[gmx-developers] stuff in double precision

David Mobley dmobley at gmail.com
Mon Feb 5 19:35:44 CET 2007


> The problem David experienced is just due to an in a sense ill-posed
> problem, since looking for 1 in 10^6 energy differences (i.e.
> subtracting large numbers) is asking for trouble (think diverging
> trajectories due to round off with different average energies). This is
> why people generally shy away from absolute free energies.

No, it isn't true that this is an ill-posed problem. And if this were
the problem for absolute free energies, it would be for relative free
energies as well. All of these methods rely on being able to
*accurately* evaluate the potential energy of a particular system
configuration in several different potentials (i.e. different lambda
values) (except TI, which requires accurate evaluation of a potential
energy derivative). If this energy evaluation cannot be done
accurately enough that subtraction of, say, V(lambda) from
V(lambdaprime) is accurate to levels better than a fraction of a
kJ/mol, NO free energy calculations will work. (For example, the FEP
approach uses the Zwanzig relation, which takes the exponential
average of the difference in potential energies of two systems).

The reason free energy calculations (absolute or relative) work (or
are supposed to work) isn't that they avoid subtracting large numbers
-- it's that they evaluate the potential energy of a particular
snapshot in different Hamiltonians (or, similarly, the free energy
derivative for a particular snapshot).

If you go down this route, David, you're effectively making the claim
that GROMACS CANNOT be used for free energy calculations of any sort.
I don't think that's where you want to go.

> A very simple workaround would be to always use the free energy loops,
> also for "reference no-free energy simulations", then you are running
> the same code twice.

I agree that that works in this particular case, and that's what we're
doing. But obviously this hasn't been checked. What if this happens in
other cases? i.e., do soft core parameters affect energies at
lambda=0? In general one would like to know that if one evaluates the
potential energy of a particular snapshot in a particular Hamiltonian,
one will get the same energies to accuracies well below a kJ/mol
(preferably a lot better -- we can get statistical uncertainties in
free energy calculations down to 0.1 kJ/mol or less in some cases;
you'd like to be sure your potential energy evaluations are reliable
to better than this).


> --
> David.
> ________________________________________________________________________
> David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
> Dept. of Cell and Molecular Biology, Uppsala University.
> Husargatan 3, Box 596,          75124 Uppsala, Sweden
> phone:  46 18 471 4205          fax: 46 18 511 755
> spoel at xray.bmc.uu.se    spoel at gromacs.org   http://folding.bmc.uu.se
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