[Pw_forum] scan the lattice constant

Konstantin Kudin konstantin_kudin at yahoo.com
Thu Sep 8 21:17:27 CEST 2005

> Basically, as you enalarge your unit cell, your brillouin zone
> shrinks,
> and at constant cutoff it means that more lattice vectors (i.e. plane
> waves) enter into the fixed cutoff sphere. More plane waves means a 
> systematically larger basis set (this is one of the good things
> of plane waves, it's easy to make the basis set more and more
> complete -
> a nightmare in Gaussian), and, variationally, a lower energy. You see
> in 
> fact your energy drop going to the left.

 I'd like to chime in here. While indeed reaching the basis set limit
is sort of difficult with Gaussian basis sets, there is this powerful
principle called "cancellation of errors". This allows one to chase not
the full convergence, but convergence with the basis set that is good
enough. As it turns out, such convergence is actually rather easy to

 Then one has to care that the energy is fully variational and smooth
(i.e. differentiable) with respect to changes in atomic coordinates and
lattice vectors. While indeed PWs do reach the basis set limits easier,
the smoothness of the potential energy surfaces on the other hand
leaves something to be desired. The smoothness issue is usually much
better taken care of with Gaussians. So there you go ... :-)


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