From owner-chemistry@ccl.net Sun Jun 12 12:11:01 2016 From: "James Buchwald buchwj\a/rpi.edu" To: CCL Subject: CCL: Coupling constant (Jab) - Why more unpaired electrons means a smaller coupling? Message-Id: <-52240-160611192739-13010-RAX1DXn+oJweW3B6N0/Jzg_+_server.ccl.net> X-Original-From: James Buchwald Content-Type: multipart/alternative; boundary="------------BA46CE5A56C59D6F17AA7D38" Date: Sat, 11 Jun 2016 19:27:24 -0400 MIME-Version: 1.0 Sent to CCL by: James Buchwald [buchwj . rpi.edu] This is a multi-part message in MIME format. --------------BA46CE5A56C59D6F17AA7D38 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Hi Henrique, The diminishing Jab that you're predicting assumes that (E[HS] - E[BS]) does not grow as quickly as the spin term in the denominator. Depending on the system, this is not necessarily the case, and the energy spacing can grow faster. The reason that the equations appear to cause this is that the Heisenberg-Dirac-van Vleck Hamiltonian (which the three equations were derived from) has a "spin ladder" of solutions ranging from the low-spin to the high-spin states. If your low-spin state is a singlet, you'll also have triplets, pentets, and so on until you reach the high-spin state. Similarly, if you start from a doublet, you'll have intermediate quartets, etc. As you introduce more and more unpaired electrons, the spin of the high-spin state increases - but all of the intermediate states between the high-spin and low-spin limits still exist. You can work out the splitting between these individual states in terms of J, and what ends up happening is that the states spread out. The denominator essentially corrects for that spacing, rather than saying anything about the strength of the magnetic coupling. Best, James On 06/11/2016 05:54 PM, Henrique C. S. Junior henriquecsj-x-gmail.com wrote: > I hope this is not a "homework" question, but I'm having a bad time > trying to figure this out. > Available literature proposes 3 equations to calculate the coupling > constant during a Broken-Symmetry approach: > > J(1) = -(E[HS]-E[BS])/Smax**2 > J(2) = -(E[HS]-E[BS])/(Smax*(Smax+1)) > J(3) = -(E[HS]-E[BS])/(HS-BS) > > I'm intrigued by the fact that, from the equations, the more the > system have unpaired electrons, the minor will be Jab. Why does this > happen? Doesn't more unpaired electrons increase magnetic momenta (and > an increase in magnetic coupling)? > > -- > *Henrique C. S. Junior* > Químico Industrial - UFRRJ > Mestrando em Química Inorgânica - UFRRJ > Centro de Processamento de Dados - PMP -- James R. Buchwald Doctoral Candidate, Theoretical Chemistry Dinolfo Laboratory Dept. of Chemistry and Chemical Biology Rensselaer Polytechnic Institute http://www.rpi.edu/~buchwj --------------BA46CE5A56C59D6F17AA7D38 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: 8bit

Hi Henrique,

The diminishing Jab that you're predicting assumes that (E[HS] - E[BS]) does not grow as quickly as the spin term in the denominator.  Depending on the system, this is not necessarily the case, and the energy spacing can grow faster.

The reason that the equations appear to cause this is that the Heisenberg-Dirac-van Vleck Hamiltonian (which the three equations were derived from) has a "spin ladder" of solutions ranging from the low-spin to the high-spin states.  If your low-spin state is a singlet, you'll also have triplets, pentets, and so on until you reach the high-spin state.  Similarly, if you start from a doublet, you'll have intermediate quartets, etc.

As you introduce more and more unpaired electrons, the spin of the high-spin state increases - but all of the intermediate states between the high-spin and low-spin limits still exist.  You can work out the splitting between these individual states in terms of J, and what ends up happening is that the states spread out.  The denominator essentially corrects for that spacing, rather than saying anything about the strength of the magnetic coupling.

Best,
James

On 06/11/2016 05:54 PM, Henrique C. S. Junior henriquecsj-x-gmail.com wrote:
I hope this is not a "homework" question, but I'm having a bad time trying to figure this out.
Available literature proposes 3 equations to calculate the coupling constant during a Broken-Symmetry approach:

J(1) = -(E[HS]-E[BS])/Smax**2
J(2) = -(E[HS]-E[BS])/(Smax*(Smax+1))
J(3) = -(E[HS]-E[BS])/(<S**2>HS-<S**2>BS)

I'm intrigued by the fact that, from the equations, the more the system have unpaired electrons, the minor will be Jab. Why does this happen? Doesn't more unpaired electrons increase magnetic momenta (and an increase in magnetic coupling)?

--
Henrique C. S. Junior
Químico Industrial - UFRRJ
Mestrando em Química Inorgânica - UFRRJ
Centro de Processamento de Dados - PMP

