Electron Configuration and Abbreviated Molecular Orbital Diagram of a Low-Spin Species of Ferryl Heme: My First "Bid"

Sketching these things helps me pin down some of these things, for my own, personal leisure and meditation-like benefit. The articles on this type of thing tend to actually be totally inconsistent, and the differences can't be explained in terms of differences in the spin state of the high-spin vs. low-spin states of ferryl heme, for example. According to some articles, two of the four d-electrons of iron(IV) in ferryl heme are nonbonding and are in a dxy orbital [a.k.a. a would-be sigma*(xy) antibonding molecular orbital], but that doesn't make sense to me. Shaik et al. (2005) [Shaik et al., 2005: (http://pubs.acs.org/doi/abs/10.1021/cr030722j)] reported, as other authors have reported, that iron's two other electrons are in the d(x^2-y^2) orbital, which is unusual in the sense that the lobes of that orbital point in between the nitrogens, toward the meso carbons. Usually, that d-orbital is the highest because its four lobes are oriented directly toward the ligands. But the strange thing is that some of these articles make it sound like the double bond in the Fe=O moiety has only two electrons in it [two singly-occupied d(pi)-p(pi) antibonding orbitals, which are pi*(xz) and pi*(yz), as shown below]. That would mean that the oxygen would have four nonbonding electrons, in sp2 or sp3 or pi nonbonding (or antibonding) orbitals. That would make six total and could explain some of these more or less totally confusing uses of random charge symbols, such as the whole Fe(4+)=O(2-). The formal bond order is either 1/2(bonding-antibonding) or 1/2(bonding)-antibonding, and I can't tell because of the way the person phrased it. If that were the case, there would be a -2 bond order? That might explain the crazy "-2" value that keeps showing up, but come now. The authors of other sources (such as the terror-tome that is my advanced inorganic chemistry 12,000-reference book, among others--seriously, it lists 5-10 references per page, in footnotes, and is 1500 pages but is a compact little ditty) have reported that the bond order of the Fe=O "double bond" is greater than 2, but some experimental numbers from another group show the bond orders of the Fe-O bonds, in different intermediates of the catalytic cycles of peroxidase enzymes or CYP450 enzymes, to range from something like 0.7 to 1.34. A lot is evidently not known about "compound II," as shown below (ferryl heme), and compound I (perferryl heme), but I tend to favor the bookkeeping model in which O has, effectively, 6 valence electrons in ferryl heme and perferryl heme and 7 in ferric hemes and protonated ferryl or perferryl heme. In any case, it's possible to understand the reactions without having perfect knowledge, but I generally like to know how many valence electrons are in an atom, etc. I'll try to gradually go through some more spin states and heme species and modify those sketches to show their electron configurations. It's not that complicated. The porphyrin ring's molecular orbital is usually referred to as the a(2u) orbital and has one unpaired electron in ferryl heme. It's interesting the way the nitrogens only contribute two electrons to iron, too. The confusing part is the inconsistent use of notation and shorthand, etc., and it basically means that it's impossible to tell what a lot of the articles' authors are trying to say. It's as if there's the layer of knowledge that allows one to do most of the research very effectively and then this "seedy" underside to the research, as a whole, in which heme species are "up for grabs," like a big market with everyone haggling and using auctioneers' voices...I'm joking. "Give 'em ten-ten-ten-Spin 5/2, gimme 5/2, 5/2, 5/2, geddem 2, give 'em 2, spin 2, spin 2." It's an interesting and challenging area. The mathematical-solution-to-the-Schrodinger-equation type of electron distribution in the d(pi)-p(pi) orbital that I'm showing (a.k.a. the pi*(xy)antibonding molecular orbital) is consistent with a computer-based analysis. I don't feel like citing the article now. There's another molecular orbital that's in the yz plane and is identical to that one. I can't find any information on the type of orbital that the oxygen's lone pair or pairs (in the event, in the latter case (pairs), that the double bond contains two electrons), but I suppose that doesn't matter. Groves and Nemo (1983) [Groves and Nemo, 1983: (http://pubs.acs.org/doi/abs/10.1021/ja00358a009)] show a single lone pair along the z-axis, along with one xz or yz pi*-antibonding orbital containing one electron. I suppose that could mean that a similar situation exists in the other pi*-antibonding orbital that, along with the first, comprises the Fe=O "double bond." But that sounds strange to me. The molecular orbital I'm showing below is the result of the dxz-px overlap shown in the xz-plane, in the diagram above the molecular orbital.

In the above diagram, the t2g "subshell" of d-orbitals usually comprises the dxz, dyz, and dxy orbitals (each of which is also known as a "d(pi) orbital"), but the ligand environment in heme causes the lobes of the d(x^2-y^2) orbital to be oriented, as discussed above, toward the meso carbons. That makes it the lowest-energy orbital. It's usually in the higher-energy eg set. In an unliganded Fe(IV) ion (Fe4+, if it existed) or an Fe2+ or Fe3+ ion, all the d-orbitals are degenerate (at the same energy level), lower than the relative energy level of the t2g set. The formation of any complex, including the most basic hexaquo-iron(III) or hexaquo-iron(II) complexes, causes the first "splitting" of the energy levels of the orbitals, into the eg set and t2g set (or subshells), and then the complex interplay of the interactions of iron(IV) or iton(III) with the nitrogen ligands and various axial substrates or ligands and cysteine residue or tyrosine residue or histidine residue (as one of the two axial ligands) causes further splitting of the energy levels of the individual d-orbitals in the eg and t2g sets. The spin is the sum of the individual spin values for each unpaired electron. If there are 3, then it's 3/2, etc.

This is one of the two molecular orbitals that are visual approximations of mathematical solutions to the dxz-px overlap, shown above. The + and - have no basis in reality and signify the positive phase and negative phase of a waveform, just as a sine wave can be greater than zero or less than zero. The overlap of a lobe with a positive phase and a lobe of an orbital exhibiting a negative phase is meant to signify destructive overlap, leading to the formation of an (supposed, mathematically) antibonding orbital. Constructive overlap occurs when two lobes are in phase. The different solutions to the (nonrelativistic) Schrodinger equation provide a crude prediction of electron density but mainly explain bonding geometries/orientations.

This is the presumed-to-be-accurate case, with each pi* orbital containing two electrons: