Subject: Re: CCL:Are methods based on DFT ab initio?

From: [email-masked] (Ross M. Dickson)
Date: Mon, 15 May 1995 17:15:47 -0600

I don't normally get into nomenclature arguments, but I'll bite this
time.  I'm not familiar with Prof. Cioslowski's arguments in favour of
calling DFT "semi-empirical", so I can't answer them directly, but I
take the position that DFT is better characterized as a branch of the
ab initio family.

I most often hear this question raised in connection with one
functional or another which contains some parameter (usually one,
sometimes as many as three) determined by fitting to experiment.  A
classic example is the local exchange functional variously known as
X-alpha, Hartree-Fock-Slater (HFS), or Slater exchange.  There were
non-empirical physical arguments for a value of either 2/3 or 1 (one)
for alpha.  Eventually many workers settled on a compromise value of
0.7 for empirical reasons.

Does this make HFS a semi-empirical theory?  I think not:  There is
one and only one adjustable parameter, and the functional should be
equally applicable in any part of any molecule.  If you insisted on
calling such a scheme semi-empirical, then you'd have to call Hartree-
Fock frequencies adjusted by the famous 10% factor semi-empirical as
well.  (If you already do, that's fine with me.  You're a purer man
than I am, Gunga Din.)  In a semi-empirical method, parameters are
chosen for *each atom*, and if you don't have parameters for cesium,
you simply cannot do semi-empirical calculations on cesium chloride.
But once you have this one DFT parameter -- or even two or three -- 
you can do calculations anywhere on the periodic table (modulo
relativity).

Now there have been calculations carried out in which this HFS alpha
parameter *was* different for each atomic environment (the so-called
muffin-tin method), and those I *would* call semi-empirical.  But 
that does not represent the main body of present-day density functional
theory.

There are certainly more recent examples of density functionals
containing one or more fitted parameters; my former boss Axel Becke
frequently ends up with one unknown left over when he's inventing a new
functional.  Nevertheless, in every case I know of the result after the
fitting has been a density functional intended to be universally
applicable.  What we are pursuing, after all, is Hohenberg's and Kohn's
universal functional of the density -- you only need, in principle, one
functional and you can then calculate all nondegenerate ground states.
If we try to derive this functional from physics, we are working "from
first principles" -- or "ab initio".

The other sense in which I can imagine DFT being characterized as
"semi-empirical" is the manner in which the recent proliferation of
functionals has been greeted by the user community.  I've seen more
papers and talks and posters than I can count that had the nature of
"try six different density functionals and see which one gives the best
results for my systems."  If some thought then goes into the
relationship between the underlying physics of the functionals and
their performance, this is quite reasonable.  But if the lowest average
deviation from experiment -- sometimes by a vanishingly small margin --
is then taken as the only reason for choosing functional X over
functional Y for further studies on analogs of these systems, then we
are at some risk of passing straight through semi-empirical methods
into pure empiricism, and neither DFT nor semi-empirical specialists
might care to claim such work as characteristic of their field.
(Although I should confess I'm prone to this disease myself. Mea culpa.)

In conclusion, I don't really care what DFT is called except inasmuch
as naming affects understanding.  I myself try not to use language
which classes DFT as either ab initio or semi-empirical, because those
terms have accreted fairly specialized meanings over the last twenty
years and DFT really doesn't fit comfortably into either.

Cheers,
Ross M. Dickson, Ph.D. ([email-masked])
Chemistry Dept., The University of Calgary, Alberta, Canada.