From chemistry-request@ccl.net Fri Jul 9 19:30:27 2004 Received: from relay1.scripps.edu (relay1.scripps.edu [137.131.200.29]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id i6A0UQga018307 for ; Fri, 9 Jul 2004 19:30:26 -0500 Received: from degas.scripps.edu (degas [137.131.252.44]) by relay1.scripps.edu (8.12.11/TSRI-5.0.1rAV) with ESMTP id i6A0aHIe006465; Fri, 9 Jul 2004 17:36:17 -0700 (PDT) Received: (from lou@localhost) by degas.scripps.edu (8.11.7+Sun/TSRI-4.1.0) id i6A0aH616021; Fri, 9 Jul 2004 17:36:17 -0700 (PDT) Date: Fri, 9 Jul 2004 17:36:17 -0700 (PDT) From: Lou Noodleman Message-Id: <200407100036.i6A0aH616021(at)degas.scripps.edu> To: scerri(at)chem.ucla.edu Subject: Re: CCL:Question on molecular structure and QM Cc: lou(at)scripps.edu, chemistry(at)ccl.net X-Sun-Charset: US-ASCII X-CanItPRO-Stream: admin redirected to 10_OptOut X-Spam-Score: undef - spam-scanning disabled X-Canit-Stats-ID: 1164731 - 844cafec3475 X-Scanned-By: CanIt (www . canit . ca) X-Spam-Status: No, hits=3.6 required=7.5 tests=FVGT_s_OBFU_Q1,MY_CHARPARENS, OPT_HEADER autolearn=no version=2.61 X-Spam-Checker-Version: SpamAssassin 2.61 (1.212.2.1-2003-12-09-exp) on servernd.ccl.net The Born-Oppenheimer Approximation is very good under very well known physical conditions and fails when these conditions are not met. It works for most ground states and over a fairly wide range of geometries in most cases. In principle and usually in practice, one can test if BO breakdown is at all likely, and then more sophisticated methods can be used where needed. My own view is: "Molecules have shapes most of the time, and when they don't, they tell you if you ask politely." That is, there are experimental signatures, and one can also do a good quality calculation to find out if BO breakdown is a likely problem. For a good exposition of the basic issues, see M. Tinkham, Group Theory and Molecular Quantum Mechanics, McGraw-Hill, 1964, Chapter 7, pp.210-213. Specifically and especially for ground states "Serious errors arise only in symmetrical molecules, where some of the zero-order eigenfunctions are actually degenerate. Then these neglected terms are able to exert decisive influence in splitting the degeneracy and determining the symmetries of the actual eigenfunctions."(Tinkham) For example, see pp.252-255, "Effect of Nuclear Statistics on Molecular Rotation". Born-Oppenheimer Breakdown is observed more often for excited electronic states (near conical intersections), transition states, where there are electronic state crossings (or "very near crossings" due to "true" degeneracy or "accidental degeneracy") with small changes in nuclear geometry. For conical intersections, see work on NO2 (Jackels and Davidson), for photoelectron spectra and related issues, see Cederbaum's work, for electron transfer, look at "nonadiabatic electron transfer theory and experiment", in inorganic chemistry, see recent work in valence tautomerism and metal-ligand radical chemistry, and related state crossings, and for Rydberg molecules, BO breakdown is very well known from the results of experiment and multichannel quantum defect theory. All of this is scientifically fascinating, but molecules do have structure most of the time, unless there are in transit. Of course, tunneling does modify a simple classical view of molecular structure, as for example in the ammonia maser (see the Feynman Lectures on Physics). Most of us doing quantum chemistry assume the Born-Oppenheimer separation most of the time because for most problems it works fine, and it is much more complicated (read "a pain") to calculate potential energy surfaces without it, and where the situation is very dicey, you can test, and then do a vibronic mixing calculation if you need it (and you have grant money and resources). I certainly have great respect for the work of Prof. Wooley and Primas, but I do not see that there are great philosophical problems here. Great philosophical problems are inherent in quantum mechanics itself, and to me the most dramatic are (in no particular order): Zero-point vibrational energy, and even worse ZPE for photons (which gives spontaneous emission); identical particles- Pauli's principle for fermions is very strange, also: is there a simple reason why a proton should be spin 1/2 and charge +1 like the much simpler electron spin 1/2 and charge -1, when it is a complex particle-is it sufficient that it be made of three quarks of spin 1/2 and why are they spin 1/2? Does the Standard Model of Particle Physics really tell us why this is? Bose-Einstein statistics for bosons (photons, phonons); "proper Boltzmann counting (related to the fact that matter is made from bosons and fermions)" and the relationship of "proper Boltzmann counting" (Gibbs paradox) to entropy (See K.Huang-Statistical Mechanics, Wiley, 1963 or most stat. mech. books); The Einstein-Podolsky-Rosen paradox and the relation of spin to statistics (Pauli's work). All of these problems have been around for 70-100 years or more, and who really understands them in a deep way beyond what the old guys discovered? Best Regards, Lou Noodleman Dept. of Molecular Biology, TPC15 The Scripps Research Institute La