[gmx-developers] Buckingham potential force calculation correct ?

[David van der Spoel]

Mathias PUETZ wrote:
> 
> Hi,
> 
> while tuning the force kernels for BlueGene I stumbled across the 
> following.
> 
> The C (also Fortran) code generated by mknb for calculating the 
> Buckingham potential is the following:
> 
>   rinvsq = rinv * rinv
>   br = cexp2 * rsq * rinv
>   Vvdwexp = cexp1 * exp (-br)
>   Vvdw6 = C6 / (rinvsq*rinvsq*rinvsq)
>   fscal = (br * Vvdwexp - 6.0 * Vvdw6) * rinvsq;
> 
>   fx = dx * fscal
>   fy = dy * fscal
>   fz = dz * fscal
> 
> This does not look right to me, because the br * Vvdwexp part in the 
> calculation of
> fscal should only be scaled by rinv and not rinvsq as deduced by 
> following calculation:
> 
> The Buckingham potential is defined by the following form:
> 
>   V(r) =   C1 * exp ( - C2 * r) -  C6 / r**6
> 
> The force on particle 1 is calculated by the formula:
> 
>   Fx = -  dx / r  *  d/dr V(r)
>        =  -dx / r  * { - C1*C2*r * exp( -C2 * r)  + 6.0 * C6 / r**7 }
>        = -dx *  { 1/r**2  * 6.0 * C6 / r**6  + 1/r * br * C1 * exp (-C2 
> * r) }
>        = -dx * { rinvsq * 6.0 * Vvdw6  + rinv * br * Vvdwexp }
> 
>       != -dx * rinvsq * { 6.0 * Vvdw6  + br * Vvdwexp }
> 
> Am I making a mistake here or is the GROMACS code wrong ?
> 
> Viele Grüsse / Best regards,
> Dr. Mathias Pütz
> 
> IT Specialist for Application Perfomance
> 
> Deep Computing - Strategic Growth Business
> IBM Systems & Technology Group
> 
> e-mail:  mpuetz at de.ibm.com
> mobile: + 49-(0)160-7120602
> fax:         + 49-(0)6131-84-6660
> 
> snailmail:
>  IBM Deutschland GmbH
>  Department B458
>  Hechtsheimer Str. 2 / Building 12
>  55131 Mainz
>  Germany
> 
> 
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I think it is correct because there is an extra r in the br term.

-- 
David.
________________________________________________________________________
David van der Spoel, PhD, Assoc. Prof., Molecular Biophysics group,
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596,  	75124 Uppsala, Sweden
phone:	46 18 471 4205		fax: 46 18 511 755
spoel at xray.bmc.uu.se	spoel at gromacs.org   http://folding.bmc.uu.se
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