CCL: Proper way of doing a Boltzmann average

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 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 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 the
 Boltzmann averaged property in this case.
 > However, I have strong theoretical and experimental evidences that my
 molecule forms a hydrogen bonded dimer. The dimerization process does not affect
 the flexibility of each monomer and they still have the same two conformations A
 and B as before. I have no problems dealing with the averaging process 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 are technically
 equal), but I still know which monomer has each conformation.
 > 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:>
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 --
 _____________
 Prof. Dr. André Farias de Moura
 Department of Chemistry
 Federal University of São Carlos
 São Carlos - Brazil
 phone: +55-16-3351-8090