[gmx-users] cutt offs

[baptista at itqb.unl.pt]

Just one further comment, to avoid misunderstandings:

Sentences like "different cutoffs for different molecules", etc, in my
previous message obviously refer to different cutoffs between different
_pairs_ of molecules: eg, use one cutoff for interactions A-A and another
for A-B. I'm making this clarification since I realized that it could seem
that I was advocating the use of a cutoff when computing the force of A on
B, and of another cutoff when computing the force of B on A. That would be
complete nonsense in terms of mechanics, of course!

Best,
Antonio

--
Antonio M. Baptista
Instituto de Tecnologia Quimica e Biologica, Universidade Nova de Lisboa
Av. da Republica, EAN, ITQB II, Piso 6, Apartado 127
2781-901 Oeiras, Portugal
phone: +351-214469619(NEW!)   email: baptista at itqb.unl.pt
fax:   +351-214411277         WWW:   http://www.itqb.unl.pt/~baptista
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On Tue, 30 Dec 2003 baptista at itqb.unl.pt wrote:

> Dear Ilya, David and Eric,
>
> I don't see any thermodynamic inconsistency in using different cutoffs for
> different molecules in the system. From a theoretical viewpoint, choosing
> a cutoff is just part of specifying the Hamiltonian of the system, which
> is what really _defines_ your system. Thus, if you try out different
> cutoffs you are actually simulating different systems, whose thermodynamic
> properties would differ from those of the real system in different ways.
> Which one should be the best? It may be tempting to say that the best
> thing would be to run the simulations using the largest possible cutoff,
> since it will correspond to the least "approximated" energy, but this is
> not quite so. Each force field provides an _effective_ energy function
> that is parameterized with a fixed set of cutoffs (or at least it
> should...), and thus these should be the ones used in any subsequent
> simulation, unless one has very strong reasons to go beyond them (eg, when
> you suspect that the force field cannot handle properly your particular
> system, as in Ilya's example of a very large cavity). In any case, the use
> of different cutoffs for different molecules (eg, protein and solvent)
> will not send you to "thermodynamic neverland". You stay in the ensemble
> implied by your choice of thermal and pressure baths, regardless of your
> choice of cutoffs. That is, changing the Hamiltonian changes the nature of
> the system, but not the thermodynamics.
>
> I don't think that David's example of the two halves of a box having
> different cutoffs is a particular illustration of the issue raised by
> Ilya. Here you don't have different cutoffs for different _molecules_, but
> rather for different _regions_. Thus, whatever manipulation you do to
> your Hamiltonian, you will never be able to write it down in a way that is
> independent of the reference frame. It is not possible to assign the
> different cutoffs to different "pseudo-molecules", even if the latter are
> artificial constructs made up from collecting assorted Hamiltonian terms.
> The only formal way of making physical sense of this situation is to
> assume that there is some kind of _external_ field that imposes the
> different cutoffs in each half. Obviously, the nature of this "field" is
> not electrostatic, nor gravitational, nor of any other usual type. This
> field is just a formal construct that allows us to think of the situation
> in physical terms. The consequence of introducing this field is that the
> equilibrium will be attained between both halves when the _total_ chemical
> potential is the same, as implied by thermodynamics. For example, if we
> imagine for a moment that the field was electrostatic or gravitational,
> the two halves would have the same _electrochemical_ or _gravitochemical_
> potential. In that sense, I agree with David that the _strictly_chemical_
> potentials need not be the same in both halves, but the _total_ chemical
> potentials must certainly be identical. (Note that the splitting of the
> total chemical potential can be highly artificial, as in the
> electrochemical case; see Guggenheim or Denbigh on this.) Therefore, I
> don't see any problem in defining the ensemble being modeled: eg, if you
> are using thermal and pressure baths, the ensemble being modeled would be
> the isothermal-isobaric _with_ the applied field (traditionally, external
> fields are not included in the designation of the ensemble, but rather
> added as an additional external "parameter"). Of course, the situation is
> very strange in terms of the actual simulation, with atoms experiencing a
> sudden change of interactions when they move from one half to the other.
> In particular, I would expect some instabilities, which could even result
> in a total crash of the numerical solution of the equations of motion.
> However, even in this case (which is _not_ the one discussed by Ilya), I
> don't see any theoretical problem. Again: you don't screw up
> thermodynamics just by messing up the Hamiltonian; you just get a
> different system.
>
> As for the range of different interactions, I think that Ilya's point is
> right, in the sense that we _could_ use a lower cutoff for dipole-dipole
> interactions than for charge-dipole ones and still get comparable errors,
> because the former falls off faster than the latter. Actually, the now
> standard procedure of using group-based electrostatic cutoffs came from
> the fact that most charge groups can be arranged to be neutral, and
> therefore most of the interactions in the system become dipole-dipole,
> some charge-dipole, and only a few charge-charge. By arranging things in
> this way the truncation error is somewhat minimized.
>
> And if you really want to make a simulation with such a big cavity, I
> don't think you have much choice: since there is no danger of
> thermodynamic mess up, be bold and make a hack to increase the cutoff of
> your LJ particle! Then check if the small-cavity case still gives the same
> properties as before. If so, I guess you could proceed (at your own
> risk!). Of course, you should do all this with your fingers crossed! ;-)
>
> Best,
> Antonio
>
>