[gmx-developers] What is dH/dl functional for Coulomb interaction?

ggroenh ggroenh at gwdg.de
Tue Jun 24 09:05:28 CEST 2008

Explicit lambda dependence comes in if the charges of both atoms  
involved inthe interaction are scaled by lambda. What I suspect is  
that you have no interactions within the QM subsystem (i atoms), and  
there is only interaction between the perturbed i aotms and the  
environment atoms j.

Do you use QM/MM, or is the name QM system just chosen like that?



   only between interactions o
On 24 Jun 2008, at 02:35, Leontyev Igor wrote:

> Dear gmx-developers,
> I am confused by the fact that dhdl-values calculated with the same
> molecular structure for different values of the Coulomb interaction  
> coupling
> parameter lambda (L) does not depend on the lambda. According to the  
> Gromacs
> 3.3 Manual the L-dependence of Coulomb part of Hamiltonian has form  
> given by
> Eq.(4.103) such as dH(L)/dL should explicitly depend on lambda.  
> However, my
> tests show opposite. I have tried to calculate a charging free  
> energy of
> QM-system (solute) for two different systems:
> 1) QM-system (solute) in protein. The QM-system consist of metal  
> center
> alone with imidozole rings of ligating residues (35 atoms) and the  
> protein
> is represented by 11938 atoms. The QM-system has non-zero atomic  
> charges in
> both the initial and final states. Total charge difference of the  
> system
> between final and initial state is -1.
> 2) Solute alone (no solvent). The model QM-system is constituted by  
> two
> point charges separated by 1nm . Point charges have values (0,0) in  
> the
> initial state and (-1,1) in the final state.
> The independence of dhdl-values on the parameter lambda (L) was  
> observed for
> both systems. For the model system (2 point charges), dhdl-values   
> can be
> calculated manually. According to Eq. (4.103), H(L)=f/ 
> (1nm)*L*(-1)*L*(1),
> thus:
>     H(L)=-138.935*L*L                        (1)
> and
>     dH(L)/dL=-2*138.935*L
> However, results obtained by Gromacs 3.3.2 are not described by the  
> above
> functional (1). The results are:
>   L              Potential energy             dhdl
> 0.00000         0.00000e+00     -1.38935e+02
> 0.50000       -6.94677e+01      -1.38935e+02
> 1.00000       -1.38935e+02      -1.38935e+02
> It is interesting to notice that these results are precisely  
> described by
> the conventional functional form for Coulomb coupling:
>          H(L)=HA+L*(HB-HA),                        (2)
> where HB and HA are Hamiltonians in the final and initial states,
> respectively. Thus, could someone confirm that the Coulomb coupling  
> actually
> implemented in Gromacs is given by functional (2) instead of  
> fuctional given
> by Eqs (4.103)-(4.106) of the Manual ?
> Thanks,
> Igor
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Gerrit Groenhof
MPI biophysical chemistry

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