-- 
James R. Buchwald
Doctoral Candidate, Theoretical Chemistry
Dinolfo Laboratory
Dept. of Chemistry and Chemical Biology
Rensselaer Polytechnic Institute
http://www.rpi.edu/~buchwj
--------------BA46CE5A56C59D6F17AA7D38-- From owner-chemistry@ccl.net Sun Jun 12 19:05:01 2016 From: "Henrique C. S. Junior henriquecsj:-:gmail.com" To: CCL Subject: CCL: Coupling constant (Jab) - Why more unpaired electrons means a smaller coupling? Message-Id: <-52241-160612151328-25214-tgcPs67quQpsv+1k6xuA2w*server.ccl.net> X-Original-From: "Henrique C. S. Junior" Content-Type: multipart/alternative; boundary=001a113e0258c7d5a70535199017 Date: Sun, 12 Jun 2016 16:12:43 -0300 MIME-Version: 1.0 Sent to CCL by: "Henrique C. S. Junior" [henriquecsj*gmail.com] --001a113e0258c7d5a70535199017 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Thank you for your explanations, Professor Rodriguez and James, now it is very clear! Thanks. 2016-06-11 20:27 GMT-03:00 James Buchwald buchwja/rpi.edu < owner-chemistry++ccl.net>: > Hi Henrique, > The diminishing Jab that you're predicting assumes that (E[HS] - E[BS]) > does not grow as quickly as the spin term in the denominator. Depending = on > the system, this is not necessarily the case, and the energy spacing can > grow faster. > > The reason that the equations appear to cause this is that the > Heisenberg-Dirac-van Vleck Hamiltonian (which the three equations were > derived from) has a "spin ladder" of solutions ranging from the low-spin = to > the high-spin states. If your low-spin state is a singlet, you'll also > have triplets, pentets, and so on until you reach the high-spin state. > Similarly, if you start from a doublet, you'll have intermediate quartets= , > etc. > > As you introduce more and more unpaired electrons, the spin of the > high-spin state increases - but all of the intermediate states between th= e > high-spin and low-spin limits still exist. You can work out the splittin= g > between these individual states in terms of J, and what ends up happening > is that the states spread out. The denominator essentially corrects for > that spacing, rather than saying anything about the strength of the > magnetic coupling. > > Best, > James > > On 06/11/2016 05:54 PM, Henrique C. S. Junior henriquecsj-x-gmail.com > wrote: > > I hope this is not a "homework" question, but I'm having a bad time tryin= g > to figure this out. > Available literature proposes 3 equations to calculate the coupling > constant during a Broken-Symmetry approach: > > J(1) =3D -(E[HS]-E[BS])/Smax**2 > J(2) =3D -(E[HS]-E[BS])/(Smax*(Smax+1)) > J(3) =3D -(E[HS]-E[BS])/(HS-BS) > > I'm intrigued by the fact that, from the equations, the more the system > have unpaired electrons, the minor will be Jab. Why does this happen? > Doesn't more unpaired electrons increase magnetic momenta (and an increas= e > in magnetic coupling)? > > -- > *Henrique C. S. Junior* > Qu=C3=ADmico Industrial - UFRRJ > Mestrando em Qu=C3=ADmica Inorg=C3=A2nica - UFRRJ > Centro de Processamento de Dados - PMP > > > -- > James R. Buchwald > Doctoral Candidate, Theoretical Chemistry > Dinolfo Laboratory > Dept. of Chemistry and Chemical Biology > Rensselaer Polytechnic Institutehttp://www.rpi.edu/~buchwj > > --=20 *Henrique C. S. Junior* Qu=C3=ADmico Industrial - UFRRJ Mestrando em Qu=C3=ADmica Inorg=C3=A2nica - UFRRJ Centro de Processamento de Dados - PMP --001a113e0258c7d5a70535199017 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Thank you for your explanations, Professor Rodriguez and James= , now it is very clear!
Thanks.

=
2016-06-11 20:27 GMT-03:00 James Buchwald buchwj= a/rpi.edu <owner-chemistry++ccl.net>:
=20 =20 =20

Hi Henrique,

The diminishing Jab that you're predicting assumes that (E[HS] - E[BS]) does not grow as quickly as the spin term in the denominator.=C2=A0 Depending on the system, this is not necessarily the case, and the energy spacing can grow faster.

The reason that the equations appear to cause this is that the Heisenberg-Dirac-van Vleck Hamiltonian (which the three equations were derived from) has a "spin ladder" of solutions ranging f= rom the low-spin to the high-spin states.=C2=A0 If your low-spin state is a singlet, you'll also have triplets, pentets, and so on until you reach the high-spin state.=C2=A0 Similarly, if you start from a doublet= , you'll have intermediate quartets, etc.

As you introduce more and more unpaired electrons, the spin of the high-spin state increases - but all of the intermediate states between the high-spin and low-spin limits still exist.=C2=A0 You can wo= rk out the splitting between these individual states in terms of J, and what ends up happening is that the states spread out.=C2=A0 The denominator essentially corrects for that spacing, rather than saying anything about the strength of the magnetic coupling.

Best,
James
= I hope this is not a "homework" question, but I'm= having a bad time trying to figure this out.
= Available literature proposes 3 equations to calculate the coupling constant during a Broken-Symmetry approach:
=
= J(1) =3D -(E[HS]-E[BS])/Smax**2
= J(2) =3D -(E[HS]-E[BS])/(Smax*(Smax+1))
= J(3) =3D -(E[HS]-E[BS])/(<S**2>HS-<S**2>BS)
=
= I'm intrigued by the fact that, from the equations, the more the system have unpaired electrons, the minor will be Jab. Why does this happen? Doesn't more unpaired electrons increase magnetic momenta (and an increase in magnetic coupling)?

--
<= font face=3D"monospace, monospace">Henrique C. S= . Junior
Qu=C3=ADmico Industrial - UFRRJ
<= font face=3D"monospace, monospace">Mestrando em Qu=C3=ADmica Inorg=C3=A2nica - UFRRJ
Centro de Processamento de Dados - PMP

=
--=20
James R. Buchwald
Doctoral Candidate, Theoretical Chemistry
Dinolfo Laboratory
Dept. of Chemistry and Chemical Biology
Rensselaer Polytechnic Institute
http://www.rpi.edu=
/~buchwj



--
Henriq= ue C. S. Junior
Qu=C3=ADmico Industrial - UFRRJ=
Mestrando em Qu=C3=ADmica Inorg=C3=A2nica - UFRRJCentro de Processamento de Dados - PMP
=
--001a113e0258c7d5a70535199017--