From owner-chemistry@ccl.net Wed Apr 24 04:47:00 2013 From: "Mariusz Radon mariusz.radon.:.gmail.com" To: CCL Subject: CCL: Spin contamination Message-Id: <-48595-130424044554-22081-lyLVK3CYjpJgBU3G27hiQw!^!server.ccl.net> X-Original-From: Mariusz Radon Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=ISO-8859-1 Date: Wed, 24 Apr 2013 10:45:43 +0200 MIME-Version: 1.0 Sent to CCL by: Mariusz Radon [mariusz.radon[*]gmail.com] On 23.04.2013 14:51, Christopher Cramer cramer:-:umn.edu wrote: > > Sent to CCL by: Christopher Cramer [cramer]^[umn.edu] > Bonoit, > > For a particularly succinct picture of why spin contamination enters > as a consequence of dynamical correlation, see slide numbered 13 of > > http://pollux.chem.umn.edu/8021/Lectures/OpenShell_8.pdf > Dear Christopher: Many thanks for providing these valuable lectures! Don't you think, however, that it would be more appropriate to call this effect (responsible for spin contamination) a nondynamical (or static) correlation, rather than a dynamical one? Surely, there is no firm boundary between these two flavors of electronic correlation, but the effect considered here have typical "symptoms" of nondynamical correlation: 1) it arises due to near-degeneracy of two (and just two) electronic configurations, 2) unlike a typical dynamical correlation (occurring in the cusp region), this is a long-range correlation effect: the electron pair is correlated along a chemical bond (this is called sometimes a "left-right" correlation), 3) this is the same type of correlation effect which appears in H2 dissociation, and the latter one is a typical example of static correlation. Thank you in advance for your comments. > On Apr 23, 2013, at 6:16 AM, bonoit bonoit bonoit_10-,-yahoo.fr wrote: > >> I've an inquiry about spin contamination (UHF method for example) when working on open shell molecules. In books, they said that the origin of this phenomenun is the next high spin state which is mixed with the desired one. >> Could someone tell me the explanation of that and where it is originated from, please? >> Dear Bonoit: There is also a good reading on HF instabilities in the famous Helgaker and Jorgensen textbook ("Molecular Electronic Structure Theory", ch. 10), but perhaps you already know it. Best regards, Mariusz -- Dr Mariusz Radon, Ph.D. Coordination Chemistry Group Faculty of Chemistry Jagiellonian University ul. Ingardena 3, 30-060 Krakow, Poland http://www.chemia.uj.edu.pl/~mradon From owner-chemistry@ccl.net Wed Apr 24 07:59:01 2013 From: "Christopher Cramer cramer~~umn.edu" To: CCL Subject: CCL: Spin contamination Message-Id: <-48596-130424075508-3236-uxLo9BYL0a9Amrfiao5mQA-,-server.ccl.net> X-Original-From: Christopher Cramer Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=us-ascii Date: Wed, 24 Apr 2013 06:54:44 -0500 Mime-Version: 1.0 (Apple Message framework v1085) Sent to CCL by: Christopher Cramer [cramer[A]umn.edu] Mariusz, An interesting point. On the one hand, a very small active space (3 in 3) for an MCSCF would do just fine for the allyl radical problem, so one might reasonably call it "non-dynamical" correlation. On the other hand, it's driven by a spin polarization phenomenon associated with its open-shell character, and the frontier orbital separation between the relevant orbitals is quite a bit larger than that typically found in "classic" near degeneracy cases. To be honest, I've always found the distinction between non-dynamical and dynamical correlation somewhat less than satisfying, at least once one goes beyond trivial model systems, although I acknowledge that people have worked hard to try better to define the boundaries between the two. Occasionally it seems as though non-dynamical correlation simply means "all the correlation associated with the active space I ended up using in my multi-reference calculation" (with dynamical correlation being, of course, everything else!) That being said, your point below with respect to cusp behavior vs. global behavior is compelling. I would agree that for the allyl radical, your preference for nomenclature is on firm ground. Thanks for further illuminating the discussion! Chris On Apr 24, 2013, at 3:45 AM, Mariusz