[gmx-developers] Re: [gmx-users] Scaling Coulomb interactions with lambda, on a pair-wise basis

[Matt Wyczalkowski]

Berk Hess wrote:
>> From: Matt Wyczalkowski <maw2 at cec.wustl.edu>
>> Reply-To: Discussion list for GROMACS users <gmx-users at gromacs.org>
>> To: gmx-users at gromacs.org
>> Subject: [gmx-users] Scaling Coulomb interactions with lambda,on a 
>> pair-wise basis
>> Date: Wed, 05 Dec 2007 15:10:57 -0600
>>
>> Hi,
>>
>> I am looking to scale non-bonded interactions between two atoms with 
>> the lambda parameter, while keeping other interactions unchanged.  I 
>> am not sure how to do this for Coulomb interactions.
>>
>> Scaling the Lennard-Jones interactions between a specific atom pair 
>> seems straightforward, by setting VA, WA, VB, WB for that pair in the 
>> [PAIRS] directive.  However, in order to modify Coulomb interactions 
>> between an atom pair, it seems I need to modify qA and qB for each 
>> atom -- this then affects the interactions between this atom and all 
>> other atoms as well, something I need to avoid.
>>
>> Is there a way to scale Coulomb interactions for a specific pair of 
>> atoms only?
>
> Unfortunately this can not be done easily.
> The only way would be to use user tables for the interactions between
> these two atoms and use the dispersion table for LJ and the repulsion
> table for Coulomb and the Coulomb table zero. In that way you can use 
> WA/WB
> as charge parameters.
>
> It would be useful to have Coulomb scaling for pairs, mainly for 
> forcefield issues
> where you could have different scaling parameters for different 
> molecules.
>
> But why would you only want to turn of the Coulomb interaction between 
> two atoms?
> I don't see how that could be of use.
>
> Berk.
(This discussion seems more pertinent to the developers list.)

The idea is to interpolate smoothly between bonded (lambda=0) and 
non-bonded (lambda=1) interactions between a particular pair of atoms.  
For instance, at l=0 the atoms experience a harmonic potential with 
coulomb and LJ interactions turned off; as lambda increases the LJ and 
coulomb interactions scale up while the harmonic potential relaxes, so 
that at l=1 regular non-bond interactions are recovered.  This would be 
useful for free energy calculations, for example.

The downside of using tabulated energy functions (a different table per 
lambda value) is that the idea of dU/d[lambda] is lost.

This does bring up a useful generalization of "foreign energies" 
discussed here previously, where the energy for a particular 
configuration is evaluated using a potential corresponding to a 
different ("foreign") lambda value during run-time (useful for FEP and 
BAR free energy calculations).  Ideally, one could also evaluate foreign 
energies not just for "foreign lambda" values, but for "foreign 
tabulated potentials" as well. 

Regards,

Matt

-- 
Matt Wyczalkowski
Doctoral Candidate, Biomedical Engineering
Pappu Lab: http://lima.wustl.edu
Washington University in St. Louis
maw2 at cec.wustl.edu