Re: DOF during alchemical simulations

From: Brian Radak (bradak_at_anl.gov)
Date: Mon Nov 30 2015 - 12:30:33 CST

On 11/30/2015 12:05 PM, Grace Brannigan wrote:
> Hi Brian,
>
> Yes, I think it makes sense that alchDecouple on/off should affect
> this error, but I can't tell if it's in the way you're thinking.
>
> With alchDecouple on, the translational and intramolecular dof of the
> decoupled molecule should be preserved - so I wouldn't think there
> would be any dof-associated error.
>
Sorry, yes, this is what I meant to convey. The code currently seems to
favor the "alchDecouple" on scenario.
> I'm not sure how the periodic images are relevant to calculating the
> dof - it may be useful here to view them as just changing the
> potential energy. The 'ideal gas' or translational contribution of
> the decoupled molecule to the pressure is determined by the bounds on
> xyz, which is independent of whether pbc is used, and shouldn't change
> much over decoupling.
>
I only meant that a periodic molecule or set of atoms is not an ideal
gas because there is a configurational component. In that case though,
there /is/ a coupling between the two systems since they share a box and
both push on.

> For alchDecouple off I think things get more complicated, but
> primarily due to a change in intramolecular dof - which would probably
> be trickier to correct for in a general way. The error in the
> estimated pressure should become negligible for n << N, so it could be
> an issue if a double-annihilation thermodynamic cycle had two FEP
> calculations with really different N.
>
I agree that the error is likely negligible. This is all an exercise in
fastidiousness and I doubt any changes would affect anyone's results in
a hugely discernible way. I'm not entirely repulsed by the sudden
introduction of degrees of freedom when moving away from lambda = 0,1,
as this is more in line with single coordinate transformations, just
with a alchemical path. Although this might also add interesting shifts
to the TI derivative.

