SUMMARY:SOMO of the radical

From: "Adrian Radomir Jaszewski" <ADRIAN # - at - # WCHUWR.CHEM.UNI.WROC.PL>
Organization: University of Wroclaw (Chemistry)
Subject: SUMMARY:SOMO of the radical
Date: Tue, 18 Apr 2000 17:43:25 MET
Dear CCL'ers,
 Last week I asked this question on the CCL :
 >From N linearly independent basis functions of the radical
 >(S=1/2) one can construct N alpha and N beta orbitals:
 >N alfa = (n-1) CORE + 1 SOMO occupied + (N-n) VIRTUAL
 >N beta = (n-1) CORE + 1 SOMO unoccupied + (N-n) VIRTUAL
 >where n denotes the number of electrons.
 >
 >Unrestricted DFT wavefunctions of the radicals are usually
 >constructed using identical (or almost identical) spatial
 >orbitals for different spins (alpha, beta) in the case of
 >CORE and VIRTUAL MO. Lowest energy (occupied) alpha-spin
 >SOMO and highest energy (unoccupied) beta-spin SOMO can be
 >also very similar to each other but sometimes they are
 >strongly asymmetrical. A knowledge of the SOMO contour can
 >be helpful in the analysis of the spin density distribution
 >as well as the values of the calculated hyperfine coupling
 >constants for the radicals.
 >
 >My question is:
 >When SOMO occupied (alpha) and SOMO unoccupied (beta) are
 >dissimilar which of them (or what combination of these SOMOs)
 >can be used to aid spin density analysis? In some cases I
 >have observed that the spin density contours were similar
 >to the highest energy beta-spin SOMO (unoccupied!!) contour
 >rather than to the occupied alpha-spin SOMO; and what is
 >the energy (in Hartree) of that SOMO when:
 >E(lowest energy VMO)= -0.06916(alpha) -0.06008(beta)
 >E(highest energy SOMO)= -0.12635(beta)
 >E(lowest energy SOMO)= -0.26301(alpha)
 >E(highest energy DOMO)= -0.24908(alpha) -0.24319(beta)?
 >
 I summarize below the replies I obtained very quickly to my
 question. They have been very helpful. I thank very much all
 those who supplied information.
 With my best regards,
 Adrian
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 This is pretty normal behavior and has a fairly simple explanation.
 Imagine a molecule with 3 electrons (2 alpha and 1 beta) and imagine
 orbital energy increases #1 < #2 < #3 ... This makes the occupied
 orbitals MO #1 alpha, MO #2 alpha and MO #1 beta, and the unoccupied
 orbitals MO #2 beta, MO #3 (alpha or beta) and so on. The orbitals
 that you are called "SOMO occupied (alpha)" and "SOMO unoccupied
 (beta)" are MO #2 alpha and MO #2 beta in my nomenclature.
 Now consider two cases:
 Case #1: MO #1 alpha looks like MO #1 beta. In this case, the spin
 density distribution looks like MO #2 alpha (this will be true even
 if MO #2 alpha and MO #2 beta do not look like each other).
 Case #2: MO #1 alpha looks like MO #2 beta, and MO #2 alpha looks like
 MO #1 beta. In this case, the spin density distribution looks like
 MO #1 alpha, and because of the similarity between MO #1 alpha and
 MO #2 beta, it also looks like MO #2 beta.
 Bigger molecules can behave the same way. The point here is that
 UNrestricted wavefunctions allow different energy orderings for the
 alpha and beta orbitals (even when each alpha orbital looks like a
 beta orbital). This can lead to situations where the spin density
 distribution resembles an alpha orbital (or a group of orbitals)
 other than the alpha HOMO (what you call the alpha SOMO).
 Hope this helps. Good luck,
 -Alan
 --------------
 Alan Shusterman
 Department of Chemistry
 Reed College
 Portland, OR
 www.reed.edu/~alan
 Alan.Shusterman # - at - # directory.reed.edu
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 It may happen that the nth alpha orbital resembles the n-1th beta
 orbital and that the nth beta orbital resembles the n-1th alpha orbital.
 That could be the explanation for the similarity you noticed between the
 lowest beta unoccupied orbital and the total spin density.
 If you are using Gaussian, you might try calculating the unrestricted
 wavefunction as usual, and then read in that wavefunction as the guess
 for a restricted open-shell calculation, that is, use  Guess(Read,Only).
 You can do the population analysis, but you won't find orbital energies.
 If you really want those orbital energies, a restricted open-shell
 calculation can be done.
 Curt Hoganson
 University of Delaware
 hoganson # - at - # dplus.net
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 Your orbital energies indicate that there might be a heavy mixing of the
 alpha-spin "DOMO" and "SOMO".
 Is there any reason not to perform a spin-restricted DFT calculation? This makes
 your analysis much easier since the spin-density comes from the SOMO alone.
 --
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 ---------------------------+------------------------------------------------
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 I'm happy to share my feelings about this subject with you. In my opinion
 the only way to properly calculate hyperfine couplings and spin densities
 is to evaluate the spin up and spin down densities, subtract them from each
 other and calculate the hyperfine coupling as the expectation value of the
 appropriate operator using this spin density. Using the unoccupied beta-MO
 is rather unphysical and maybe quite basis set dependent. Using the alpha
 MO is also unphysical because any (unitary) mixing of  alpha MOs produces
 the same total wavefunction. Thus, if another MO is close in energy to the
 spin up "SOMO" it will mix with it and thereby obscure the picture.
 However, the physics contained in the total electron and spin density
 matrices are not affected by this mixing. Having said all this, many people
 have observed in open shell transition metal complexes that the unoccupied
 spin down orbitals give a clearer picture of the bonding. This is because
 the corresponding spin-up orbitals maybe deeply buried under or within
 ligand based orbitals due to strong exchange stabilization. Noodleman
 refers to this as 'inverted bonding'. In a pictorial sense it might be o.k.
 to look at the unoccupied MOs but for calculation of observables I would
 personally certainly not rely on anything else but the densities themselves.
 Best regards,
 Frank
 Frank.Neese # - at - # uni-konstanz.de
 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 You appear to assume alpha means lower energy. I think most progems just
 arbritarilly assign alpha and beta spins. Hence in your case what the
 program calls the lowest unoccupied beta is actually the SOMO i.e where
 the unpaired electron (density) is.
 Patrick J O'Malley
 patrick.o'malley # - at - # umist.ac.uk
 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++