Radon mariusz.radon.:.gmail.com wrote: > > Sent to CCL by: Mariusz Radon [mariusz.radon[*]gmail.com] > On 23.04.2013 14:51, Christopher Cramer cramer:-:umn.edu wrote: >> >> Sent to CCL by: Christopher Cramer [cramer]^[umn.edu] >> Bonoit, >> >> For a particularly succinct picture of why spin contamination enters >> as a consequence of dynamical correlation, see slide numbered 13 of >> >> http://pollux.chem.umn.edu/8021/Lectures/OpenShell_8.pdf >> > > Dear Christopher: > > Many thanks for providing these valuable lectures! > > Don't you think, however, that it would be more appropriate to call this > effect (responsible for spin contamination) a nondynamical (or static) > correlation, rather than a dynamical one? Surely, there is no firm > boundary between these two flavors of electronic correlation, but the > effect considered here have typical "symptoms" of nondynamical correlation: > > 1) it arises due to near-degeneracy of two (and just two) electronic > configurations, > 2) unlike a typical dynamical correlation (occurring in the cusp > region), this is a long-range correlation effect: the electron pair is > correlated along a chemical bond (this is called sometimes a > "left-right" correlation), > 3) this is the same type of correlation effect which appears in H2 > dissociation, and the latter one is a typical example of static correlation. > > Thank you in advance for your comments. > > >> On Apr 23, 2013, at 6:16 AM, bonoit bonoit bonoit_10-,-yahoo.fr wrote: >> >>> I've an inquiry about spin contamination (UHF method for example) > when working on open shell molecules. In books, they said that the > origin of this phenomenun is the next high spin state which is mixed > with the desired one. >>> Could someone tell me the explanation of that and where it is > originated from, please? >>> > > Dear Bonoit: > > There is also a good reading on HF instabilities in the famous Helgaker > and Jorgensen textbook ("Molecular Electronic Structure Theory", ch. > 10), but perhaps you already know it. > > > Best regards, > Mariusz > > > > > > > -- > Dr Mariusz Radon, Ph.D. > Coordination Chemistry Group > Faculty of Chemistry > Jagiellonian University > ul. Ingardena 3, 30-060 Krakow, Poland > http://www.chemia.uj.edu.pl/~mradon> > -- Christopher J. Cramer Elmore H. Northey Professor University of Minnesota Department of Chemistry 207 Pleasant St. SE Minneapolis, MN 55455-0431 Phone: (612) 624-0859 || FAX: (612) 626-7541 -------------------------- Faculty Liaison for eLearning Initiatives Office of the Senior Vice President for Academic Affairs and Provost 236 Morrill Hall Phone: (612) 626-1215 -------------------------- Mobile: (952) 297-2575 Email: cramer|umn.edu Twitter: |ChemProfCramer Website: http://pollux.chem.umn.edu From owner-chemistry@ccl.net Wed Apr 24 08:34:00 2013 From: "David A Case case%x%biomaps.rutgers.edu" To: CCL Subject: CCL: Release of AmberTools13 Message-Id: <-48597-130424080334-5241-qlcZUYMqvyBN8ftngHamMw[]server.ccl.net> X-Original-From: David A Case Content-Disposition: inline Content-Type: text/plain; charset=us-ascii Date: Wed, 24 Apr 2013 08:03:26 -0400 Mime-Version: 1.0 Sent to CCL by: David A Case [case^^biomaps.rutgers.edu] The Amber development team is pleased to announce the release of AmberTools13. This is a significant update to AmberTools: http://ambermd.org/#AmberTools. Among the new features: * Greatly expanded and improved cpptraj program for analyzing trajectories; * New options for PBSA calculations, including new solvers and dielectric models; * updates to MMPBSA.py, including access through NAB of two new GB models; * new documentation and tools for inspecting and modifying Amber parameter files; Please note: If you already have AmberTools12, you do not need to download anything. Simply run "patch_amber.py --update" in your AMBERHOME directory to update AmberTools to patch-level 37 (you may have to run this command twice,) then type "./update_amber --upgrade". You then need to re-run the configure script (and accept all updates) and re-compile. If you are a new user, click on the "Download AmberTools13" link at http://ambermd.org. Follow the installation instructions in the Reference Manual. (Special