CCL:G: Question on calculation of charge center of electrons in a
molecule
- From: Jiabo Li <jiaboli]_[yahoo.com>
- Subject: CCL:G: Question on calculation of charge center of
electrons in a molecule
- Date: Sat, 27 Nov 2010 18:02:19 -0800 (PST)
To understand what is wrong, you can look at a simple example: the hydrogen
atom in its excited state with the single electron on a SP hydride orbital. In
this case, the electron density is not central symmetric but polarized, and the
dipole moment is not zero (a big dipole moment), while in this case the net
atomic charge is zero (neutral).
Jiabo
--- On Fri, 11/26/10, Herbert Fruchtl herbert.fruchtl[#]st-andrews.ac.uk
<owner-chemistry,ccl.net> wrote:
> From: Herbert Fruchtl herbert.fruchtl[#]st-andrews.ac.uk
<owner-chemistry,ccl.net>
Subject: CCL:G: Question on calculation of charge center of electrons in a
molecule
To: "Li, Jiabo " <jiaboli,yahoo.com>
Date: Friday, November 26, 2010, 6:25 AM
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
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<table cellspacing="0" cellpadding="0"
border="0" ><tr><td valign="top"
style="font: inherit;"><DIV>To understand what is wrong, you
can look at a simple example: the hydrogen atom in its excited state with the
single electron on a SP hydride orbital. In this case, the electron density is
not central symmetric but polarized, and the dipole moment is not zero (a big
dipole moment), while in this case the net atomic charge is zero
(neutral).</DIV>
<DIV> </DIV>
<DIV>Jiabo<BR><BR>--- On <B>Fri, 11/26/10, Herbert
Fruchtl herbert.fruchtl[#]st-andrews.ac.uk
<I><owner-chemistry,ccl.net></I></B>
wrote:<BR></DIV>
<BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT:
rgb(16,16,255) 2px solid"><BR>From: Herbert Fruchtl
herbert.fruchtl[#]st-andrews.ac.uk
<owner-chemistry,ccl.net><BR>Subject: CCL:G: Question on
calculation of charge center of electrons in a molecule<BR>To: "Li,
Jiabo -id#3p9-" <jiaboli,yahoo.com><BR>Date: Friday,
November 26, 2010, 6:25 AM<BR><BR>
<DIV class=plainMail><BR>Sent to CCL by: Herbert Fruchtl
[herbert.fruchtl::st-andrews.ac.uk]<BR>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?<BR><BR>
Herbert<BR><BR>Ulf Ekström ulfek(~)few.vu.nl
wrote:<BR>> Sent to CCL by: =?ISO-8859-1?Q?Ulf_Ekstr=F6m?=
[ulfek],[few.vu.nl]<BR>> On Thu, Nov 25, 2010 at 9:56 AM, Herbert
Fruchtl<BR>> herbert.fruchtl-.-st-andrews.ac.uk
<owner-chemistry . ccl.net> wrote:<BR>>> Sent
to CCL by: Herbert Fruchtl
[herbert.fruchtl*_*st-andrews.ac.uk]<BR>>> I don't have time
to look at the maths of it, but I think the centre of<BR>>>
charge of the electron density
should be identical to the centre of the<BR>>> Mulliken
charges, which would be easy to calculate (analogous to the
centre<BR>>> of mass).<BR>> <BR>>
This will not work, for example if you have a single centre basis set
all<BR>> Mulliken charge would be on that center. What you should
do is to compute<BR>> the dipole moment of the molecule and use
that to work out the center<BR>> of charge.<BR>>
<BR>> Sincerely,<BR>> Ulf Ekstrom>
<BR><BR>-- Herbert Fruchtl<BR>Senior Scientific Computing
Officer<BR>School of Chemistry, School of Mathematics and
Statistics<BR>University of St Andrews<BR>--<BR>The University
of St Andrews is a charity registered in Scotland:<BR>No
SC013532<BR><BR><BR><BR>-= This is automatically added
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