Jolla, CA 92037 P.S. In answer to: "They point to the fact that the Hamiltonians for two isomers of an organic compound, for example, are identical in the absence of the B-O approximation", a single Hamiltonian can have several solutions, H(PSI(n)) =E(n)PSI(n), so the two isomer are two different solutions, usually with energies different enough that the Born-Oppenheimer seperation applies (like trans versus cis stilbene (diphenylethylene). From chemistry-request@ccl.net Fri Jul 9 21:40:43 2004 Received: from mail.site.ntu.edu.au (mail.site.ntu.edu.au [138.80.69.54]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id i6A2eega020448 for ; Fri, 9 Jul 2004 21:40:41 -0500 Received: from mail.site.ntu.edu.au ([138.80.48.39]) by mail.site.ntu.edu.au with Microsoft SMTPSVC(6.0.3790.0); Sat, 10 Jul 2004 12:16:20 +0930 Received: by mail.site.ntu.edu.au (sSMTP sendmail emulation); Sat, 10 Jul 2004 12:11:59 +0930 Date: Sat, 10 Jul 2004 12:11:59 +0930 From: Brian Salter-Duke To: ccl Subject: Re: CCL:Question on molecular structure and QM Message-ID: <20040710024159.GB4049.-at-.monster.ntu.edu.au> Reply-To: Brian Salter-Duke Mail-Followup-To: ccl References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.5.4i X-OriginalArrivalTime: 10 Jul 2004 02:46:20.0750 (UTC) FILETIME=[14D5D6E0:01C46628] X-Spam-Status: No, hits=3.3 required=7.5 tests=FVGT_s_OBFU_Q1,NO_RDNS2 autolearn=no version=2.61 X-Spam-Checker-Version: SpamAssassin 2.61 (1.212.2.1-2003-12-09-exp) on servernd.ccl.net On Thu, Jul 08, 2004 at 11:59:33PM -0700, Eric Scerri wrote: > > > The following is a somewhat general philosophical question. > I would very much appreciate the comments of computational chemists. > > In the philosophy of chemistry literature much has been made of the > fact that molecular structure cannot be strictly deduced from QM. I > am referring to the work of Guy Wooley in the UK and Hans Primas at > the ETH. > > The basis of this claim is that structure comes after applying the > Born-Oppenheimer approximation to fix the nuclei. These authors > claim that in this sense molecular structure has not been "reduced" > to QM. > > They point to the fact that the Hamiltonians for two isomers of an > organic compound, for example, are identical in the absence of the > B-O approximation and they conclude that a strictly QM calculation > cannot therefore distinguish between the two structures in question. > > I would be happy to pull some references together for anyone > interested in studying the original articles. But I just wanted to > hear some general reactions to such claims. I think your conclusions are essentially correct. It is what we do with them that is the problem. A key point that I like to demonstrate this and which I owe to Brian Sutcliffe is the point that quantum mechanics says that all identical particles are indistinguishable. The Born-Oppenheimer approximation changes a system where all electrons are indisdinquishable and all like nuclei are indistinguishable to one of indistinquishable electrons in the field of distiquishable like nuclei. For example CO2 with two O-16 isotopes has two indisquishable O nuclei and we teach students that this leads to alternate lines in the rotational fine structure of the IR spectrum to be missing. However the standard quantum chemistry methods have the two O nuclei as distinguishable. There is a lot that has to be worked out here. See Brian Surcliffe's article in the Lowdin memorial volume. Molecular structure is not as of now reducible to pure quantum mechanics but this does not mean it is not reducible to physics since the Born-Oppenheimer approximation is part of physics and the calculations agree with experiment. I am not so clear about the point about isomers. A pure non-B-O calculation would lead to all isomers and the dynamics of interconversion I think. Maybe people who do non-B-O calculations on small sytems could comment. > > > > -- > > > Dr. Eric Scerri , > UCLA, > Department of Chemistry & Biochemistry, > 607 Charles E. Young Drive East, > Los Angeles, CA 90095-1569 > USA > > E-mail : scerri.-at-.chem.ucla.edu > tel: 310 206 7443 > fax: 310 206 2061 > Web Page: http://www.chem.ucla.edu/dept/Faculty/scerri/index.html > > Editor of Foundations of Chemistry > http://www.kluweronline.com/issn/1386-4238 > > Also see International Society for the Philosophy of Chemistry > http://www.georgetown.edu/earleyj/ISPC.html > > > -= This is automatically added to each message by the mailing script =- > To send e-mail to subscribers of CCL put the string CCL: on your Subject: > line > and send your message to: CHEMISTRY.-at-.ccl.net > > Send your subscription/unsubscription requests to: > CHEMISTRY-REQUEST.-at-.ccl.net HOME Page: http://www.ccl.net | Jobs Page: > http://www.ccl.net/jobs > If your mail is bouncing from CCL.NET domain send it to the maintainer: > Jan Labanowski, jlabanow.-at-.nd.edu (read about it on CCL Home Page) > -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ > > > > -- Brian Salter-Duke (Brian Duke) b_duke.