shout-out to Jason Swails for his help in preparing the update scripts and the release.) ...regards...dave case From owner-chemistry@ccl.net Wed Apr 24 11:05:00 2013 From: "Pedro Silva pedro.dft::gmail.com" To: CCL Subject: CCL: Why is ROHF not usually applied to Fe-S clusters? Message-Id: <-48598-130424103453-6819-EjjkVOMaJJhYl8vZB4KiOw-*-server.ccl.net> X-Original-From: "Pedro Silva" Date: Wed, 24 Apr 2013 10:34:52 -0400 Sent to CCL by: "Pedro Silva" [pedro.dft^^gmail.com] Dear CCLers, As far as I understand it, in Louis Noodleman's classic proposal of the broken Symmetry approach to the computation of the ground states of Fe-S clusters a suitable reference wavefunction is manipulated (by means of "shuffling" electron from the alpha to the beta orbitals) in order to get a trial wavefunction of the desired multiplicity. The complete spin ladder can then be computed after obtaining the J coupling parameter (by comparing the energies of the uncontaminated high-spin state with the optimized broken symetry state). Why is this approach commonly used, instead of a straightforward computation of a ROHF wavefunction of the desired multiplicity? As far as I can tell, in Fe-S clusters the problem of spatially distant unpaired "up" and "down" electrons (present e.g. in P450 compound I) does not arise, therefore ROHF would seem to me to be a proper strategy. Any thoughts? Pedro S. From owner-chemistry@ccl.net Wed Apr 24 12:31:00 2013 From: "Chang, Christopher Christopher.Chang%nrel.gov" To: CCL Subject: CCL: Why is ROHF not usually applied to Fe-S clusters? Message-Id: <-48599-130424122758-2874-GbIRzJX0tDm61iL7HNQdUg*_*server.ccl.net> X-Original-From: "Chang, Christopher" Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset="us-ascii" Date: Wed, 24 Apr 2013 10:27:48 -0600 MIME-Version: 1.0 Sent to CCL by: "Chang, Christopher" [Christopher.Chang*|*nrel.gov] That is in fact the problem. Fe-S clusters are antiferromagnetically coupled, so that despite a state being, e.g., S=0 (take a diferric [2Fe2S] cluster for example), there are many unpaired electrons (10 in the example, five nominally on each iron). H2 dissociation is the model problem, similar static correlation effect. Restricted open-shell single-determinant wavefunctions would pair the electrons (i.e., force spatial co-occupancy of alpha and beta pairs), and so provide a more qualitatively wrong structure than broken-symmetry spin-unrestricted methods do. -----Original Message----- > From: owner-chemistry+christopher.chang==nrel.gov ~ ccl.net [mailto:owner-chemistry+christopher.chang==nrel.gov ~ ccl.net] On Behalf Of Pedro Silva pedro.dft::gmail.com Sent: Wednesday, April 24, 2013 8:35 AM To: Chang, Christopher Subject: CCL: Why is ROHF not usually applied to Fe-S clusters? Sent to CCL by: "Pedro Silva" [pedro.dft^^gmail.com] Dear CCLers, As far as I understand it, in Louis Noodleman's classic proposal of the broken Symmetry approach to the computation of the ground states of Fe-S clusters a suitable reference wavefunction is manipulated (by means of "shuffling" electron from the alpha to the beta orbitals) in order to get a trial wavefunction of the desired multiplicity. The complete spin ladder can then be computed after obtaining the J coupling parameter (by comparing the energies of the uncontaminated high-spin state with the optimized broken symetry state). Why is this approach commonly used, instead of a straightforward computation of a ROHF wavefunction of the desired multiplicity? As far as I can tell, in Fe-S clusters the problem of spatially distant unpaired "up" and "down" electrons (present e.g. in P450 compound I) does not arise, therefore ROHF would seem to me to be a proper strategy. Any thoughts? Pedro S.http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/chemistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txt From owner-chemistry@ccl.net Wed Apr 24 13:48:00 2013 From: "Sebastian Kozuch kozuchs],[yahoo.com" To: CCL Subject: CCL: Spin contamination Message-Id: <-48600-130424115939-25570-Nw5EDkfZn012Q/KggTHanA|server.ccl.net> X-Original-From: Sebastian Kozuch Content-Type: multipart/alternative; boundary="1916699159-1374162046-1366819169=:94745" Date: Wed, 24 Apr 2013 08:59:29 -0700 (PDT) MIME-Version: 1.0 Sent to CCL by: Sebastian Kozuch [kozuchs]|[yahoo.com] --1916699159-1374162046-1366819169=:94745 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable This debate is quite interesting. I have another related question for the D= FT community.