From chemistry-request@ccl.net Wed May 28 11:07:55 2003 Received: from smtp2.ruc.dk (smtp2.ruc.dk [130.225.220.70]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id h4SF7sgC007006 for ; Wed, 28 May 2003 11:07:55 -0400 Received: by smtp2.ruc.dk (Postfix, from userid 504) id 2898EC854A1; Wed, 28 May 2003 17:07:54 +0200 (CEST) Received: from virgil.ruc.dk (virgil.ruc.dk [130.225.220.110]) by smtp2.ruc.dk (Postfix) with ESMTP id 352AAC85498 for ; Wed, 28 May 2003 17:07:52 +0200 (CEST) Received: from VIRGIL/SpoolDir by virgil.ruc.dk (Mercury 1.47); 28 May 03 17:07:52 +0100 Received: from SpoolDir by VIRGIL (Mercury 1.47); 28 May 03 17:07:49 +0100 From: "Jens Spanget-Larsen" Organization: Roskilde Universitetscenter To: chemistry$at$ccl.net Date: Wed, 28 May 2003 17:07:23 +0100 Subject: Re: CCL:Orbitals Reply-To: spanget$at$ruc.dk Message-ID: <3ED4DEBC.98.1BBEF37@localhost> X-Confirm-Reading-To: spanget$at$ruc.dk X-pmrqc: 1 Priority: normal In-reply-to: <3ED4C513.BD36ECFA$at$trentu.ca> X-mailer: Pegasus Mail for Windows (v4.01) X-Spam-Status: No, hits=-6.5 required=5.0 tests=IN_REP_TO,QUOTED_EMAIL_TEXT version=2.53 X-Spam-Level: X-Spam-Checker-Version: SpamAssassin 2.53 (1.174.2.15-2003-03-30-exp) E. Lewars: > Are MOs physically real? This is a meaningful question only if there > is some experiment or observation that could provide an answer _yes_ > or _no_. Is there, at least in principle, such an experiment or > observation? I don't agree. For a many-electron system, one-electron wavefunctions are BY DEFINITION physically unreal. They can only be defined by neglecting certain very physical aspects, corresponding to a model where electron correlation effects are neglected. According to basic Physics, real electrons instantaneously correlate their individual movements, but electrons in orbitals don't. Electrons in orbitals are 'quasi-particles', not 'real particles'. > As J S-L points out, MOs are one-electron functions; does this mean > that for hydrogenlike atoms they _do_ correspond to physical reality? For an isolated hydrogen atom, the orbital wavefunctions, using the reduced mass and relativistic quantum mechanics, probably corresponds closely to what one might choose to consider as 'reality'. But in the end, the question becomes entirely philosophical; for example, no-one has ever observed an isolated atom. > If MOs have no physical reality for multielectron species, why (a) is > Koopmans' theorem useful, why (b) do photoelectron spectra match the > predictions of MO energy-level diagrams, and why (c) does the Hueckel > 4n+2 rule, which is based on MO diagrams, work? Of course, it is > probably possible to formulate an MO-free electronic molecular theory > that leads to the same predictions a-c, but I suspect that in some > sense (but what sense?) MOs exist--occupied MOs; the meaning of a > virtual MO is harder to see. The MO concept is very useful, forming the basis for excellent models of chemical and spectroscopic behaviour. For example, if you adopt Koopmans' approximation (neglect of electronic correlation and reorganization effects on ionization), Koopmans' well-known theorem applies. This is frequently a very good model, largely because the different errors introduces by the adoption of Koopmans' approximation tend to cancel each other out. But sometimes Koopmans' approximation is a bad approximation, and Koopmans' theorem does not apply. Or in the other words: The MO picture of ionization is sometimes a good model, and sometimes it is not. In any case: MOs don't exist in the physical sense. But of course, you may say that they 'exist' in our minds! Jens >--< =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= JENS SPANGET-LARSEN Office: +45 4674 2710 Department of Chemistry Fax: +45 4674 3011 Roskilde University (RUC) Mobile: +45 2320 6246 P.O.Box 260 E-Mail: spanget$at$ruc.dk DK-4000 Roskilde, Denmark http://virgil.ruc.dk/~spanget =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=