Re: [AMBER] 3D-RISM in NAB AmberTools: 2) what is tolerance

From: Tyler Luchko <>
Date: Fri, 2 Jul 2010 10:08:41 -0400

On 2010-07-01, at 12:16 PM, Andrey Frolov wrote:

> Dear NAB and 3D-RISM Developers,
> I would like to run some simulation in NAB of AmberTools with 3D-RISM
> and i have some questions (in addition to my previous message):
> 1.
> What is the "tolerance" statement (like:
> mm_options("tolerance=1e-11");)? In manual it is written that this is
> residual, but how actually it is calculated: is it a L2 norm for the 3D
> total correlation functions h (or maybe c or gamma):
> tolerance = (\sum_{number of 3D functions} [ \int_{V} (h_new -
> h_old) dV ] ) / {number of 3D functions}
> where h_new and h_old - 3D arrays functions of two subsequent
> iterations.?

The pair distribution function, g, is used (though h, c or gamma would also be acceptable). The residual is the root mean squared difference between the last two iterations.

residual = sqrt[(\sum (g_0(i,j,k) - g_1(i,j,k))^2)/ (Nx*Ny*Nz*Nspecies)]

> 2.
> If i gave a right definition of the "tolerance", why the proposed value
> for minimization (and i suppose for one point calculation) with
> 3D-RISM is so small 10-11? I suppose that the accuracy 10-5 is more
> the enough if we want to calculate chemical potential out of total
> correlation functions.
> Are there some obstacles that i do not see so far?

For minimizations it is important for the calculated gradient of the energy to be as close as possible to the true gradient of the calculated energy. Since 3D-RISM is a grid-based iterative calculation, the residual tolerance will affect how well the energy and the forces agree. Note that even for low tolerances, such as 1e-11, minimization will be practically limited to an RMS gradient of 1e-3 or 1e-4.

> And what is an appropriate value of "tolerance" to use for 1 point
> calculation of chemical potential without wasting too much of computer
> resources?

It depends on the level of numerical precision you require. As a rough guide when calculating the solvation free energy, you can expect three significant digits for a tolerance of 1e-3, four for 1e-4 and five for 1e-5.

Hope this helps,

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Received on Fri Jul 02 2010 - 07:30:05 PDT
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