-at-.octa4.net.au Honorary Fellow (Chemistry), Charles Darwin University, Darwin, Australia. Post: Box 1028, Humpty Doo, NT 0836, Australia. Phone 08-89881600. Fax 08-89881302. http://www.octa4.net.au/linden/brian/ From chemistry-request@ccl.net Sat Jul 10 18:26:39 2004 Received: from exmails1.chem.ucla.edu (exmails1.chem.ucla.edu [169.232.134.2]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id i6ANQcXJ014979 for ; Sat, 10 Jul 2004 18:26:38 -0500 Received: from [169.232.128.32] (dial32.chem.ucla.edu [169.232.128.32]) (authenticated bits=0) by exmails1.chem.ucla.edu (8.12.8/8.12.8) with ESMTP id i6ANWREb005522 for ; Sat, 10 Jul 2004 16:32:31 -0700 Mime-Version: 1.0 X-Sender: scerri..at..chlorine.chem.ucla.edu (Unverified) Message-Id: Date: Sat, 10 Jul 2004 16:31:14 -0700 To: ccl From: Eric Scerri Subject: CCL:Question on molecular structure and QM Content-Type: multipart/alternative; boundary="============_-1122620210==_ma============" X-Spam-Status: No, hits=0.3 required=7.5 tests=FVGT_s_OBFU_Q1,HTML_MESSAGE autolearn=no version=2.61 X-Spam-Checker-Version: SpamAssassin 2.61 (1.212.2.1-2003-12-09-exp) on servernd.ccl.net --============_-1122620210==_ma============ Content-Type: text/plain; charset="us-ascii" ; format="flowed" Thanks for your interesting response Brian and all others who have responded off-list. Please keep your replies coming. Your point about structure being reduced to physics, if not pure QM with no B-O, is well taken. I see little point in trying to demarcate between QM and physics in this context. For example the status of the Pauli Exclusion principle vis a vis QM has never been quite settled. And yet nobody would claim that introducing the spin quantum number to Schrodinger's non-relativistic model represents a problem with the reduction of chemistry to QM. Here is another thought on the subject which I hope is not too trivial. The importation of B-O allows the molecule to have some structure but of course does not in itself dictate the details of the molecular structure. It just allows the calculation to get off the ground, so to speak. It is not as if the calculations are semi-empirical as when certain experimental data are introduced although they are semi empirical in the broad sense of saying that nuclei are much heavier than electrons. What is behind this thinking is that there are many claims to a lack of full reduction of chemical phenomena to QM (or physics). I am trying to weight up whether the molecular shape question is more or less serious than say the inability to strictly predict chemical periodicity without using the experimental order of orbital filling (n + l rule). Also discussed in the Lowdin volume and something you and I have talked about. regards, eric >On Thu, Jul 08, 2004 at 11:59:33PM -0700, Eric Scerri wrote: > > >> >> The following is a somewhat general philosophical question. >> I would very much appreciate the comments of computational chemists. >> >> In the philosophy of chemistry literature much has been made of the >> fact that molecular structure cannot be strictly deduced from QM. I >> am referring to the work of Guy Wooley in the UK and Hans Primas at >> the ETH. >> >> The basis of this claim is that structure comes after applying the >> Born-Oppenheimer approximation to fix the nuclei. These authors >> claim that in this sense molecular structure has not been "reduced" >> to QM. >> >> They point to the fact that the Hamiltonians for two isomers of an >> organic compound, for example, are identical in the absence of the >> B-O approximation and they conclude that a strictly QM calculation >> cannot therefore distinguish between the two structures in question. >> >> I would be happy to pull some references together for anyone >> interested in studying the original articles. But I just wanted to >> hear some general reactions to such claims. > >I think your conclusions are essentially correct. It is what we do with >them that is the problem. > >A key point that I like to demonstrate this and which I owe to Brian >Sutcliffe is the point that quantum mechanics says that all identical >particles are indistinguishable. The Born-Oppenheimer approximation >changes a system where all electrons are indisdinquishable and all like >nuclei are indistinguishable to one of indistinquishable electrons in >the field of distiquishable like nuclei. For example CO2 with two O-16 >isotopes has two indisquishable O nuclei and we teach students that this >leads to alternate lines in the rotational fine structure of the IR >spectrum to be missing. However the standard quantum chemistry methods >have the two O nuclei as distinguishable. There is a lot that has to be >worked out here. See Brian Surcliffe's article in the Lowdin memorial >volume. > >Molecular structure is not as of now reducible to pure quantum mechanics >but this does not mean it is not reducible to physics since the >Born-Oppenheimer approximation is part of physics and the calculations >agree with experiment. > >I am not so clear about the point about isomers. A pure non-B-O >calculation would lead to all isomers and the dynamics of >interconversion I think. Maybe people who do non-B-O calculations on >small sytems could comment. --------------- --============_-1122620210==_ma============ Content-Type: text/html; charset="us-ascii" CCL:Question on molecular structure and QM

