# existence of HF-SCF solutions

*From*: Pablo Echenique Robba <pnique/at/unizar.es>
*Subject*: existence of HF-SCF solutions
*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
------------------------------------