From owner-chemistry@ccl.net Mon Nov 29 11:36:01 2010 From: "James Eilers jeilers!^!siue.edu" To: CCL Subject: CCL:G: Question on calculation of charge center of electrons in a molecule Message-Id: <-43237-101129100357-1506-hUf/xn1d7Drf0aZ6EbEGzA]=[server.ccl.net> X-Original-From: James Eilers Content-Type: multipart/alternative; boundary=Apple-Mail-2--796939897 Date: Mon, 29 Nov 2010 09:01:12 -0600 Mime-Version: 1.0 (Apple Message framework v624) Sent to CCL by: James Eilers [jeilers-,-siue.edu] --Apple-Mail-2--796939897 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Mulliken charges also include the "shared" electron density or cross =20 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 =20 > hydrogen atom in its excited state with the single electron on a SP =20= > hydride orbital. In this case, the electron density is not central =20 > symmetric but polarized, and the dipole moment is not zero (a big =20 > dipole moment), while in this case the net atomic charge is zero =20 > (neutral). > =A0 > Jiabo > > --- On Fri, 11/26/10, Herbert Fruchtl =20 > herbert.fruchtl[#]st-andrews.ac.uk wrote: > > >> From: Herbert Fruchtl herbert.fruchtl[#]st-andrews.ac.uk =20 >> > Subject: CCL:G: Question on calculation of charge center of electrons =20= > in a molecule > To: "Li, Jiabo " > 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 = =20 > nucleus if you have atom-centred basis functions. The Mulliken charge =20= > is the sum of those functions, multiplied with their occupation =20 > number. Shouldn't this sum have its centre on the nucleus as well? And = =20 > the sum of all of them (over all atoms) gives the complete charge =20 > distribution. Where am I going wrong? > > =A0 Herbert > > Ulf Ekstr=F6m ulfek(~)few.vu.nl wrote: >> Sent to CCL by: =3D?ISO-8859-1?Q?Ulf_Ekstr=3DF6m?=3D = [ulfek],[few.vu.nl] >> On Thu, Nov 25, 2010 at 9:56 AM, Herbert Fruchtl >> herbert.fruchtl-.-st-andrews.ac.uk 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 = =20 >>> of >>> charge of the electron density should be identical to the centre of =20= >>> the >>> Mulliken charges, which would be easy to calculate (analogous to the = =20 >>> centre >>> of mass). >> >> This will not work, for example if you have a single centre basis set = =20 >> all >> Mulliken charge would be on that center. What you should do is to =20 >> 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 > > > > -=3D This is automatically added to each message by the mailing script = =20 > =3D-=A0 =A0=A0=A0http://www.ccl.net/cgi-bin/ccl/send_ccl_message=A0 =20= > =A0=A0=A0http://www.ccl.net/cgi-bin/ccl/send_ccl_message > > Subscribe/Unsubscribe:=A0 =A0 =A0 =20Conferences: =20 > http://server.ccl.net/chemistry/announcements/conferences/=A0 =20 > =A0=A0=A0http://www.ccl.net/spammers.txt--0-160776249-1290909739=3D:8785= 1 > Content-Type: text/html; charset=3Diso-8859-1 > Content-Transfer-Encoding: quoted-printable > >
valign=3D"top" style=3D"font: inherit;">
To understand what is = wrong, =20 > you can look at a simple example: the hydrogen atom in its excited =20 > state with the single electron on a SP hydride orbital. In this case, =20= > the electron density is not central symmetric but polarized, and the =20= > dipole moment is not zero (a big dipole moment), while in this case =20= > the net atomic charge is zero (neutral).
>
 
>
Jiabo

--- On Fri, 11/26/10, Herbert Fruchtl =20 > herbert.fruchtl[#]st-andrews.ac.uk =20 > <owner-chemistry]*[ccl.net> wrote:
>
rgb(16,16,255) 2px solid">
From: Herbert Fruchtl =20 > herbert.fruchtl[#]st-andrews.ac.uk =20 > <owner-chemistry]*[ccl.net>
Subject: CCL:G: Question on =20 > calculation of charge center of electrons in a molecule
To: "Li, =20= > Jiabo " <jiaboli]*[yahoo.com>
Date: Friday, November =20= > 26, 2010, 6:25 AM

