0.
I am sure you can figure this out yourself. My argument was not
involving mathematical programs but only one-dimensional calculus.
Cheers,
Tim
On 09/14/2012 04:46 PM, Ian Tickle wrote:
> On 14 September 2012 15:15, Tim Gruene <[log in to unmask]>
> wrote:
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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.
>
> Tim & Niu, oops yes a small slip in the paper there, it should
> have read "4 Gaussians + constant term": this is clear from the
> ITC reference given and the $CLIBD/atomsf.lib table referred to.
> In practice it's actually rendered as a sum of 5 Gaussians after
> you multiply the f(s) and atomic Biso factor terms, so unless Biso
> = 0 (very unphysical!) there is actually no constant term. My
> integral for rho(r) certainly doesn't oscillate between plus and
> minus infinity as d_min -> zero. If yours does then I suspect that
> either the Biso term was forgotten or if not then a bug in the
> integration routine (e.g. can it handle properly the point at r = 0
> where the standard formula for the density gives 0/0?). I used
> QUADPACK
> (http://people.sc.fsu.edu/~jburkardt/f_src/quadpack/quadpack.html)
> which seems pretty good at taking care of such singularities
> (assuming of course that the integral does actually converge).
>
> Cheers
>
> -- Ian
>
- --
- --
Dr Tim Gruene
Institut fuer anorganische Chemie
Tammannstr. 4
D-37077 Goettingen
GPG Key ID = A46BEE1A
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