> HTH,
> Grace
>
> On Mon, Nov 30, 2015 at 10:36 AM, Brian Radak <bradak_at_anl.gov
> <mailto:bradak_at_anl.gov>> wrote:
>
> I'm glad this is intriguing rather than a non-issue. I agree that
> whatever systematic errors are present are likely quite
> negligible. Nonetheless, they can still be discerned from simple
> tests and I dislike being incorrect when the right answer can be
> easily achieved.
>
> My thought was that the degrees of freedom ought to depend on the
> decoupling scheme (alchdecouple on/of), as this determines whether
> or not the annihilated atoms see their images (exist as a periodic
> "gas") or not (are an ideal gas molecule). Does it make sense for
> ideal gas degrees of freedom to impact the pressure? My first
> thought would be that they should not impact sampling at all; I
> believe manipulations with ideal gas partition functions ought to
> confirm this is true.
>
> Would it make sense to have different behavior when alchDecouple
> is on or off? This would only meaningfully differ at alchLambda =
> 0,1, as the intervening values are totally arbitrary, so long as
> sampling is not grossly impacted.
>
> Brian
>
>
> On 11/27/2015 03:31 AM, Jérôme Hénin wrote:
>> On 26 November 2015 at 19:28, Aron Broom <broomsday_at_gmail.com
>> <mailto:broomsday_at_gmail.com>> wrote:
>>
>> This is really interesting. My knowledge of alchemical
>> transformations in limited, but given their successes I'd
>> like to understand more (and will happily be corrected on my
>> errors in thinking).
>>
>> If you leave those degrees of freedom in, then the end-point
>> simulations are actually different than a similar simulation
>> of that system where you aren't doing an alchemical
>> transformation. That raises for me a kind of intuitive
>> red-flag, which I think is the same point you are making?
>>
>>
>> I agree with you on this. This is among the terms that we neglect
>> when doing alchemical calculations in an isobaric simulations. If
>> you decouple n particles among N and have a barostat set at
>> pressure P0, you will generate an ensemble for the (N-n)
>> particles at pressure P = P0 - Pn, where Pn is the kinetic
>> pressure from just n particles at the given volume and
>> temperature. If I get my orders of magnitude right: decoupling
>> one particle in a thousand from a condensed phase will
>> underestimate the pressure by (on the order of) 1 bar. That's
>> something I can live with: I can say worse things about my
>> simulations.
>>
>> But on the other hand, if at the end-points you suddenly
>> eliminate those degrees of freedom completely, doesn't that
>> create a discontinuity in the transformation, which is a bad
>> thing and source of much misery?
>>
>>
>> Unless you do TI, it's not a problem in and of itself: other
>> estimators explicitly give FE differences between discrete
>> states. The tricky part may be to account for that explicitly in
>> the free energy estimator.
>>
>> Probably an idiotic question from someone with limited
>> physics understanding, but I suppose non-integer degrees of
>> freedom are disallowed (assuming similar fractional counting
>> of mass and velocity)?
>>
>>
>> Nothing prevents us from using a fractional number when
>> calculating kinetic pressure, although it doesn't have much
>> physical meaning. That's pretty much the spirit of alchemical
>> transformations. Again, I'd be totally happy with it if the
>> estimators were rewritten with that in mind.
>>
>> Jerome
>>
>> On Thu, Nov 26, 2015 at 1:00 PM, Jérôme Hénin
>> <jerome.henin_at_ibpc.fr <mailto:jerome.henin_at_ibpc.fr>> wrote:
>>
>> Brian,
>>
>> I might be missing something, but I'd say the degrees of
>> freedom of non-interacting particles should be counted
>> for the purpose of kinetic pressure calculation.
>>
>> Jerome
>>
>> On 25 November 2015 at 17:31, Brian Radak <bradak_at_anl.gov
>> <mailto:bradak_at_anl.gov>> wrote:
>>
>> After some griping about this, I've finally
>> implemented a (preliminary) correction to the
>> Lennard-Jones tail correction that accounts for
>> alchemical modifications. Once this is integrated
>> with other improvements to the alchemical code, I
>> hope this will become part of the 2.11 release.
>>
>> However, I recently noticed that a similar problem
>> crops up in the degrees of freedom calculation. That
>> is, alchemical atoms get counted at the endpoints
>> even when they are only ideal gas particles. This was
>> obvious when I started double checking single
>> coordinate endpoint energies and pressures with dual
>> coordinate alchemical energies and pressures; that
>> is, the energies match but the pressures do not quite
>> match.
>>
>> The error is admittedly much less than 0.1%, as
>> multiplying a "more different" large number by a
>> small number is still just another "kind of large"
>> number. Nonetheless, one could view this as an error
>> in the specified target pressure for an alchemical
>> simulation (i.e. the pressure you input is not the
>> pressure you simulate). Then again, this behavior
>> might be exactly what one is expecting, depending on
>> how one draws the thermodynamic cycle.
>>
>> I guess my question for the community is, does this
>> matter? How do people expect degrees of freedom to be
>> determined? Do people usually draw their cycles such
>> that non-interacting particles should not contribute?
>> This might not be the case, for example, in ligand
>> binding calculations where the ligand continues to
>> interact with its own images (although in that case,
>> one essentially has two simulations going at the same
>> time when the ligand is decoupled).
>>
>> Brian
>>
>>
>> --
>> Brian Radak
>> Theta Early Science Program Postdoctoral Appointee
>> Leadership Computing Facility
>> Argonne National Laboratory
>>
>> 9700 South Cass Avenue
>> Building 240, 1.D.16
>> Lemont, IL 60439-4871
>> Tel: 630/252-8643 <tel:630%2F252-8643>
>> email: bradak_at_anl.gov <mailto:bradak_at_anl.gov>
>>
>>
>>
>>
>>
>> --
>> Aron Broom M.Sc
>> PhD Student
>> Department of Chemistry
>> University of Waterloo
>>
>>
>>
>> --
>> Brian Radak
>> Theta Early Science Program Postdoctoral Appointee
>> Leadership Computing Facility
>> Argonne National Laboratory
>>
>> 9700 South Cass Avenue
>> Building 240, 1.D.16
>> Lemont, IL 60439-4871
>> Tel: 630/252-8643 <tel:630%2F252-8643>
>> email: bradak_at_anl.gov <mailto:bradak_at_anl.gov>
>
>
>
>
> --
> Grace Brannigan, Ph.D.
> Assistant Professor
> Center for Computational and Integrative Biology (CCIB) &
> Department of Physics
> Rutgers University, Camden, NJ
> (856)225-6780 <tel:%28856%29225-6780>
> http://branniganlab.wordpress.com
>
> --
> Brian Radak
> Theta Early Science Program Postdoctoral Appointee
> Leadership Computing Facility
> Argonne National Laboratory
>
> 9700 South Cass Avenue
> Building 240, 1.D.16
> Lemont, IL 60439-4871
> Tel: 630/252-8643
> email: bradak_at_anl.gov

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