From owner-chemistry #at# ccl.net Wed Jun 10 10:10:01 2015 From: "=?UTF-8?Q?Andr=C3=A9_Farias_de_Moura?= moura|,|ufscar.br" To: CCL Subject: CCL: Proper way of doing a Boltzmann average Message-Id: <-51439-150610092720-22587-uohzEWuFj72l/wF/S18Cjw::server.ccl.net> X-Original-From: =?UTF-8?Q?Andr=C3=A9_Farias_de_Moura?= Content-Type: multipart/alternative; boundary=001a113cee2a2d2835051829d5dd Date: Wed, 10 Jun 2015 10:27:12 -0300 MIME-Version: 1.0 Sent to CCL by: =?UTF-8?Q?Andr=C3=A9_Farias_de_Moura?= [moura]*[ufscar.br] --001a113cee2a2d2835051829d5dd Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Dear Gustavo, apart from considering formal arguments on symmetry and (in)distinguishability of molecules, you might also consider the outcome of a typical molecular dynamics or Monte Carlo simulation, both of which will sample the specified ensemble without actually knowing/solving the partition function. If a stable dimer is observed, each monomer may sample its available configurations A and B, and unless the configuration of one monomer affects the configuration of the other, which would be the case for strongly interacting, cooperative systems, then each monomer would sample its configurations independently and you would have A-A, A-B, B-A and B-B with equal weights. This is not always observed. Consider for instance amino acids forming an alpha-helix within any protein: each new amino acid which you add to the system will sense the strong, collective dipole moment arising from the amino acids which are already there, so the incoming monomer is not actually free to sample any orientation, instead it will most likely align its dipole to the alpha-helix dipole moment. Please mind that amino acids comprising an alpha helix interact by means of 1-4 hydrogen bonds (between every first and fourth monomers), just like your model dimer does, but the strong and cooperative interaction in this case is the dipole-dipole interaction between the alpha-helix and the incoming monomers, which modulates which regions of the phase space will be sampled most likely. IMHO, the most tricky part of partition function approaches to study more complex system is the fact that you have to know a priori how strong and complex the mixed interactions between particles might be, and that's why I prefer to rely on either MD or MC simulations to sample the phase space without actually knowing the partition function. But I have to admit that success is not always guaranteed, since poor sampling is quite often observed as the complexity of the potential energy surfaces increases. For a (not so large) dimer, this should not be the case and you should be able to perform a high quality MD/MC sampling, either proving or disproving that each monomer can sample its configurational phase space independently from the other. best, Andre On Wed, Jun 10, 2015 at 7:10 AM, Sebastian Kozuch seb.kozuch||gmail.com < owner-chemistry%ccl.net> wrote: > Sent to CCL by: Sebastian Kozuch [seb.kozuch|gmail.com] > Dear Gustavo, > The matter you are pointing to is not obvious. The partition function may > depend on the symmetry number and the indistinguishability of the two > systems, factors that can change the Boltzmann distribution. I hope someo= ne > with real knowledge can help you, but maybe you can obtain some guidance > from the work on reaction rates of Fernandez-Ramos et al. ( > http://link.springer.com/article/10.1007/s00214-007-0328-0). > > Best, > Sebastian > > On 10/06/2015 03:37, Gustavo L.C. Moura gustavo.moura|a|ufpe.br wrote: > > Sent to CCL by: "Gustavo L.C. Moura" [gustavo.moura%x%ufpe.br] > Dear CCL community, > I am seeking advice about the proper way of calculating a Boltzmann avera= ge. > For the sake of argument, let us say that I have a molecule that may assu= me only two distinct conformations A and B. I have no problems calculating = the Boltzmann averaged property in this case. > However, I have strong theoretical and experimental evidences that my mol= ecule forms a hydrogen bonded dimer. The dimerization process does not affe= ct the flexibility of each monomer and they still have the same two conform= ations A and B as before. I have no problems dealing with the averaging pro= cess for the dimers in conformations AA and BB (they are unique). My proble= m is with conformations AB and BA. The two dimers can be superimposed (and = are technically equal), but I still know which monomer has each conformatio= n. > My question is: should I include both dimers in the Boltzmann average or = should I include only one of them in the Boltzmann average? > Your advice is most welcome. > Thank you very much in advance. > Sincerely yours, > Gustavo L.C. MouraE-mail to subscribers: CHEMISTRY---ccl.net or use:> > E-mail to administrators: CHEMISTRY-REQUEST---ccl.net or usehttp://www.ccl.net/c= hemistry/sub_unsub.shtml > > -=3D This is automatically added to each message by the mailing script = =3D-look u= p > the X-Original-From: line in the mail header. E-mail to subscribers: > CHEMISTRY%ccl.net or use:Before posting, check wait > time at: http://www.ccl.netConferences: > http://server.ccl.net/chemistry/announcements/conferences/ Search > Messages: http://www.ccl.net/chemistry/searchccl/index.shtml If your mail > bounces from CCL with 5.7.1 error, check:> --=20 _____________ Prof. Dr. Andr=C3=A9 Farias de Moura Department of Chemistry Federal University of S=C3=A3o Carlos S=C3=A3o Carlos - Brazil phone: +55-16-3351-8090 --001a113cee2a2d2835051829d5dd Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Dear Gustavo,

