[Pw_forum] Display of forces in a pure scf run

[Stefano Baroni]

On Dec 7, 2011, at 4:23 PM, Cristian Degli Esposti Boschi wrote:

> Dear Stefano and Axel, thanks for your replies. Actually question can be 
> rephrased as follows. Thanks to the Hellmann-Feynman theorem
> in order to compute the ionic forces I need only the partial
> derivatives of the total energy with respect to the ionic coordinates

this is not what you need, this is *the* definition of ionic force: $\mathbf{F}_I=\frac{\partial E}{\partial\mathbf{R}_I}$, with obvious notation and hopefully no LaTeX errors ...

> (see for instance 7.5 and 7.8 in Payne et al., RMP 64, p. 1045).
> If no real displacements of the atoms are needed to compute
> these derivatives, then I guess that they can be simply calculated
> as expectation values of the Hamiltonian on the current wavefunction

NO: they can be computed as expectation values of the derivative of the external potential wrt ionic coordinates

> because they can written down once a (parametrized) expression of the
> ionic potential is chosen. Am I right?

I am afraid you aren't, but I am not sure because I could not quite understand your last statement. There is nothing to choose in the parametric dependence of the external potential on the ionic coordinates. It depends the way it must [something like v(r-R), if the notation is clear enough ...], not the way we choose ...

> 
> Thanks for still devoting time to this...

you are most wlcome, as long as we can help ...

S.


---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget

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