[CPMD-list] highest levels of theory

[Robert Williams]

Dear Axel, Juerg, cpmd-list,

I am looking at table 1 in
X. Xu and W.A. Goddard III, PNAS 101, 2673-2677 (2004)
showing how various methods and functionals perform
compared to experiment, particularly wrt dispersion
forces.   This paper shows that reasonable results for
dispersion interactions can be obtained even
without HF exchange, in particular for the GGA PBEPBE
(M. Ernzerhof & G.E. Scuseria, J. Chem. Phys,
110, 5029-5036 (1999), and - more so - for the GGA XLYP:

1.0 Ex(Slater) + 0.722\Delta Ex(Bech88) + 0.347\Delta Ex(PW91) + 1.0 Ec(LYP)

where \Delta E for He2 and Ne2 are very close indeed to experiment.

So, perhaps my question should be:

How might I implement one of these, PBEPBE or XLYP,
in CPMD?

It is not at all clear to me how I should relate
various values of the CUTOFF in cpmd to the levels of theory
I am more accustomed to thinking about.  The
advice given in the list archive is to perform
a series of calculations to determine a cutoff that
gives acceptable results.  In writing a grant application,
proposing to perform a series of calculations,
it is useful to be able to say with some confidence
that the work will be performed at a level
equivalent to or better than ... double numeric
with polarization - for example.
My calculations on N-methylacetamide
in one unit cell were initially performed with a CUTOFF
of 120 Ry, and I've move to 150 Ry,
but it seems to me that I should be
able to report the results in a context that
doesn't depend on how much personal experience
the reader has with CPMD.

Is the appropriate CUTOFF related to the
size of the molecule or cell?

Has anyone worked out a general relationship between
the CUTOFF and the approximate accuracy of the results
in terms that might be related to previous ab initio codes?


Best wishes,
Bob


On Fri, 26 Nov 2004, Robert Williams wrote:
RW> What might be regarded as the highest
RW> levels of theory available in cpmd,
RW> double numerical with polarization or better,
RW> particularly that include functionals
RW> appropriate for estimating dispersion forces -
RW> such as pbe?

Axel Kohlmeyer wrote:
AK> hmm, i am not sure, if i have fully understood
AK> what you mean by 'level of theory'. but if you
AK> see this in a similar way of programs like gaussian,
AK> then you have to realize, that the basis set in cpmd
AK> are plane waves which are in so far different from
AK> local basis sets, that they have the same 'quality'
AK> everywhere and that your basis set size solely
AK> determined by the plane wave energy cutoff
AK> (CUTOFF keyword).

I was using the phrase 'level of theory' loosely, in
a way that is sometimes used in the literature
to refer to both basis set and method.

Juerg Hutter (JH) wrote:
JH> The level of theory in CPMD is always Kohn-Sham DFT.
JH> Within this you can have different XC functionals.
JH> Once you have specified the functional you have
JH> the option to specify the basis (through the cutoff)
JH> and choose the pseudopotentials.
JH> The theory is defined by the functional and with
JH> cutoff and pseudopotential you can "adjust" the
JH> accuracy within the given theory.

AK> as far as the 'method' is concerned, there are
AK> different LDA and GGA functionals available
AK> (see FUNCTIONALS keyword or the sourcecode).
AK> all of them share the general problem of DFT,
AK> that their representation of dispersion interactions
AK> is not very good. there is a feature implemented,
AK> which can correct for it, by adding an empirical VDW
AK> term and, if i understood correctly, the inclusion
AK> of hartree-fock exchange should be an alternative,
AK> though computational very expensive solution.

JH> dispersion forces and DFT is a difficult combination.
JH> The best you can hope for is a decent description on
JH> intermediate distances where there is still charge
JH> overlap. Which functionals give good results, depends
JH> on the system and probably also on your expectation
JH> on the accuracy.

-- 
Dr. Robert Williams
Dept. of Biomedical Informatics
Uniformed Services University
301-295-3568