Subject: existence of HF-SCF solutions

From: Pablo Echenique Robba <pnique/at/unizar.es>
Date: Tue, 07 Jun 2005 18:37:34 +0200

Hello everybody.

What I wanted to know is whether someone could indicate to me where may 
I find a discussion on the existence of solutions of the HF-SCF 
iterative procedure. I first enumerate briefly what I know:

1) The HF equations HAVE solutions (Lieb and Simon, 1977).
2) Any solution of the HF equations is an extremal, with no indication 
about its being a maximum, a saddle point or a minimum whatsoever.
3) The SCF method DOES NOT always converge. Of course, when it does 
converge, the wave function that results is indeed a solution of the HF 
equations. Again, with no indication about its being a maximum, a saddle 
point or a minimum.

My two questions are related to point 3:

a) When does the SCF converge?
b) How do we know, if it converged, that it did it to a minimum (and not 
to a maximum or to a saddle point)?

I would thank very much any hint to articles or books discussing this. I 
mean, further than the typical "we hope it converge because our basis 
sets and our starting point are so good".

 Pablo Echenique.

-- 

------------------------------------
  Pablo Echenique Robba

  Departamento de Fisica Teorica
                &
  Instituto de Biocomputacion y
  Fisica de los Sistemas Complejos
  BIFI

  Universidad de Zaragoza
  50009 Zaragoza
  Spain

  Tel.:    34 976761260
  E-mail:  pnique/at/unizar.es
------------------------------------