Subject: DFT questions

From: Wolfram Koch <[email-masked]>
Date: Fri, 21 Aug 1998 16:25:07 +0200 (DFT)

Dear netters,

I have three questions regarding some basic aspects of the Hohenberg-Kohn-Sham
fomulation of density functional theory.

1) The first Hohenberg-Kohn theorem states that the GROUND STATE energy
and all related properties are uniquely determined by the ground state
density n(r). This is, because n(r) determines the external potential,
which in turn (together with the number of electrons, which is given by
the integral of n(r)dr) fixes the Hamiltonian. Now my question: If n(r)
uniquely determines the Hamiltonian, we have in principle access to the
complete spectrum of this operator and hence to information about ALL
STATES of the system. So, where in this process does the limitation to
the GROUND STATE come in? 
Thus, naive as I am, I would think that n(r) through H determines not only the
ground state but also all excited states of our system. 
That the second HK theorem, i.e., the variational principle is limited to 
the ground state is of course trivial to understand.

2) The exact wave function for the non-interacting reference system in
the Kohn-Sham version of DFT is in many cases a single Slater determinant. 
Could you pls. help me to find out  and understand the criteria under which 
a single determinant is NOT the exact solution? What is it then - a limited 
linear combination of determinants which has the proper spin and spatial 
symmetry (i.e., a "configuration state function")?

3) One frequently reads that UNRESTRICTED Kohn-Sham theory is to be preferred
over the restricted version in open shell situations. What are the exact
reasons for this statement? I look for a physically sound explanation, not
a pragmatic one! I remember an explanation given by Nick Handy, that using 
restricted strategies the exp. known  beta spin density in Ms=1/2 states  
cannot be achieved. But, the same argument applies to UHF (vs. RHF) and
we all know about the problems connected with the UHF approach. So, is there
a fundamental difference between UKS vs. RKS and UHF vs RHF? And, what is it? 

I appreciate your help and will summarize the replies.

With my thanks in advance,

Wolfram

Please reply to [email-masked]
-- 
_________________________________________________________________________

 Prof. Dr. Wolfram Koch     Institut fuer Organische Chemie, Sekr.C3
                            Technische Universitaet Berlin
                            Strasse des 17.Juni 135, D-10623 Berlin
                            Fon: +49 30 314 27870, Fax: +49 30 314 21102
                            e-mail: [email-masked]
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