[gmx-users] second derivative of force

Mark Abraham Mark.Abraham at anu.edu.au
Wed Jun 21 03:33:52 CEST 2006

Nguyen Hoang Phuong wrote:
> Dear All,
> I would like to obtain the second derivative of the total force 
> d^2f_i/dr_i^2 at every atom i along the trajectory. In principle, this 
> can be
> obtained from the Hessian matrix. However, I don't need the cross terms 
> like d^2f_i/dr_i dr_j, therefore it will be very time consumming to 
> calculate
> the Hessian matrix along the trajectory if I just need the off-diagonal 
> terms. Does anyone know a way to do that? Thanks.

I don't think you'll find any short-cut, because I can't see that there 
is another use for this type of calculation, hence nobody will have 
included it already in GROMACS. Hessian matrices are expensive to 
calculate for QM because they scale with something like the fourth power 
of the number of basis vectors. The cost of finding Hessian matrices in 
MM is roughly linear in the number of atoms, so it ought not to be too 
scary. In fact, it would only be more expensive by a factor of N over an 
algorithm that only calculates the diagonal terms. If it is too 
expensive, you also might want to reconsider doing it at every 
trajectory snapshot :-) Otherwise, your only recourse will be to find 
the piece of code that computes the Hessian, and rework the loops over i 
and j so that i=j always.


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