These types of issues with the molecular orbitals of heme species are not all that relevant to much that's of practical value, but it really helps me to be able to think of the ways the reactions of heme with oxidants and reductants fit into the theoretical framework of bonding...theory. Then there's the fact that inorganic chemistry is interesting, and I'm a first-class nerd in having had an inorganic chemistry book for ten+ years and puttered around with it (without learning much of it in detail). I can explore the chemistry for longer periods of time than I can write for, on a given day, maybe because the chemistry is visual or something and not as much verbal, etc.
This article is interesting [Harcourt et al., 1986: (http://pubs.acs.org/doi/abs/10.1021/ja00278a005)], and Harcourt et al. (1986) argued that the lone pairs of oxygen in carboxylate-coordinated copper(II) complexes can overlap with copper's d(x^2-y^2) orbitals and interact in sigma orbitals. Even though the lone pairs wouldn't really be oriented toward the iron in ferryl or perferryl heme, as they are in the compound discussed by Harcourt et al. (1986), some researchers have found evidence for the formation of sigma bonding interactions between iron's dz2 orbital and oxygen's pz orbital in ferryl heme [Lehnert et al., 2001: (http://www.ncbi.nlm.nih.gov/pubmed/11516278); Decker et al., 2004: (http://pubs.acs.org/doi/abs/10.1021/ja0498033)] and have argued that the biradical (or "diradical") model cannot entirely explain the bonding in the Fe=O moiety of ferryl heme (or, at least, perhaps, in some high-spin, excited states of ferryl or perferryl heme). One way of looking at the sigma molecular orbitals in Fe=O, as modeled by Lehnert et al. (2001), might be to say that the dz^2-p(sigma) antibonding orbital (beta<33>, discussed on the top of column 2 of p. 8287 of Lehnert et al., 2001) would be like a cross between a lone pair and a conventional sigma bond. In the diagram on p. 8289 (Lehnert et al., 2001), the authors show that oxygen has four electrons in the pi bonds (the px-d(xz) and py-d(yz) pi antibonding orbitals I diagrammed in the previous posting), and that's not the same ferryl heme spin state discussed in much of the text (because the d(x^2-y^2) orbital is shown as being unoccupied in the diagram on p. 8289 but is described, in much of the text, as being occupied in the spin-2 state of ferryl heme). But the point is that two of the four "lone-pair" electrons of oxygen could be in a kind of intermediate state between a sigma bond and unshared pairs in different spin states. In the spin 1 state, oxygen donates both electrons to a dz^2-p(sigma) sigma antibonding molecular orbital (the p-contribution comes from the pz atomic orbital of oxygen) that has "53% metal and 21% oxo character corresponding to a strong [sigma] bond" (Lehnert et al., 2001, p. 8287), but that sigma orbital would be oriented away from the iron, largely, and would behave like a lone pair, from a bookkeeping and bonding-theory standpoint. Also in the spin 1 state, shown in the diagram on page 8289, iron would have two nonbonding electrons in the dxy orbital, as discussed by other authors, and oxygen would donate an extra two of its six electrons to the pi molecular orbitals (the px-d(xz) and py-d(yz) orbitals). Those could also be essentially "both" lone-pair electrons and pi bonding electrons, given the complexity of the electron distribution in those orbitals.
Similarly, in the spin 2 state, according to Lehnert et al. (2001), one of those electrons from the d(xy) orbital of iron would be excited into occupying the d(x^2-y^2) orbital, as discussed on p. 8289, and would interact with both the heme nitrogens and the oxygens (both of which would function as donor ligands and create a sigma bonding molecular orbital that's very delocalized and has what amounts to 1/2 of an electron contribution from oxygen and half from the nitrogens) in the d(x^2-y^2)-N(p) orbital, discussed on p. 8287 and shown in figure 8, that's also referred to as beta<32>. There would still be one electron from oxygen in the dz^2-p(sigma) molecular orbital and zero from iron in that orbital (one of iron's four electrons remains in the d(xy) orbital). Part of the reason it's confusing is that different authors use different notation to refer to essentially the same molecular orbitals. In the spin 2 state, one electron or one-half of an electron from oxygen could be in another highly-delocalized, so-called N(p)/p(sigma)-d(sigma) orbital (beta<21>), discussed in column two of p. 8287. Also, Lehnert et al. (2001) use notation in which the p(sigma)-dz^2 orbital (a.k.a. beta<25>) is a sigma bonding molecular orbital and is not the same as the dz^2-p(sigma) orbital, which is beta<33> and is an antibonding molecular orbital. That's basically what Lehnert et al. (2001) are saying.
Yeah, I think the upshot of that article is that four of oxygen's electrons in Fe=O could be like lone pairs that are also donated to the iron (to form sigma bonding and antibonding molecular orbitals that iron doesn't make a contribution to). The other main point made by the authors is that the bonding in Fe=O can be very similar in both the spin 1 and spin 2 states but that one of iron's "sigma" electrons is excited from the d(xy) to the d(x^2-y^2) orbital in the spin 2 state. One of or, from a bookkeeping standpoint, one-half of an oxygen electron is donated to that orbital in the spin 2 state, but, in each of the two spin states, four of oxygen's electrons could behave and be thought of as being "lone pairs" that are in these psychedelic d(sigma)-p(sigma) bonding and antibonding molecular orbitals.
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