From chemistry-request@ccl.net Fri May 30 19:00:38 2003 Received: from einstein.physics.drexel.edu (einstein.physics.drexel.edu [129.25.7.60]) by server.ccl.net (8.12.8/8.12.8) with ESMTP id h4UN0bgC000537 for ; Fri, 30 May 2003 19:00:38 -0400 Received: from silicon.physics.drexel.edu (silicon.physics.drexel.edu [129.25.8.33]) by einstein.physics.drexel.edu (8.11.6/8.11.6) with ESMTP id h4UN4wF03981 for ; Fri, 30 May 2003 19:04:58 -0400 Date: Fri, 30 May 2003 19:00:43 -0400 (EDT) From: Avijit Ghosh To: chemistry/at/ccl.net Subject: Re: CCL:Orbitals In-Reply-To: <5CF08BBFE6DE97478C1E76E654CAF90801BC0BEC/at/lvlxch02.ntdomain.americas.sc-world.com> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Hi all, let me first qualify this as I am far removed from quantum dynamics/electronic structure/semiclassical physics and am just putting some thoughts in as someone who has been listening to the discussion w/ great interest. I think orbitals used as "basis set expansions" as in many electronic structure calculations might be considered a mathematical trick to solve a differential equation and there should be treated as mathematical constructs since they are being treated as such. However there are several issues here. (1) If I take the term orbital to mean the "wave function" of a single e-, is it "real"? I would say no as the wave function is a thing that exists in complex space and is not as such observable property. In this sense the "many e-" wavefunction is not observable either, so that statement I think has less to do w/ "orbitals" but more to do w/ wavefunctions as the thing that one "operates" on to get observables. (2) Does the single e- wavefunction density have any meaning? Let me decompose this a bit. To me the fact that organic chemists can "hybridize" orbitals (aka "handwaving quantum mechanics") is a testament to the contribution of e-e- correlation as actually not being that much at least for the first part of the periodic table. In fact that elements have the properties that they do is also a testament to this. Let me rephrase this w/ a model, suppose epsilon_0 for e-e- interactions only were some other value. That is we could scale down the correlation function, at arbitrarily small scaling (i.e large epsilon_0) the "orbital" approximation (as observable single e- densities) By construction the "orbital" approximation is closer to "reality" as I scale my hamiltonian. That is the wavefunction would become a product of single e- wavefunctions, even though technically I can not *ever* write the wavefunction as a product of single e- wavefunctions as long as I have even an arbitrarily small amount of e-e- correlation. I think that the assertion of orbitals "existing" is just an assertion of that e-e- is 0.5 % of the answer allowing the organic chemists to "write" the wavefunction as a product of single e- wavefunctions. It seems to me that if one is allowed to posit the total electronic wavefunction density has a "reality" on its own and corresponding measurements and eigenstates (i.e. decoupling the nuclear/electronic kinetic terms ala born oppenheimer) as having a reality, then one in the same manner should be allowed to posit orbitals as having a "reality" since it seems to me to be the same approximation just on a different part of the hamiltonian. -avi Asst. Prof. Avijit Ghosh Dept of Physics Drexel University