=0AIt is known that pure DFT is more robust to multi-reference= systems and has less spin contamination than HF or hybrid DFT. Why is that= ? The non-interacting field may be different than the mean field approximat= ion of HF, and that may partly correct the lack of static correlation. But = why? Aren't both "fields" giving a singly determinant system? There was a p= aper (by Scuseria?) postulating that the self-interaction error of DFT comp= ensates for this. Any insight on this matter?=0AInterestingly, I just saw a= paper by Radom et al explaining that double-hybrids have good behavior for= high spin-contamination since the HF exchange and the MP2 correlation have= opposite trends, compensating each other (at least when using KS orbitals)= .=0A=0ASebastian=0A=0A=0A=0A=0A________________________________=0A From: Ch= ristopher Cramer cramer~~umn.edu =0ATo: "Kozuch, S= ebastian " =0ASent: Wednesday, April 24, 2013 6= :54 AM=0ASubject: CCL: Spin contamination=0A =0A=0A=0ASent to CCL by: Chris= topher Cramer [cramer[A]umn.edu]=0AMariusz,=0A=0A=A0 An interesting point.= On the one hand, a very small active space (3 in 3) for an MCSCF would do = just fine for the allyl radical problem, so one might reasonably call it "n= on-dynamical" correlation. On the other hand, it's driven by a spin polariz= ation phenomenon associated with its open-shell character, and the frontier= orbital separation between the relevant orbitals is quite a bit larger tha= n that typically found in "classic" near degeneracy cases.=0A=0A=A0 To be = honest, I've always found the distinction between non-dynamical and dynamic= al correlation somewhat less than satisfying, at least once one goes beyond= trivial model systems, although I acknowledge that people have worked hard= to try better to define the boundaries between the two. Occasionally it se= ems as though non-dynamical correlation simply means "all the correlation a= ssociated with the active space I ended up using in my multi-reference calc= ulation" (with dynamical correlation being, of course, everything else!)=0A= =0A=A0 That being said, your point below with respect to cusp behavior vs.= global behavior is compelling. I would agree that for the allyl radical, y= our preference for nomenclature is on firm ground. Thanks for further illum= inating the discussion!=0A=0AChris=0A=0AOn Apr 24, 2013, at 3:45 AM, Marius= z Radon mariusz.radon.:.gmail.com wrote:=0A=0A> =0A> Sent to CCL by: Marius= z Radon [mariusz.radon[*]gmail.com]=0A> On 23.04.2013 14:51, Christopher Cr= amer cramer:-:umn.edu wrote:=0A>> =0A>> Sent to CCL by: Christopher Cramer = [cramer]^[umn.edu]=0A>> Bonoit,=0A>> =0A>> For a particularly succinct pict= ure of why spin contamination enters =0A>> as a consequence of dynamical co= rrelation, see slide numbered 13 of =0A>> =0A>> http://pollux.chem.umn.edu/= 8021/Lectures/OpenShell_8.pdf=0A>> =0A> =0A> Dear Christopher:=0A> =0A> Man= y thanks for providing these valuable lectures!=0A> =0A> Don't you think, h= owever, that it would be more appropriate to call this=0A> effect (responsi= ble for spin contamination) a nondynamical (or static)=0A> correlation, rat= her than a dynamical one? Surely, there is no firm=0A> boundary between the= se two flavors of electronic correlation, but the=0A> effect considered her= e have typical "symptoms" of nondynamical correlation:=0A> =0A> 1) it arise= s due to near-degeneracy of two (and just two) electronic=0A> configuration= s,=0A> 2) unlike a typical dynamical correlation (occurring in the cusp=0A>= region), this is a long-range correlation effect: the electron pair is=0A>= correlated along a chemical bond (this is called sometimes a=0A> "left-rig= ht" correlation),=0A> 3) this is the same type of correlation effect which = appears in H2=0A> dissociation, and the latter one is a typical example of = static correlation.=0A> =0A> Thank you in advance for your comments.