>

Sent to CCL by: Herbert Fruchtl =20 > [herbert.fruchtl::st-andrews.ac.uk]
The centre of charge of each =20= > Gaussian function is its origin, i.e. the nucleus if you have =20 > atom-centred basis functions. The Mulliken charge is the sum of those =20= > functions, multiplied with their occupation number. Shouldn't this sum = =20 > have its centre on the nucleus as well? And the sum of all of them =20 > (over all atoms) gives the complete charge distribution. Where am I =20= > going wrong?

  Herbert

Ulf Ekstr=F6m =20 > ulfek(~)few.vu.nl wrote:
> Sent to CCL by: =20 > =3D?ISO-8859-1?Q?Ulf_Ekstr=3DF6m?=3D [ulfek],[few.vu.nl]
> On = Thu, Nov =20 > 25, 2010 at 9:56 AM, Herbert Fruchtl
> =20 > herbert.fruchtl-.-st-andrews.ac.uk <owner-chemistry . ccl.net> =20= > wrote:
>> Sent to CCL by: Herbert Fruchtl =20 > [herbert.fruchtl*_*st-andrews.ac.uk]
>> I don't have time to =20= > look at the maths of it, but I think the centre of
>> charge =20= > of the electron density > should be identical to the centre of the
>> Mulliken =20 > charges, which would be easy to calculate (analogous to the =20 > centre
>> of mass).
>
> This will not work, for =20= > example if you have a single centre basis set all
> Mulliken =20 > charge would be on that center. What you should do is to =20 > compute
> the dipole moment of the molecule and use that to work = =20 > out the center
> of charge.
>
> Sincerely,
> =20= > Ulf Ekstrom>

-- Herbert Fruchtl
Senior Scientific =20 > Computing Officer
School of Chemistry, School of Mathematics and =20= > Statistics
University of St Andrews
--
The University of St =20= > Andrews is a charity registered in Scotland:
No =20 > SC013532



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James E. Eilers Professor Chemistry Department Southern Illinois University Edwardsville (618)650-3559 --Apple-Mail-2--796939897 Content-Transfer-Encoding: quoted-printable Content-Type: text/enriched; charset=ISO-8859-1 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). =A0 Jiabo --- On Fri, 11/26/10, Herbert Fruchtl herbert.fruchtl[#]st-andrews.ac.uk < wrote: From: Herbert Fruchtl herbert.fruchtl[#]st-andrews.ac.uk < Subject: CCL:G: Question on calculation of charge center of electrons in a molecule To: "Li, Jiabo " < 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? =A0 Herbert Ulf Ekstr=F6m ulfek(~)few.vu.nl wrote: Sent to CCL by: =3D?ISO-8859-1?Q?Ulf_Ekstr=3DF6m?=3D [ulfek],[few.vu.nl] On Thu, Nov 25, 2010 at 9:56 AM, Herbert Fruchtl herbert.fruchtl-.-st-andrews.ac.uk < 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>=20 -- 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 -=3D This is automatically added to each message by the mailing script =3D-=A0 =A0=A0=A0http://www.ccl.net/cgi-bin/ccl/send_ccl_message=A0 =A0=A0=A0http://www.ccl.net/cgi-bin/ccl/send_ccl_message Subscribe/Unsubscribe:=A0 =A0 =A0=A0 =A0=A0=A0http://www.ccl.net/spammers.txt--0-160776249-1290909739=3D:87851 Content-Type: text/html; charset=3Diso-8859-1 Content-Transfer-Encoding: quoted-printable <<<<<
<
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<
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--- 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 Ekstr=F6m ulfek(~)few.vu.nl wrote:<
> Sent to CCL by: =3D?ISO-8859-1?Q?Ulf_Ekstr=3DF6m?=3D [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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HelveticaJames E. Eilers Professor Chemistry Department Southern Illinois University Edwardsville (618)650-3559 --Apple-Mail-2--796939897--