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From: Tyler Luchko <tluchko.ualberta.ca>

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,

Tyler

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

Date: Fri, 2 Jul 2010 10:08:41 -0400

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

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)]

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.

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,

Tyler

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

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