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On Wed, 5 Feb 2003, Michael Patzschke wrote:
> there is no easy way to compare ADF calculations with calculations made
> with other programs. This is partly due to the fact, that the total
> energy
> of the assembly at hand is nowhere calculated.

Yes, this is something what comes as a complete surprise to many new
users of ADF, particularly those coming from the "standard" molecular
quantum chemistry world. To a large degree, this is simply a
misunderstanding:
ADF -does- calculate and print the total energy; it is just that ADF's
choice of the energy scale is different from programs like Gaussian.

Gaussian chooses to calculate the total energy with respect to bare
nuclei and electrons separated to infinity. This choice has the
obvious advantage of simplicity.

ADF chooses to calculate the total energy with respect to sperically
averaged, closed shell atoms. This looks strange, but there are good
reasons to do it this way.

For light nuclei (say first-row elements), the choice does not matter
much - total energies (in the bare-nuclei sense) are still reasonably
small, and their changes in chemical reactions are in the range of
0.1 to 1% - easily accessible by calculating finite differences of
total energies (of either sense).

Already for the second main-row elements, this is no longer true - the
bare-nuclei total energies are well over 100 hartree, but chemical
reactions are all below 0.2 hartree. To get potential energy surfaces
to chemical accuracy (say 0.6 kcal/mol - 0.001 hartree), one therefore
has to calculate bare-nuclei total energies to at least 5-6 digits.

It gets worse once one moves lower in the periodic table - total energy
of the cadmium atom, for examplem is around 11,000 hartree. To get
meaningful reaction energies for cadmium, using bare nuclei total
energies, one would have to calculate these energies to at least
eight significant digits. And, of course, cadmium is only in the
4d transition row - there is plenty of heavier elements around.

Evaluating total energies to eight or ten significant digits may be
possible in programs like Gaussian or CADPAC or Gamess (although I do
have my doubts in this respect), but this is out of the question
for a program like ADF - it would require numerical integration grids
and fit sets, which are simply too unwieldy. Instead, ADF chooses
to use a different energy reference, and gets a value of the same
accuracy by doing less numerical work.

Obviously, something like this happens in "standard" molecular codes,
too. None of the molecular DFT codes I am familiar with actually
evaluates exchange-correlation energies to much more than four
significant digits (at least with the standard grids). There is
really no point - the bulk of the total XC energy comes from the
inner atomic regions, which are not substantially changed by
chemical reactions. As long as similar grids are used for this
region in both reactants and products, any inaccuracies will
approximately cancel - so that the energy difference will still
be fairly accurate.

Of course, if you are -really- interested in bare-nuclei total
energies in ADF, you can always calculate them. Simply calculate
the "total bonding energy" of bare nucleus of each element in
your molecule with ADF, and adjust your energy scale. It won't
be very accurate (for the reasons I've outlined above), but it
for the first and second main row elements, you should be within
a few millihartrees/atom of the "standard" results - provided
that you use basis sets of comparable quality. (I find that TZ2P
in ADF is about comparable to cc-pVTZ in gaussian world in this
respect).

Best regards,

Serguei

---
Dr. Serguei Patchkovskii
Tel: +1-(613)-990-0945
Fax: +1-(613)-947-2838
E-mail: Serguei.Patchkovskii_at_nrc.ca
Coordinator of Modelling Software
Theory and Computation Group
Steacie Institute for Molecular Sciences
National Research Council Canada
Room 2011, 100 Sussex Drive
Ottawa, Ontario
K1A 0R6 Canada