Hi,
Thanks for your question about user-defined functionals. I would like to
take the opportunity and comment on why the choice of density functionals
in TURBOMOLE is limited, and why certain functionals are not supported.
Fitting of density functionals to limited sets of empirical data is
much more involved than, e.g., basis set optimization or density
fitting used in RI-type methods. To the best of my knowledge, there is
no guarantee that such fits of a density functional converges to anything
reasonable. Some highly fitted functionals yield accurate atomization
energies, but produce spurious potential energy surfaces [A. D. Boese,
private communication]. Even for functionals with fewer fitted
parameters such as B97-1, substantial errors (up to 20 pm in bond
lengths) may occur, even within the training sets [R. Ahlrichs,
F. Furche, S. Grimme, Chem. Phys. Lett. 325 (2000), 317].
Density functionals work not because they are empirically fitted, but because
they are based on certain simple models containing important aspects of
exchange and correlation in molecules. These models satisfy a number of
constraints, such as sum rules, scaling relations, bounds, or limiting
behaviors. It is important to understand that functionals
of a given form, e.g., GGAs or meta-GGAs, have an intrinsic accuracy limit
which will show up in a certain scatter of the results for a wide range of
properties and systems. While empirical fits can change the mean value of
the error distribution, they generally do not reduce the scatter [see, e.g,
the discussion at the end of F. Furche, J. P. Perdew, J. Chem. Phys. 124
(2006), 044103]. In other words, such fits do not improve upon the
predictive value, but merely shift errors around.
There has been a great proliferation of empirical density functionals
in recent years. The trend goes to highly specialized functionals fitted for
specific properties and applications, e.g., weakly bonded closed-shell
systems, transition states, hydrogen bonds etc. These functionals do not
contain new physics, but minimize the errors of existing models on
different subsets. While I do not dispute that such functionals might
be useful, I believe that their value is overrated. Many
empirical functionals have had very short lives, and were outdated
before they were released in quantum chemistry programs.
Some users of quantum chemistry codes (not TURBOMOLE users, though) do
not care much about the origin of a result as long as it agrees with
experiment. If the result does not agree, the functional is
modified. I do not see the point of such "calculations". While
some referees still consider results obtained using "designer
functionals" as independent evidence for experimental results, the
number of critics will continue to increase.
Axel Becke realized the limitations of empirical functionals around the
year 2000. Two years before, he had demonstrated that highly fitted
functionals can reach an accuracy of less than 2 kcal/mol mean absolute
error on the extended G2 set [H. L. Schmider, A. D. Becke, J. Chem. Phys.
108 (1998), 9624]. He did not pursue this direction and has been critical
of highly fitted functionals since then: "Ultimately, this is not
satisfactory".
John P. Perdew, arguably an expert in functional development, discourages
the use of empirical functionals: "Strange fits of passion have I known"
[J. P. Perdew, A. Ruzsinszky, J. M. Tao, V. N. Staroverov, G. E. Scuseria,
G. I. Csonka, J. Chem. Phys. 123 (2005), 062201]. He emphasizes that
functionals can, and thus should, be constructed non-empirically, e.g.,
following his "Jacob's Ladder" hierarchy.
As a TURBOMOLE developer I am committed to provide the scientific community
with efficient and stable tools for electronic structure calculations. These
tools should work for a wide range of properties and systems that are important
to chemists. It is a good tradition of TURBOMOLE to offer a limited
choice of carefully selected and maintained options to the user.
The mission of TURBOMOLE is, in the first place, a scientific one,
and it is against our standards to implement, support, and maintain
methods or density functionals whose scientific value is
doubtful.
Best regards,
Filipp Furche
CEO and partner, TURBOMOLE GmbH
