Subject: The ab initio basis of DFT and semi-emp methods

From: <[email-masked]>
Date: Tue, 16 May 95 0:30:16 CDT

On the subject of DFT, semi-empirical methods, and ab initio theory:

	At first sight it may appear that DFT methods have a stronger
"ab initio" basis than semi-empirical methods, in fact I will argue that
the reverse is actually true because the ab initio basis of semi-empirical
methods are more highly developed and has been more extensively researched
than DFT.  In order to say that there exists an ab initio basis for 
either DFT and/or semi-empirical methods, I argue that there must exist
(1) a formal mathematical theory linking the exact molecular
electronic Schr\"odinger equation and the approximate method
(DFT or Semi-Emp)
(2) an ab initio method which can compute all of the mathematical
parameters (be them matirx elements, functionals, densities, etc)
in the approximate method
(3) tests of the assumptions of the approximate method using the
ab initio techniques described in (2)
(4) [the hardest and most challenging requirement] actual and meaningful
improvements must have been sugested and incoproated into the
approximate methods based on the ab initio tests.

For both Semi-Emp methods and DFT I do not believe that all 4 requirements
have been met, however, I beleive that the ab initio theory of
Semi-Emp methods has been more highly developed than the DFT.

It can be argued that the Hohenberg-Kohn (HK) theorem and
the Kohn-Sham equations provide (1) for DFT, however, I must point out 
that niether of these provide an exact presecription for computing
the density function for an arbitrary molecular system 
the state of DFT theory lies somewhere between requirements (1) and
(2).  I know of of only one paper which describes an ab initio
algorithm for computing the universal density functional using
ab initio techniques for a general molecular system (Karl F. Freed
and Mel Levy, JCP vol 77, page 396 1 July 1982).  Some recent
work by Parr describes ab initio techniques for (3), however;
Parr provides some diagnostic tools for testing the assumptions
of DFT with out actually computing the functionals themselves
(I saw this in a recent talk  Parr and I do not know how well
this is described in his book on DFT). Likewise, other work in the 
literature exists which describes how to express the exact functional
for some model systems (I can not recall all of the work.  I recall
that Bob Harris at U.C. Berkeley has some intersting work in the area.)
If there is other important work in the area plase bring the attention
of the CCL forum.  

In contrast, the theory of semi-empirical methods is more highly
developed as requirements (1)-(3) have been met with the
use of the effective valence shell effective Hamiltonian (Hv) ab initio
method (see, for instance, Charles H. Martin and Karl F. Freed, JPC,
Vol 99, page 2701, 1995, and Karl F. Freed, In Conceptual Trends
In Computational Chemistry; VCH:  New York, 1991; Vol II)
I do not beleive that condition (4) has been fully borne
out by the Hv theory, however, some suggestions have been discussed
by Walter Thiel (Tetrahedron vol 44, page 7393, 1988), and other
semi-empirical methods have been based on related ab initio
theories (Malieru's work, the PCLIO of Peter Fulde)

Neither DFT nor Semi-empirical methods desrve full ab initio status
at this time, however, because neither method may be systematically
corrected with higher levels of theory.  It is this feature
that distinguishes ab initio theory from other approximate
methods as it is always possible, although not always practical,
to systematically extend the methods as close as possible to
the exact solution of the Schr\"odinger equation (or to extend
the Schr\"odinger equation, for that matter) to any desired
accuracy obtainable with current experimental techniques.

I find it most unfortuneate that the ab initio basis of both
Semi-empirical methods and DFT has not been more rigorously
explored; there is tremendous room for advancement in these
areas of research, especially in the area of semi-empirical
methods.  Indeed, the ultimate goal of such research would be 
to obtain ab initio accuarcies with semi-empirical speeds,
a most formidable challenge.