[Pw_forum] scan the lattice constant-seems not a closed question
Nicola Marzari
marzari at MIT.EDU
Tue Sep 13 17:28:16 CEST 2005
> But I still have two questions: First, in the diamond
> case, the lowest energy at an ecutoff seems closer to
> the left side of the red curve(ecutoff=26Ryd)(which is
> on the small lattice parameter side) and this seems to
> be contradictory to the more plane wave basis fact at
> small lattice constants. (but there is no such a
> problem for the ecutoff=24Ryd case, why)
The exact E(V) curve will be a smooth curve closely resembling
the mathematical form of a Murnaghan or Birch equation of
state. If you have a low cutoff, there will be discontinuities
every time an infinitesimal increase in your lattice constant
introduces one more plane wave in your basis set, lowering by
a discrete amount the total energy.
In order to answer your questions, you might want to try an
E(V) curve for very many lattice parameters (e.g. 100), at a
low cutoff, and try to find out the discontinuities mentioned.
> What is the relationship between ecutrho
> and the total energy (if monotonic lowering of the
> energy with increasing ecutrho is not always the case)
None relevant to your case - mostly it is related to
describing properly the augmentation charges of the Vanderbilt
ultrasoft pseudopotentials. This can be very important to predict
correctly magnetic multiplets, or empty states (for what they are
worth). So it's an important parameter to check, but we can't
say if it will lower or raise the energy.
Last - different codes treat differently the augmentation charges.
PWSCF represents them on the fine real-space mesh for which ecutrho is
provided. CP represents them with a localized real-space box-grid
(technically called a "scatoletta"), of a resolution given by ecutrho,
but identical to zero outside this box-grid. While infinite ecutrho
will always work, I believe that the CP-way is a bit faster in reaching
convergence (and, on top, very very efficient due to the small size
of the box-grid - this is all due to Alfredo Pasquarello's work,
discussed in detail in the 1993 PRB).
Best,
nicola
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Prof Nicola Marzari Department of Materials Science and Engineering
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