[gmx-users] How to add another electrostatic summation methodinGromacs

Mark Abraham Mark.Abraham at anu.edu.au
Sat Mar 28 02:34:35 CET 2009

Shuangxing Dai wrote:
> ----- Original Message ----- From: "Mark Abraham" <Mark.Abraham at anu.edu.au>
> To: "Discussion list for GROMACS users" <gmx-users at gromacs.org>
> Sent: 27 March, 2009 5:01 PM
> Subject: Re: [gmx-users] How to add another electrostatic summation 
> methodinGromacs
>> Shuangxing Dai wrote:
>>> Yes, but I still cannot write out the pair interaction for each ion 
>>> since there is cut off. With cut off, I need to assign a averge value 
>>> of the last two constants to each ion. But I cannot get the total 
>>> number of neighbours in a cut off distance in advance. So I cannot 
>>> use the user defined part to do my eletrostatic summation.
>> If N is the number of neighbours inside the cutoff distance, then you 
>> might be right. If so, then I don't understand why the inner summation 
>> constrains "j != i" and "r_ij < R_c" since the latter is implied by 
>> formation of the set over which the summations are occurring.
>> If N is the total number of ions then the last few terms are all 
>> system-wide constants.
> Sorry, (5.13) is the total electrostatic potential energy  for the 
> system and the N is the total number of ions.

So the "total number of neighbours in a cut off distance" doesn't seem 
to enter the expression...

>> I also don't understand why the limit expression exists. For any 
>> values actually used in a simulation, that expression is just a constant.
> In simulation, we simply uses r_ij = R_c, so ignore the limit.


>>> I compared carefully with Wolf summation with the Ewald summation, 
>>> the differences are:
>>> 1. There is no reciprocal term in Wolf.
>>> 2.Instead, the Wolf assums that the ions out side the truncations 
>>> sphere is exactly located at the sphere. That is how the extra two 
>>> terms come out.
> The second and third terms came from this treatment.
>>> 3. Wolf uses cut-off, while Ewald can only deal with peoriodical 
>>> boundary conditions cases.
>>> So I need to add a similiar summation like Ewald to treat with the 
>>> long-range electrostatic force, not a non-bonded interaction. Then 
>>> which parts needs to be read and modified?
>> I don't understand your conclusion, here.
> OK. I mean I need to add a eletrostatic summation method very similiar 
> to Ewald. So where is definition/algorithm of Ewald in Gromacs and how 
> to add one?

Such a summation method is algorithmically a short-range interaction, 
not a long-range one (like a reaction-field contribution, or a mesh 
contribution from PME or PPPM), which is the reason I didn't understand 
your conclusion above.

Like I said a day or two back, the nonbonded kernels do the real-space 
summation for Ewald. For speed, in the optimized kernels the 
erfc(alpha*r)/r bit is pre-computed in a table and looked up. Hence 
wanting to cast your expression to use the same trick.


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