Thanks for your interesting response Brian and all others who have responded off-list.  Please keep your replies coming.

Your point about structure being reduced to physics, if not pure QM with no B-O, is well taken.  I see little point in trying to demarcate between QM and physics in this context.  For example the status of the Pauli Exclusion principle vis a vis QM has never been quite settled.  And yet nobody would claim that introducing the spin quantum number to Schrodinger's non-relativistic model represents a problem with the reduction of chemistry to QM.

Here is another thought on the subject which I hope is not too trivial.  The importation of B-O allows the molecule to have some structure but of course does not in itself dictate the details of the molecular structure.  It just allows the calculation to get off the ground, so to speak.  It is not as if the calculations are semi-empirical as when certain experimental data are introduced although they are semi empirical in the broad sense of saying that nuclei are much heavier than electrons.

What is behind this thinking is that there are many claims to a lack of full reduction of chemical phenomena to QM (or physics).  I am trying to weight up whether the molecular shape question is more or less serious than say the inability to strictly predict chemical periodicity without using the experimental order of orbital filling (n + l rule).  Also discussed in the Lowdin volume and something you and I have talked about.

regards,
eric


On Thu, Jul 08, 2004 at 11:59:33PM -0700, Eric Scerri wrote:
>
>
> The following is a somewhat general philosophical question.
> I would very much appreciate the comments of computational chemists.
>
> In the philosophy of chemistry literature much has been made of the
> fact that molecular structure cannot be strictly deduced from QM.  I
> am referring to the work of Guy Wooley in the UK and Hans Primas at
> the ETH.
>
> The basis of this claim is that structure comes after applying the
> Born-Oppenheimer approximation to fix the nuclei.  These authors
> claim that in this sense molecular structure has not been "reduced"
> to QM.
>
> They point to the fact that the Hamiltonians for two isomers of an
> organic compound, for example, are identical in the absence of the
> B-O approximation and they conclude that a strictly QM calculation
> cannot therefore distinguish between the two structures in question.
>
> I would be happy to pull some references together for anyone
> interested in studying the original articles.  But I just wanted to
> hear some general reactions to such claims.

I think your conclusions are essentially correct. It is what we do with
them that is the problem.

A key point that I like to demonstrate this and which I owe to Brian
Sutcliffe is the point that quantum mechanics says that all identical
particles are indistinguishable. The Born-Oppenheimer approximation
changes a system where all electrons are indisdinquishable and all like
nuclei are indistinguishable to one of indistinquishable electrons in
the field of distiquishable like nuclei. For example CO2 with two O-16
isotopes has two indisquishable O nuclei and we teach students that this
leads to alternate lines in the rotational fine structure of the IR
spectrum to be missing. However the standard quantum chemistry methods
have the two O nuclei as distinguishable. There is a lot that has to be
worked out here. See Brian Surcliffe's article in the Lowdin memorial
volume.

Molecular structure is not as of now reducible to pure quantum mechanics
but this does not mean it is not reducible to physics since the
Born-Oppenheimer approximation is part of physics and the calculations
agree with experiment.

I am not so clear about the point about isomers. A pure non-B-O
calculation would lead to all isomers and the dynamics of
interconversion I think. Maybe people who do non-B-O calculations on
small sytems could comment.
---------------
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