=0A> = =0A> =0A>> On Apr 23, 2013, at 6:16 AM, bonoit bonoit bonoit_10-,-yahoo.fr = wrote:=0A>> =0A>>> I've an inquiry about spin contamination (UHF method for= example)=0A> when working on open shell molecules. In books, they said tha= t the=0A> origin of this phenomenun is the next high spin state which is mi= xed=0A> with the desired one.=0A>>> Could someone tell me the explanation o= f that and where it is=0A> originated from, please?=0A>>> =0A> =0A> Dear Bo= noit:=0A> =0A> There is also a good reading on HF instabilities in the famo= us Helgaker=0A> and Jorgensen textbook ("Molecular Electronic Structure The= ory", ch.=0A> 10), but perhaps you already know it.=0A> =0A> =0A> Best rega= rds,=0A> Mariusz=0A> =0A> =0A> =0A> =0A> =0A> =0A> -- =0A> Dr Mariusz Radon= , Ph.D.=0A> Coordination Chemistry Group=0A> Faculty of Chemistry=0A> Jagie= llonian University=0A> ul. Ingardena 3, 30-060 Krakow, Poland=0A> http://ww= w.chemia.uj.edu.pl/~mradon> =0A> =0A=0A--=0AChristopher J. Cramer=0AElmore = H. Northey Professor=0AUniversity of Minnesota=0ADepartment of Chemistry=0A= 207 Pleasant St. SE=0AMinneapolis, MN 55455-0431=0APhone:=A0 (612) 624-0859= || FAX:=A0 (612) 626-7541=0A--------------------------=0AFaculty Liaison f= or eLearning Initiatives=0AOffice of the Senior Vice President for Academic= Affairs and Provost=0A236 Morrill Hall=0APhone:=A0 (612) 626-1215=0A------= --------------------=0AMobile: (952) 297-2575=0AEmail:=A0 cramer-,-umn.edu= =0ATwitter:=A0 -,-ChemProfCramer=0AWebsite:=A0 http://pollux.chem.umn.edu= =0A=0A=0A=0A-=3D This is automatically added to each message by the mailing= script =3D-=0ATo recover the email address of the author of the message, p= lease change=0Athe strange characters on the top line to the * sign. You ca= n also=0A=0A=0AE-mail = to subscribers: CHEMISTRY*ccl.net or use:=0A=A0 =A0 =A0 http://www.ccl.net/= cgi-bin/ccl/send_ccl_message=0A=0AE-mail to administrators: CHEMISTRY-REQUE= ST*ccl.net or use=0A=A0 =A0 =A0 http://www.ccl.net/cgi-bin/ccl/send_ccl_mes= sage=0A=0A=0A=A0 =A0 =A0 http://www.ccl.net/chemistr= y/sub_unsub.shtml=0A=0ABefore posting, check wait time at: http://www.ccl.n= et=0A=0A=0AConferences: http://server.ccl.net/= chemistry/announcements/conferences/=0A=0ASearch Messages: http://www.ccl.n= et/chemistry/searchccl/index.shtml=0A=0AIf your mail bounces from CCL with = 5.7.1 error, check:=0A=A0 =A0 =A0=0A=0ARTFI= : http://www.ccl.net/chemistry/aboutccl/instructions/ --1916699159-1374162046-1366819169=:94745 Content-Type: text/html; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable
This debate is quite interesting= . I have another related question for the DFT community.
It is known tha= t pure DFT is more robust to multi-reference systems and has less spin cont= amination than HF or hybrid DFT. Why is that? The non-interacting field may= be different than the mean field approximation of HF, and that may partly = correct the lack of static correlation. But why? Aren't both "fields" givin= g a singly determinant system? There was a paper (by Scuseria?) postulating= that the self-interaction error of DFT compensates for this. Any insight o= n this matter?
Interestingly, I just saw a paper by Radom et al explaini= ng that double-hybrids have good behavior for high spin-contamination since= the HF exchange and the MP2 correlation have opposite trends, compensating= each other (at least when using KS orbitals).

Sebastian


<= span style=3D"font-weight:bold;">From: Christopher Cramer cramer= ~~umn.edu <owner-chemistry*ccl.net>
To: "Kozuch, Sebastian " <kozuchs*yahoo.com&= gt;
Sent: Wednesday, = April 24, 2013 6:54 AM
Subject: CCL: Spin contamination


Sent to CCL by: Christopher Cramer [cramer[A]umn.edu]
M= ariusz,

  An interesting point. On the one hand, a very small = active space (3 in 3) for an MCSCF would do just fine for the allyl radical problem, so one m= ight reasonably call it "non-dynamical" correlation. On the other hand, it'= s driven by a spin polarization phenomenon associated with its open-shell c= haracter, and the frontier orbital separation between the relevant orbitals= is quite a bit larger than that typically found in "classic" near degenera= cy cases.

