[gmx-developers] double precision minimization accuracy limits.

chris.neale at utoronto.ca chris.neale at utoronto.ca
Wed Jan 23 05:21:44 CET 2008

Quoting David.Osguthorpe at UCHSC.edu:

>> Unless I'm missing something, this is a users-list question. Energy
>> minimization is going to get stuck in a local minimum.
> But the local minimum should be a minimum down to machine accuracy -  
>  at least thats
> achievable with force field/MD programs I have written and used in   
> the past - unless there are problems with
> derivatives due to discontinuities (hence the use of switching   
> functions) or derivative errors (ie. there are numerical errors in the
> derivatives which are due to programming errors or approximations   
> used in computing the forces
> from the coordinates and their correspondence to the energies).
> Hence the developers list - I dont know how most users are going to   
> know the exact numerical coding
> of the derivative computation functions.

point taken.

>> The acid-test of
>> a minimization is if the resulting structure can be used to start an MD
>> run.
> Not true - energy minimization  is required for example to compute   
> normal modes
> where good convergence is needed for isolated molecules to ensure   
> the 6 lowest frequency
> modes are close to zero - such structures need to be far more   
> converged (ie. the maximum derivative
> should be less than  0.10 kJ nm-1 - we used to use < 0.001 kcal angstrom-1)
> to produce valid results whereas MD can be started from much larger   
> derivatives.
> To me a maximum derivative of 232 kJ nm-1 is too big - a double   
> precision program
> should be able to get them lower than that even for large protein systems.
> The definition of a local minimum is all derivatives are zero
> to infinite precision - otherwise its not a local minimum or minimum  
>  of any kind.
> For limited precision computers we accept a definition of say the   
> maximum derivative < 0.01 kJ nm-1.

Thank you for the detailed explanation. It appears that your usage is  
more advanced than mine. I have not done what you are attempting to  
do. I have only ever done EM in order to do MD. Although I agree with  
your definition of a local minimum, I have never found any EM routine  
to achieve zero force. That said, I have never paid attention to see  
if the remaining force actually is down to the level of machine  
precision. Therefore it seems that I answered prematurely without  
taking your energy magnitude into account. The bottom line of this  
response is an apology and an admission that I am not able to provide  
a solution. Hope you find one.


>> I don't see why you couldn't grompp your next energy minimization using
>> -t .trr -e .edr but again, that should not be necessary.
> thanks - I missed that possibility.
> David

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