apart from considering fo= rmal arguments on symmetry and (in)distinguishability of molecules, you mig= ht also consider the outcome of a typical molecular dynamics or Monte Carlo= simulation, both of which will sample the specified ensemble without actua= lly knowing/solving the partition function. If a stable dimer is observed, = each monomer may sample its available configurations A and B, and unless th= e configuration of one monomer affects the configuration of the other, whic= h would be the case for strongly interacting, cooperative systems, then eac= h monomer would sample its configurations independently and you would have = A-A, A-B, B-A and B-B with equal weights.

This is = not always observed. Consider for instance amino acids forming an alpha-hel= ix within any protein: each new amino acid which you add to the system will= sense the strong, collective dipole moment arising from the amino acids wh= ich are already there, so the incoming monomer is not actually free to samp= le any orientation, instead it will most likely align its dipole to the alp= ha-helix dipole moment. Please mind that amino acids comprising an alpha he= lix interact by means of 1-4 hydrogen bonds (between every first and fourth= monomers), just like your model dimer does, but the strong and cooperative= interaction in this case is the dipole-dipole interaction between the alph= a-helix and the incoming monomers, which modulates which regions of the pha= se space will be sampled most likely.

IMHO, the mo= st tricky part of partition function approaches to study more complex syste= m is the fact that you have to know a priori how strong and complex the mix= ed interactions between particles might be, and that's why I prefer to = rely on either MD or MC simulations to sample the phase space without actua= lly knowing the partition function. But I have to admit that success is not= always guaranteed, since poor sampling is quite often observed as the comp= lexity of the potential energy surfaces increases. For a (not so large) dim= er, this should not be the case and you should be able to perform a high qu= ality MD/MC sampling, either proving or disproving that each monomer can sa= mple its configurational phase space independently from the other.

best,

Andre

On Wed, Jun 10, 2015 at 7:1= 0 AM, Sebastian Kozuch seb.kozuch||gmail.com <owner-chemistry%ccl.net> wrote:
Sent to CCL by: Sebastian Kozuch [seb.kozuch|gmail.com] =20 =20 =20 =20
Dear Gustavo,
The matter you are pointing to is not obvious. The partition function may depend on the symmetry number and the indistinguishability of the two systems, factors that can change the Boltzmann distribution. I hope someone with real knowledge can help you, but maybe you can obtain some guidance from the work on reaction rates of Fernandez-Ramos et al. (http://link.springer.com/article/10.1007/s00214-007-0328= -0).

Best,
Sebastian

On 10/06/2015 03:37, Gustavo L.C. Moura gustavo.moura|a|ufpe.br<= /a> wrote:
Sent to CCL by: "Gustavo L.C. Moura" =
[gustavo.moura%x%ufpe.br]
Dear CCL community,
I am seeking advice about the proper way of calculating a Boltzmann average=
.
For the sake of argument, let us say that I have a molecule that may assume=
 only two distinct conformations A and B. I have no problems calculating th=
e Boltzmann averaged property in this case.
However, I have strong theoretical and experimental evidences that my molec=
ule forms a hydrogen bonded dimer. The dimerization process does not affect=
 the flexibility of each monomer and they still have the same two conformat=
ions A and B as before. I have no problems dealing with the averaging proce=
ss for the dimers in conformations AA and BB (they are unique). My problem =
is with conformations AB and BA. The two dimers can be superimposed (and ar=
e technically equal), but I still know which monomer has each conformation.
My question is: should I include both dimers in the Boltzmann average or sh=
ould I include only one of them in the Boltzmann average?
Your advice is most welcome.
Thank you very much in advance.
Sincerely yours,
			Gustavo L.C. MouraE-mail to subscribers: CHEMISTRY---ccl.net or use:
      http://www.ccl.net/cgi-bin/ccl/send_ccl_message

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--
=
_____________

Prof. Dr. Andr=C3=A9 Farias de Moura
Department of Chemistry
Federal University of S=C3=A3o Carlos
S=C3=A3o Carlos - Brazil
phone: +55-16-3351-8090
--001a113cee2a2d2835051829d5dd--