Dear Stefano Are you sure, that, even for metal, the potential energy surfaces are smooth when we use fixed number of PW's? Because some time ago, I have problem of discontinuities with Ti and I try to impose fixed number of PW's, but the discontinnuities did not disappeared. I have thought that not good enough convergence in k-point was the reason, and that the potential energy surface is perfectly smooth only in the limit of an infinit number of k-point for metal. Is it wrong?
-- Virginie Quequet <virginie.quequet at polytechnique.fr> From: Stefano Baroni <[email protected]> Subject: Re: [Pw_forum] scan the lattice constant Date: Thu, 8 Sep 2005 21:44:33 +0200 To: pw_forum at pwscf.org Reply-To: pw_forum at pwscf.org --Apple-Mail-1--274898337 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Kostya: I beg to differ here. I do not want to open a thread "PW's vs. Gaussians" which would have the same chances to be settled as "coca vs. pepsi", but what you say, while perfectly (kind of) clear to me, may be misleading to the less experienced. PW potential energy surfaces (PES) are as smooth as they can be (i.e. *perfectly smooth*, or of class C(\infty), if you prefer) *with fixed boundary conditions* (i.e. for a fixed shape/size of the unit cell which determines the periodic boundary conditions). This smoothness has strictly nothing to do with any cancellation of errors. With a fixed number of PW's, PES's are perfectly smooth, but the (variational) accuracy would depend on the size/shape of the unit cell. Discontinuities come in when varying the boundary conditions because PW basis sets depend on boundary conditions (conceptually) for exactly the same reasons why localized basis sets depend on nuclear positions. With Gaussians you have "Pulay forces" (which require a special treatment going beyond Helmann Feynman), with PW's you have "Pulay stresses" (which require an equally special ad hoc treatment). It is indeed the ease with which accuracy can be assessed and improved with PW's which make the problem appear. As said, if one was ready to use a fixed basis set for different geometries (as one does with localized basis sets without really caring about the dependence of the accuracy on the geometry), the potential energy surface would be perfectly smooth, though less accurate. As simple as that. No misterious powerful cancellation principles here. Stefano