  To be honest, I've always found the distinction be= tween non-dynamical and dynamical correlation somewhat less than satisfying= , at least once one goes beyond trivial model systems, although I acknowled= ge that people have worked hard to try better to define the boundaries betw= een the two. Occasionally it seems as though non-dynamical correlation simp= ly means "all the correlation associated with the active space I ended up u= sing in my multi-reference calculation" (with dynamical correlation being, = of course, everything else!)

  That being said, your point below with respect to cusp behavior vs. global behavior is compellin= g. I would agree that for the allyl radical, your preference for nomenclatu= re is on firm ground. Thanks for further illuminating the discussion!
Chris

On Apr 24, 2013, at 3:45 AM, Mariusz Radon mariusz.radon.:.g= mail.com wrote:

>
> Sent to CCL by: Mariusz Radon [mariusz= .radon[*]gmail.com]
> On 23.04.2013 14:51, Christopher Cramer cramer:= -:umn.edu wrote:
>>
>> Sent to CCL by: Christopher Crame= r [cramer]^[umn.edu]
>> Bonoit,
>>
>> For a par= ticularly succinct picture of why spin contamination enters
>> as= a consequence of dynamical correlation, see slide numbered 13 of
>&= gt;
>> http://pollux.chem.umn.edu/8021/Lectures/OpenS= hell_8.pdf
>>
>
> Dear Christopher:
>
> Many thanks for providing these valuable lectures!
>
&g= t; Don't you think, however, that it would be more appropriate to call this=
> effect (responsible for spin contamination) a nondynamical (or sta= tic)
> correlation, rather than a dynamical one? Surely, there is no = firm
> boundary between these two flavors of electronic correlation, = but the
> effect considered here have typical "symptoms" of nondynami= cal correlation:
>
> 1) it arises due to near-degeneracy of tw= o (and just two) electronic
> configurations,
> 2) unlike a typ= ical dynamical correlation (occurring in the cusp
> region), this is = a long-range correlation effect: the electron pair is
> correlated al= ong a chemical bond (this is called sometimes a
> "left-right" correl= ation),
> 3) this is the same type of correlation effect which appear= s in H2
> dissociation, and the latter one is a typical example of static correlation.
>
> Thank you in advance for y= our comments.
>
>
>> On Apr 23, 2013, at 6:16 AM, bo= noit bonoit bonoit_10-,-yahoo.fr wrote:
>>
>>> I've a= n inquiry about spin contamination (UHF method for example)
> when wo= rking on open shell molecules. In books, they said that the
> origin = of this phenomenun is the next high spin state which is mixed
> with = the desired one.
>>> Could someone tell me the explanation of t= hat and where it is
> originated from, please?
>>>
&g= t;
> Dear Bonoit:
>
> There is also a good reading on H= F instabilities in the famous Helgaker
> and Jorgensen textbook ("Mol= ecular Electronic Structure Theory", ch.
> 10), but perhaps you alrea= dy know it.
>
>
> Best regards,
> Mariusz
>=
>
>
>
>
>
> --
> Dr Mariusz Radon, Ph.D.
> Coordination Chemistry Group
> Facul= ty of Chemistry
> Jagiellonian University
> ul. Ingardena 3, 30= -060 Krakow, Poland
> http://www.chemia.uj.edu.pl/~mradon>
>
--
Christopher J. Cramer
Elmore H. Northey Professor
Universi= ty of Minnesota
Department of Chemistry
207 Pleasant St. SE
Minnea= polis, MN 55455-0431
Phone:  (612) 624-0859 || FAX:  (612) 626= -7541
--------------------------
Faculty Liaison for eLearning Initia= tives
Office of the Senior Vice President for Academic Affairs and Provo= st
236 Morrill Hall
Phone:  (612) 626-1215
------------------= --------
Mobile: (952) 297-2575
Email:  cramer-,-umn.edu
Twit= ter:  -,-ChemProfCramer
Website:  http://pollux.chem.umn.edu



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--1916699159-1374162046-1366819169=:94745--