Subject: Re: CCL:Orbitals

From: Avijit Ghosh <avijit/at/physics.drexel.edu>
Date: Fri, 30 May 2003 19:00:43 -0400 (EDT)

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