[Oopse-developers] Implementation of the z-constraint method

[Dan Gezelter]

Mario,

   Thanks for contacting me.  You ask an interesting question about  
the sign of the balancing forces for the non-z-constrained molecules.  
It has been a while since we implemented the z-constraint method, and  
it is certainly possible that there was a typo in equation 81.  I  
agree that if one wants to conserve total linear momentum in the  
system, the sum of forces on the constrained and unconstrained  
molecules should be zero.

However, the code appears to implement it exactly the same way as it  
appears in the OOPSE paper, so I'll have to dig a bit and run a test  
case to see if you have uncovered a bug in our code (as well as the  
paper) or if I'm just forgetting how we derived the forces on the  
unconstrained molecules.

To answer your second question, we originally tried two different z- 
constraint force policies (by-mass and by-number).  Both seemed to  
work fine, so your approach  (which I think is similar to the by- 
number policy) should be just as good.

And your third point is completely correct.  In the code we actually  
do normalize by
the total mass of the unconstrained molecules.

     return totalForce * mol->getMass() / totMassUnconsMols_;

Best regards,

  --Dan Gezelter


On Nov 6, 2008, at 5:39 AM, Orsi M. wrote:

> Dear Prof. Gezelter,
>
> I am writing in relation to your article on the OOPSE program [J  
> Comp Chem, 26, 252, 2005]. In particular, I'm interested in your  
> implementation of the z-constraint algorithm (pp. 267-268).
>
> I was very pleased to read your paper as I also thought about the  
> same problem of the z-constraint algorithm pointed out in the  
> article - it's reassuring to know that other people are aware of  
> this issue.
>
> In fact, I've also implemented the z-constraint method in my  
> simulation program. However, I've done it in a slightly different  
> way, which is not fully consistent with your approach.
> My implementation is described in the attached pdf file (note that  
> my algorithm is specific to the case where there is only one rigid- 
> body solute).
>
> To clarify the points where there is disagreement between our  
> approaches, I would be grateful if you could reply to the following  
> questions:
>
> 1. Why do you have a "-" sign in your equation 81? Shouldn't it be a  
> "+" instead?
> With this operation, we want to reintroduce in the system the force  
> on the constraint particle that has been removed, so it should be  
> added back, shouldn't it? Isn't it basically the same idea that  
> leads to the "+" sign in the following equation 82?
>
> 2. Again on equation 81, is there a reason why you are weighting on  
> the masses (m_beta_i)? In my implementation, I simply have a  
> constant term which is added to each unconstrained particle  
> (equation 2 in the attached pdf document). Actually, I believe that  
> both your approach and mine are correct here, as long as they  
> restore the total force, but I would like to know if you think  
> otherwise.
>
> 3. Doesn't equation 82 require a normalizing factor? To conserve the  
> total momentum, I think that the second term of the right hand side  
> of equation 82 should be divided by the total mass of the  
> unconstrained particles (as in my equation 1 in the attached pdf).
>
> Looking forward to hearing from you soon, I thank you for your time  
> and attention,
>
> Mario
>
> --
> Dr Mario Orsi
> Research fellow
> Email: orsi at soton.ac.uk
> Prof Jonathan W Essex research group
> School of Chemistry, University of Southampton
> Highfield, Southampton (Hants), SO17 1BJ
> Tel: +44(0)2380595560 (ext: 25560)
> http://www.personal.soton.ac.uk/orsi
> http://www.southampton.ac.uk/~chemphys/jessex
>
>
>
>
>
> <zConstraint.pdf>

***********************************************
   J. Daniel Gezelter
   Associate Professor of Chemistry
   Director of Graduate Admissions
   Department of Chemistry and Biochemistry
   251 Nieuwland Science Hall
   University of Notre Dame
   Notre Dame, IN 46556-5670

   phone:  +1 (574) 631-7595
   fax:    +1 (574) 631-6652
   e-mail: gezelter at nd.edu
   web:    http://www.nd.edu/~gezelter
************************************************