From chemistry-request-!at!-ccl.net Tue Jun 7 13:13:12 2005 Received: from relay.unizar.es (ortiz.unizar.es [155.210.11.72]) by server.ccl.net (8.13.1/8.13.1) with ESMTP id j57HD9HK020334 for ; Tue, 7 Jun 2005 13:13:10 -0400 Received: from [155.210.92.49] (neptuno.unizar.es [155.210.92.49]) (authenticated bits=0) by relay.unizar.es (8.13.4/8.12.3) with ESMTP id j57GbULB020974 for ; Tue, 7 Jun 2005 18:37:35 +0200 Message-ID: <42A5CD4E.4000006/at/unizar.es> Date: Tue, 07 Jun 2005 18:37:34 +0200 From: Pablo Echenique Robba Reply-To: pnique/at/unizar.es User-Agent: Mozilla Thunderbird 1.0 (X11/20041206) X-Accept-Language: en-us, en MIME-Version: 1.0 To: CCL list Subject: existence of HF-SCF solutions Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Mail-Scanned: Criba 2.0 + Clamd en Unizar X-Spam-Status: No, score=0.1 required=5.0 tests=FORGED_RCVD_HELO autolearn=failed version=3.0.3 X-Spam-Checker-Version: SpamAssassin 3.0.3 (2005-04-27) on server.ccl.net 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 ------------------------------------