Some of the Molecular Orbitals and Electronic States of Heme Species

I'm going to paste these diagrams for some of the major molecular orbitals of heme species and then for four "major" electronic states of perferryl heme species (in this case, the states are of compound I or another, very similar perferryl heme species that contains a proximal cysteinate ligand). In the doublet and quartet states that contain a sulfur ligand radical, there is still a pi-type bonding interaction (constructive overlap or "mixing") between a pi type lone-pair molecular orbital of cysteine. Iit's not clear to me if the 3pz or 3px nonbonding ("lone-pair") molecular orbital of the free, non-heme-bound cysteine residue forms a sigma-sigma type charge-transfer complex with the sigma*(z^2) antibonding molecular orbital of free heme, prior to its overlap with the a2u molecular orbital of heme, but the point is that some of the spin density of even the sulfur/thiolate ligand radical is in the porphyrin a2u molecular orbital (and not the a1u molecular orbital). It's not entirely clear to me what the nature of the "single" bond between the sulfur and the iron atoms is, but I've gotten a much more clear picture of the specific orbital occupations in the FeO (ferryl) moiety in different electronic states. I don't have time, at the moment, to put up diagrams that show the similarities between the different electronic states of the Fe=O moiety and the three major electronic states of dioxygen (O=O), but a lot of the articles have made the comparisons between various electronic states of ferryl and perferryl heme and the ground-state triplet, first excited singlet state ("delta singlet"), or second excited singlet state (sigma singlet) of dioxygen. In those different electronics states of dioxygen [the electronic state is more specific than the electronic configuration and specifies the relative energy levels of the molecular orbitals and the "spins" (the m(subscript)s quantum number) of the electrons in the various singly- and doubly-occupied molecular orbitals; within a given electronic configuration, any number of electronic states may exist (up to 25 or more, in some cases)] or of the Fe=O moiety, the key difference is that there is either a robust diradical (as in the states of heme species that are similar to ground-state triplet dioxygen, in which the spins of the electrons in the singly-occupied pi*(xz) and pi*(yz) molecular orbitals of O2 are both +1/2--this is the situation shown below, although other electronic states of heme species are more similar to triplet dioxygen, in terms of their orbital symmetries, than the electronic states shown below) or, I think, more of a partial diradical [in a manner analogous to the two major excited, singlet states of dioxygen, in which there is either a doubly-occupied pi*(xz) or pi*(yz) molecular orbital (singlet delta) or two singly-occupied pi*(xz) and pi*(yz) molecular orbitals containing electrons of opposite "spin" (sigma singlet)] character to the singly-occupied pi*(xz) and pi*(yz) antibonding molecular orbitals, such that the spin density is primarily localized to the Fe and the O, individually, and not shared to a significant extent. The triplet, singlet, and quartet terms in the diagrams are the spin multiplicities of the individual spin centers. The spin multiplicity is this: (the absolute value of 2S) + 1. S is the total spin for a given spin center and is this: [(# of alpha electrons ("positive spin")) x (+1/2)] + [(# of beta electrons ("negative spin")) x (-1/2)]. So S is (+1/2)(2) = 1 for the FeO moiety shown below, and 2(1)+1 = the spin multiplicity = 3 = triplet, for the FeO moiety. The FeO, porphyrin, and thiolate [as well as the iron atom itself, which can exist in more than one spin state (or, as it is sometimes referred to as being, configuration, such as d(superscript)5, d4, or d6 (or 5D or 5S or whatever the other terminology is--I'll put up diagrams on those aspects), within a given oxidation state, such as Fe(IV) or Fe(III), etc.] moieties are treated as being separate spin centers that may or may not participate in various types of "spin coupling" interactions with another spin center. Usually, the total spin for two "spin centers" can be "calculated" by just doing the calculation on the alpha and beta electrons, in the same manner as described above. In some cases, however, such as when the a1u and a2u orbitals are each singly-occupied by electrons of opposite spin, the singly-occupied porphyrin orbitals undergo "configuration interaction" and form a new orbital, basically or literally, that, effectively, contains two paired electrons that don't affect the total spin, when the new orbital(s) (I'm fairly certain that it can be a single orbital or pair of orbitals in A1g symmetry in the D4h point-group symmetry of the isolated, nonsubstituted, planar porphyrin moiety) are formed, of the would-be coupling between the porphyrin and FeO moieties. For example, in that situation, the overall singlet state [two singly-occupied molecular orbitals containing electrons of opposite spin (or referred to as alpha or beta orbitals, etc.)] of the a2u and a1u orbitals, taken together, does not figure in to the "calculation" of the total spin for the particular electronic state (it's still an overall triplet state, with the triplet designation being dictated entirely by the spins of the diradical electrons in the pi* xz and yz antibonding molecular orbitals of the FeO moiety (as shown below). I think it's either that it's like a new orbital an "A1g orbital" in a singlet state (a porphyrin molecular orbital of A1g symmetry in the D4h point group, which is different from "A1g state symmetry," referring to two doubly-occupied molecular orbitals, as shown in the diagrams below) or its symmetry is such that an interaction with the FeO moiety is symmetry-forbidden or spin-forbidden or something. I don't understand how to assign point-group symmetries to specific molecules, yet, but I can sort of work backwards and assign axes and planes of symmetry. The business of assigning molecules to point groups of symmetry and assigning orbital symmetry designations is very complex, and I need a lot more practice on that. Anyway, I don't have time to put up anything else right now.