<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Dec 7, 2011, at 4:23 PM, Cristian Degli Esposti Boschi wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div>Dear Stefano and Axel, thanks for your replies. Actually question can be <br>rephrased as follows. Thanks to the Hellmann-Feynman theorem<br>in order to compute the ionic forces I need only the partial<br>derivatives of the total energy with respect to the ionic coordinates<br></div></blockquote><div><br></div>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 ...</div><div><br><blockquote type="cite"><div>(see for instance 7.5 and 7.8 in Payne et al., RMP 64, p. 1045).<br>If no real displacements of the atoms are needed to compute<br>these derivatives, then I guess that they can be simply calculated<br>as expectation values of the Hamiltonian on the current wavefunction<br></div></blockquote><div><br></div>NO: they can be computed as expectation values of the derivative of the external potential wrt ionic coordinates</div><div><br><blockquote type="cite"><div>because they can written down once a (parametrized) expression of the<br>ionic potential is chosen. Am I right?<br></div></blockquote><div><br></div>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 ...</div><div><br><blockquote type="cite"><div><br>Thanks for still devoting time to this...<br></div></blockquote><div><br></div>you are most wlcome, as long as we can help ...</div><div><br></div><div>S.</div><div><br></div><br><div>
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