existence of HF-SCF solutions

 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.
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  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
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