CCL:G: Question on calculation of charge center of electrons in a molecule

 Sent to CCL by: Herbert Fruchtl [herbert.fruchtl::st-andrews.ac.uk]
The centre of charge of each Gaussian function is its origin, i.e. the nucleus if you have atom-centred basis functions. The Mulliken charge is the sum of those functions, multiplied with their occupation number. Shouldn't this sum have its centre on the nucleus as well? And the sum of all of them (over all atoms) gives the complete charge distribution. Where am I going wrong? 
   Herbert
 Ulf Ekström ulfek(~)few.vu.nl wrote:
 
 Sent to CCL by: =?ISO-8859-1?Q?Ulf_Ekstr=F6m?= [ulfek],[few.vu.nl]
 On Thu, Nov 25, 2010 at 9:56 AM, Herbert Fruchtl
 herbert.fruchtl-.-st-andrews.ac.uk <owner-chemistry . ccl.net> wrote:
 
 Sent to CCL by: Herbert Fruchtl [herbert.fruchtl*_*st-andrews.ac.uk]
 I don't have time to look at the maths of it, but I think the centre of
 charge of the electron density should be identical to the centre of the
 Mulliken charges, which would be easy to calculate (analogous to the centre
 of mass).
 
 This will not work, for example if you have a single centre basis set all
 Mulliken charge would be on that center. What you should do is to compute
 the dipole moment of the molecule and use that to work out the center
 of charge.
 Sincerely,
Ulf Ekstrom> 
 --
 Herbert Fruchtl
 Senior Scientific Computing Officer
 School of Chemistry, School of Mathematics and Statistics
 University of St Andrews
 --
 The University of St Andrews is a charity registered in Scotland:
 No SC013532