[CPMD-list] question about CUTOFF

[Axel Kohlmeyer]

On Mon, 25 Feb 2008, Mark Kosmowski wrote:


hello mark,

MK> AK> fix the calculation of the stress tensor for USPPs in CPMD, that is).
MK> 
MK> Is force convergence also affected by the nature of the system in
MK> addition to the atomic species involved?  For example, would ethane
MK> (H3C-CH3) and acetylene (HC-triple bond-CH) be expected to behave
MK> differently wrt force convergence at the same cutoff energy?

no. unless there is some additional symmetry involved, that is.

MK> 
MK> Regarding the small checks - are you saying, for instance, that for
MK> small cell Z=2 systems (that I'm presently working with) a lower
MK> cutoff energy with a greater number of k points may be a better use of
MK> computational resources than high cutoff and fewer k points?

ouch. convergence wrt. k-points and convergence wrt. to cutoff are 
essentially two independent processes. you cannot replace one with the 
other. you have to be converged well enough for both or else your 
results will be inaccurate (or even plain wrong). usually, the way to 
handle this is to first converge wrt. cutoff and then check for k-point 
convergence. in the latter case the energy/atom is a useful indicator.

MK> (Specifically, I am looking at geometry optimization followed by
MK> vibrational analysis.)
MK> 
MK> For a simpler version of a system, would it be reasonable (for common
MK> organic atoms) to do large cell simulated gas calculations (not using
MK> the ISOLATED MOLECULE keywords / symmetry - just a molecule in a big
MK> box) for the diatomic gasses (and perhaps methane and water for carbon
MK> and oxygen after looking at H2 - thus avoiding the problems of O2) to
MK> investigate cutoff vs. geometry accuracy?

first of all, for any of the systems you name, using an atomic basis
set code would actually be much more efficient than a plane wave based
code. plane waves have the most benefits in the condensed phase and
when you need an unbiased basis set (e.g. for free/solvated electrons).

the only effect of the ISOLATED MOLECULE keyword is to adjust the 
number of degrees of freedom. the effect of SYMMETRY 0 is to add
a calculation step where a poisson solver is used to decouple
the electrostatic interactions between periodic images. for non-polar
molecules (e.g. H2, Methane) the benefit of this step may be 
very limited and you actually may be spending more time on your
calculation without need, since due to the poisson solver the 
energy of your molecule wrt. its position in the simulation cell
will no longer be invariant, so you may have to spend additional
geometry optimization steps to have your molecule accurately
centered and rotated according to its charge distribution 
(and not the simple translation only, geometry based centering
as it is done with CENTER MOLECULE which is implicitly turned
on by using SYMMETRY 0).

[...]

MK> inclusion in the CPMD manual.  I do not know when I will have a chance
MK> to do this though, as I work full-time while studying toward a PhD
MK> part-time.
MK> 
MK> You mentioned that one cannot quantitatively project the improvement
MK> of a calculation by using "better" gaussian basis sets (i.e. 6-31G**
MK> instead of 6-31G) while one can with plane waves.  I've noted that
MK> some people who have extensive experience with atom-centered
MK> computational methods are rather unimpressed by an energy (single
MK> point, unoptimized geometry) vs. cutoff energy curve.  I think there
MK> is an attitude of, "Of course the energy decreases as you improve the
MK> basis set."  Thus the ability to quantitatively project accuracy
MK> improvement by choosing a point on a continuum (cutoff energy) is not
MK> well appreciated.

well, i sortof share that attitude. the cutoff you chose has to be
chose based on the accuracy you need. the fact that the variation
principle holds is not impressive and i disagree that you can
_quantitatively_ project the accuracy, since you do not know a priory
from the convergence of the energy how your property of interest
converges. furthermore, you are neglecting errors due to DFT itself,
k-space sampling (if applicable), working on a spline grid, finite
step sizes (when using finite differences), finite system size 
effects, and so on.

MK> This is further complicated since many people with atom-centered
MK> calculation experience are chemists coming from a single molecule
MK> background and need to learn about the intracacies of solid state /
MK> periodic calculation.  In my experience, the most vexing thing to come
MK> to grips with for solid-state calculation are k points.  And there are

you may have a point there. in fact, the whole concept of always
doing a periodic calculation with plane waves seems to be quite
difficult to adsorb for people who think "the gaussian way". ;-)
it still does not explain though, why people rather go with some
(random?) recommendation from somebody on a mailing list or 
parameters from a template file, than doing a few simple calculations 
to verify their choices. oh well...

cheers,
   axel.


MK> other significant differences between single molecule and periodic
MK> calculations that need to be learned.  Maybe the power of basis set
MK> analysis with plane waves is neglected in view of all of the other
MK> things that one must become familiar with for periodic calculation.
MK> 
MK> Thank you for the reply,
MK> 
MK> Mark
MK> 

-- 
=======================================================================
Axel Kohlmeyer   akohlmey at cmm.chem.upenn.edu   http://www.cmm.upenn.edu
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Department of Chemistry, 231 S.34th Street, Philadelphia, PA 19104-6323
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