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

From: James Eilers <jeilers*siue.edu>
Subject: CCL:G: Question on calculation of charge center of electrons in a molecule
Date: Mon, 29 Nov 2010 09:01:12 -0600

Mulliken charges also include the "shared" electron density or cross terms between atomic orbitals on different centers.

On Nov 27, 2010, at 8:02 PM, Jiabo Li jiaboli/./yahoo.com wrote:

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 --- On Fri, 11/26/10, Herbert Fruchtl herbert.fruchtl[#]st-andrews.ac.uk <owner-chemistry]*[ccl.net> wrote: </DIV>
<BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: rgb(16,16,255) 2px solid"> 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 
<DIV class=plainMail> 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 -= This is automatically added to each message by the mailing script =-<BR the strange characters on the top line to the ]*[ sign. You can also<BR E-mail to subscribers: <A href="http://us.mc369.mail.yahoo.com/mc/compose?to=CHEMISTRY]*[ccl.net" ymailto="mailto:CHEMISTRY]*[ccl.net">CHEMISTRY]*[ccl.net</A> or use:      <A href="http://www.ccl.net/cgi-bin/ccl/send_ccl_message" target=_blank>http://www.ccl.net/cgi-bin/ccl/send_ccl_message</A> E-mail to administrators: <A href="http://us.mc369.mail.yahoo.com/mc/compose?to=CHEMISTRY-REQUEST]*[ccl.net" ymailto="mailto:CHEMISTRY-REQUEST]*[ccl.net">CHEMISTRY-REQUEST]*[ccl.net</A> or use      <A href="http://www.ccl.net/cgi-bin/ccl/send_ccl_message" target=_blank>http://www.ccl.net/cgi-bin/ccl/send_ccl_message</A> Subscribe/Unsubscribe:      <A href="http://www.ccl.net/chemistry/sub_unsub.shtml" target=_blank>http://www.ccl.net/chemistry/sub_unsub.shtml</A> Before posting, check wait time at: <A href="http://www.ccl.net/"
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James E. Eilers
Professor
Chemistry Department
Southern Illinois University Edwardsville
(618)650-3559