[gmx-users] PME accuracy

[Erik Lindahl]

On Wednesday, May 7, 2003, at 13:45 America/Los_Angeles, Jason  
DeJoannis wrote:

> I think you mean the other way around. In other
> words alpha (the Ewald parameter) is chosen from:
>
>   ewald_rtol  = erfc(alpha*rcoulomb)
>

Yep, that's what I meant :-)


> The manual was kind of vague about that. For Ewald
> simulations it would be more useful to select alpha from
> the condition that the real-space and Fourier-space
> have the same level of error... but as most people
> use PME that's just a detail.

That would be great, but as far as I know, that is not easy (possible?)  
to calculate for smooth PME with arbitrary systems and triclininc  
boxes! If you have any good suggestions (even approximate), send me a  
pointer to it and we'll see what happens :-)

Cheers,

Erik



>
> Thanks!
>
>    -Jason
>
> ---
> Jason de Joannis, Ph.D.
> Chemistry Department, Emory University
> 1515 Pierce Dr. NE, Atlanta, GA 30322
> Phone: (404) 712-2983
> Email: jdejoan at emory.edu
> http://userwww.service.emory.edu/~jdejoan
>
>
>
> Quoting Erik Lindahl <lindahl at stanford.edu>:
>
>> Hi Jason,
>>
>> The alpha parameter is calculated so that the "switched off"  
>> real-space
>> interaction is PME_rtol fraction of the nonswitched interaction at the
>> cutoff, just as it is in Tom Darden's original reference code.
>>
>> The fourierspacing value is the largest gridspacing you can tolerate.
>> The actual grid used is calculated to optimize the dimensions for FFTW
>> - you'll see a line about it when running grompp. In other words, if
>> you only increase the gridspacing marginally it sounds quite normal
>> that the actual grid dimensions didn't change.
>>
>> Cheers,
>>
>> Erik
>>
>> On Wednesday, May 7, 2003, at 06:47 America/Los_Angeles, Jason
>> DeJoannis wrote:
>>
>>> Hi gmx-users,
>>>
>>>   Unfortunately, as I think it was David who pointed it
>>> out to me: there is no analytical error estimate for
>>> smooth PME yet. But as the error-estimates for Ewald, P3M
>>> and regular PME would suggest, the error varies with several
>>> things including the number of charges. Keep this in mind
>>> as well as the fact that the Ewald parameter is probably
>>> being adjusted "behind the scenes" in order to deliver
>>> the specified "ewald_rtol".
>>>
>>>   If anyone knows of a way to find out what Ewald parameter
>>> (alpha) is being used, let me know. Also I am not very clear
>>> on what is being done, if anything, to the PME parameters
>>> behind the scenes. For example I have on occasion reduced the
>>> Fourier spacing to find no change was actually made in the
>>> mdout.mdp file. Is that possible? or am I mistaken?
>>>
>>> best regards,
>>>
>>>   Jason
>>>
>>> ---
>>> Jason de Joannis, Ph.D.
>>> Chemistry Department, Emory University
>>> 1515 Pierce Dr. NE, Atlanta, GA 30322
>>> Phone: (404) 712-2983
>>> Email: jdejoan at emory.edu
>>> http://userwww.service.emory.edu/~jdejoan
>>>
>>>
>>>
>>> Quoting Vincent Ballenegger <vcb25 at cam.ac.uk>:
>>>
>>>> Dear gmx-users,
>>>>
>>>> According to the gromacs manual, the PME method is such that "with a
>>>> grid spacing of 0.1nm and cubic interpolation (i.e. pme_order=4),  
>>>> the
>>>> electrostatic forces have an accuracy of 2-3e-4".
>>>> I did a small test and obtained the following results for the  
>>>> electric
>>>> force between two ions (charge +e and -e) a distance 2.35nm apart
>>>> along
>>>> the diagonal of a cubic box of 3.5nm:
>>>>
>>>> * Ewald method with fourier_nx=25:
>>>>                force = -10.824      "exact result"
>>>> * PME method with fourier_spacing=0.1, pme_order=4:
>>>>                force = -7.789         error: 28% !!!
>>>> * PME method with fourier_spacing=0.05, pme_order=4:  (very slow!)
>>>>                force = -10.932         error: 1%
>>>> * PME method with fourier_spacing=0.1, pme_order=6:
>>>>                force = -10.716       error: 1%
>>>>
>>>> Where is the claimed accuracy of 3e-4?
>>>>
>>>> Thanks,
>>>>   Vincent
>>>>
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>>>
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>> ---------------------------------------------------------------------- 
>> --
>> -----
>> Erik Lindahl, MSc, PhD     <lindahl at stanford.edu>
>> D109, Fairchild Building
>> Dept. Structural Biology, Stanford University School of Medicine
>> Tel. 650-7250754    Fax. 650-7238464
>>
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>
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------------------------------------------------------------------------ 
-----
Erik Lindahl, MSc, PhD     <lindahl at stanford.edu>
D109, Fairchild Building
Dept. Structural Biology, Stanford University School of Medicine
Tel. 650-7250754    Fax. 650-7238464