"Sub-states" of Singlet Delta Dioxygen; Changes in the Occupancies and Symmetries of the Orbitals of Singlet States of Dioxygen During Reactions

This article [Kearns, 1969: (http://pubs.acs.org/doi/abs/10.1021/ja01052a003)] helps me understand the difference between the two "sub-states" of singlet delta dioxygen [as discussed here: (http://hardcorephysiologyfun.blogspot.com/2010/05/three-major-electronic-states-of.html)]. This article (along with other articles by Yamaguchi and colleagues) [Yamaguchi et al., 2009: (http://linkinghub.elsevier.com/retrieve/pii/S0277538709000515)] shows the singlet delta state as comprising two "sub-states," also, except Yamaguchi et al. (2009) discuss the 2pi* diradical states of dioxygen (and Fe(IV)=O hemes) in terms of broken symmetry molecular orbitals. I guess that those are eigenfunctions, in which the 2pi* molecular orbitals are either not equivalent at all times or cease to be equivalent, in terms of their spin-density distributions (orbital "shapes"), as the charge-transfer complexes or transition states begin to form, during reactions of dioxygen with other molecules. Another point that Yamaguchi et al. (2009) make is that, as the O2 3sigma(g) molecular orbital (the "single, sigma" bond, formed by constructive overlap of two 2pz atomic orbitals) [Ochiai, 1996: (http://pubs.acs.org/doi/abs/10.1021/ed073p130)] begins to break, that 3sigma(g) molecular orbital begins to exhibit diradical character, albeit to a lesser extent than the true diradical state that the triplet ground state of dioxygen exhibits. Yamaguchi et al. (2009) (p. 2047, Fig. 5A) depicted the 3sigma(u) type (neither of the orbitals, shown as the bracketed pair at the bottom right of Fig. 5A, is symmetric with respect to the center of mass of dioxygen) of "broken-symmetry eigenfunction" molecular orbitals, formed by the configuration of the 3sigma(g) molecular orbitals (configuration interaction means like rehybridization of existing molecular orbitals to produce a new pair of molecular orbitals, with more complex patterns of "mixing" of the original molecular orbitals). I've shown 2pi*(u) "broken-symmetry orbitals" and not the 3sigma(u) type of orbitals shown in Fig. 5A [Yamaguchi et al. (2009) also depicted the pair of 4sigma(u) broken-symmetry molecular orbitals, which are unoccupied (LUMOs), at the top right of Fig. 5A, in brackets], but the concept is similar (for the types of broken-symmetry orbitals I've drawn, see Yamaguchi et al., 1983, p. 104, Fig. 1B: (http://linkinghub.elsevier.com/retrieve/pii/016612808385012X)].


This shows the way in which the lower-energy sub-state (just singlet delta) of singlet delta dioxygen can be distinguished from the higher-energy, singlet delta* sub-state of dioxygen (see Kearns, 1969, p. 6556, column 1).



In contrast to the "situations" shown above, the 2pi* orbitals in the higher-energy, singlet delta* sub-state of dioxygen, shown below, remain singly-occupied by electrons of opposite "spins" (see Kearns, 1969, p. 6556, column 1), and the net spin multiplicity for the overall dioxygen molecule, in each of the two singlet delta sub-states and in the singlet sigma state, is 1 (a singlet state, in terms of the spin multiplicity). This is because the net "spin" is zero [S = 0, and the spin multiplicity is abs.val.(2S) + 1, or 1] if the two electrons of opposite spin are in a single orbital (as in the "molecule-interacting" situations for singlet delta, shown above, or for the singlet sigma state, shown in the last diagram of this posting) or in two singly-occupied orbitals that exhibit singlet coupling (as in the "non-interacting" situation of singlet delta and singlet delta* and in the "molecule-interacting" situation for singlet delta*, as shown below):




This diagram shows the changes that occur in the relative energies of the two sub-states of singlet delta dioxygen (they're degenerate before dioxygen approaches the alkene), upon the approach of dioxygen, in either of the two sub-states, to an alkene. The diagram also shows the change that occurs, in response to the approach of dioxygen to the alkene, in the relative energies of the 2pi* orbitals, such that the 2pi* orbitals cease to be degenerate (at the same energy level):


This diagram shows the orbital occupancies for the singlet sigma state, in which the higher-energy 2pi* molecular orbital is doubly-occupied (this state, overall, is also higher in energy than the two singlet delta sub-states are and is the highest of the commonly-encountered electronic states of dioxygen):