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
