-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 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 <t...@shelx.uni-ac.gwdg.de> > wrote: >> -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 >> >> 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 -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.12 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iD8DBQFQVFSBUxlJ7aRr7hoRAoPYAKDNQu84ozIz5Mn/qmRKiLxXPw/zPgCgwd75 KUHsKzaSdi9mL5kzZBeOqUI= =mbnY -----END PGP SIGNATURE-----
integral-crop.pdf
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