Subject: CCL: Unoccupied orbitals, eigenvalues

From: Mikael Johansson <mpjohans~at~pcu.helsinki.fi>
Date: Mon, 20 Dec 2004 18:20:24 +0200 (EET)

Hello All!

Catalysed by the latest in the row of experimental observations of 
molecular orbitals (which nicely also measures the phase of the orbital) 
[1], I again started pondering on the reality of the _unoccupied_ MO's, 
this time especially between the qualitative difference (if any) between 
unoccupied orbitals with negative energies versus those with positive 
energies.

Positive orbital energies for occupied orbitals indicate the 
non-existence of the orbital, or at least the inability of the chosen 
computational method to give a proper description of it (a larger, more 
diffuse basis set will just throw the electron, "orbital", away from the 
molecule) [2].

Assuming for the moment that also unoccupied (virtual) orbitals have 
physical meaning, would then the ones with negative energies (if there 
are any for a give species) be "more real" than the ones with positive 
energies? I have not come across a disussion on this, or at least don't 
remember having done so.

[1] J. Itatani et al., "Tomographic imaging of molecular orbitals", Nature
     432 (2004) 867-871.
[2] I like the discussion in: N. Rösch, S.B. Trickey, J. Chem. Phys. 106
     (1997) 8940-8941.

Merry Christmas,
     Mikael J.
     http://www.helsinki.fi/~mpjohans/