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 pens?e - Jean Piaget -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20111207/97b4623c/attachment.htm