One Way of Thinking About the Electrons in the (Controversial & Apparent) Sigma Bonding & Antibonding Molecular Orbitals in Ferryl and Perferryl Heme

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.

Finally: Leaving the Shorthand Notation for Heme Species Behind--It's Freedom, "Everse-Style"

Finally. This [Everse, 1998: (http://www.ncbi.nlm.nih.gov/pubmed/9626592)] is an article that addresses some of the significant problems with the notation used to represent heme compounds. The notation just doesn't make any sense, in many cases. Everse (1998) also confirms, when viewed alongside the other articles I have, my suspicion that the Fe=O bond has two electrons. Some of my older mechanisms need to be corrected, because I show homolytic cleavage of a pi or d(pi)-p(pi) bond (the "pi double bond") in some instances. The mechanisms are valid, but it's necessary to not show all of the electron transfer occurring at once. But the diagram showing one electron in the pi*(xz) antibonding molecular orbital, in the previous posting, is accurate. There's another electron in the pi*(yz) antibonding molecular orbital, and those are the only electrons in the bond. It's not a double bond, and Everse (1998) refers to it as a biradical pi-bonding interaction. Or one could call it a d(pi)-p(pi) interaction. But the whole thing with [Fe(IV)O]2+ doesn't make any sense, and I think the whole thing with the [Fe(III)-OH(-)]+ is a convention left over from the whole "crystal field theory" concept of dsp3 and d2sp3 orbitals, etc. In that type of theoretical framework, the ligand "O" is treated as if it's "O2-" or something. It doesn't even have that electronic strucure, though, and Everse (1998) reiterates the point that the oxygen in Fe=O has an oxene (atomic oxygen) electron configuration and has six valence electrons. I also finally found a great article that analyzes the electronic structure of a ferric heme species (t-butoxo-iron(III)-heme) [Lehnert et al., 2001: (http://www.ncbi.nlm.nih.gov/pubmed/11516278)], and that article, as other articles have shown, shows that some ferric heme species do contain sigma bonds. But ferryl heme has no sigma bonding electrons in the molecular orbitals that are included in the ferryl (Fe(IV)=O) moiety of heme.

No Electrons in Sigma Bonding or Antibonding Molecular Orbitals for Fe=O in That Spin State of Ferryl Heme: "A 'Single' Bond But No Single Sigma Bond"

Incidentally, I was going to emphasize that there's no sigma bond with iron(IV) in that spin state of ferryl heme. A lot of researchers have compared the Fe=O bond to the triple bond ("formal bond order") that Fe can form with nitrogen atoms of some ligands. It's like a triple bond, with two sets of pi interactions, without the sigma bond, from what I can tell. That's one way of thinking about the more complex reality, in any case, especially given that the Fe=O bond length in ferryl heme is 1.65 angstroms (that's significantly shorter than a usual Fe-O bond). In that article by Shaik et al. (2005), cited in the last posting, even the sulfur of the cysteine residue, as one of the axial ligands, forms a pi bond, designated "pi(sub)S." For a pentacoordinated species of ferric heme, however, those authors do show an unpaired electron in a sigma antibonding molecular orbital. Anyway, part of the reason I think it's helpful to get a sense of the bookkeeping side is that it's almost impossible to tell what the species being referred to, in some articles, actually are, given the use of all of these different types of nonconventional notation and shorthand and so on. But it's interesting to note that there isn't a sigma bond between the oxygen of a water molecular and iron(II), for example (Shaik et al., 2005). There's a "single bond," but it's a pi*(yz or xz, depending on which coordinates one assigns to which "direction") antibonding orbital and not a sigma molecular orbital. I know that no one on the planet cares, but anyway...I guess I'll have to save some more of these "goodies" for tomorrow.

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:

Crude Picture of (Part of the) Electron Configuration of the Hydroxo-Ferric Heme Species

These articles [Shaik et al., 2005: (http://pubs.acs.org/doi/abs/10.1021/cr030722j); Silaghi-Dumitrescu, 2008: (http://macroheterocycles.isuct.ru/en/system/files/08MHC_79-81.pdf); Filatov et al., 1999: (http://zernike.eldoc.ub.rug.nl/FILES/root/1999/AngewChemFilatov/1999AngewChemIntEdFilatov.pdf)] are some "fun" articles I've been looking over. I wanted to clarify the electron configuration of the singly-bonded hydroxo-ferric heme species, and the oxygen apparently has, effectively, 7 valence electrons (as opposed to 6 in ferryl and perferryl hemes). In that species [Fe(III)-OH], apparently, three electrons are shared between iron and oxygen. From a bookkeeping standpoint, oxygen has a lone pair and an unpaired electron, but they're all pi electrons and aren't in the sigma*(xy) and sigma*(z^2) antibonding molecular orbitals for the Fe-O species. Two of these three electrons shared by iron and oxygen, in the Fe(III)-OH species, are in a dxz molecular orbital [one of the d(pi)-p(pi) interactions] (Shaik et al., 2005, Fig. 4). The other shared electron is in a pi*(xz) pi-antibonding molecular orbital. The electron configuration of ferryl heme is easier to understand than that, but it's necessary for me to understand what some of these authors are trying to refer to, with regard to the hardcore chemistry, when they "do" try to describe the electron configurations of these species.

Nitroxide Species Derived From Hydroxamate-Based Drugs as Reductants of Ferryl (and Perferryl) Heme, SOD-Mimetics, and "Catalase Activity Augmenters"

This article [Atamna et al., 2000: (http://www.jbc.org/content/275/10/6741.full.pdf+html)(http://www.ncbi.nlm.nih.gov/pubmed/10702229?dopt=Abstract); Krishna et al., 1996: (http://www.jbc.org/content/271/42/26018.full.pdf+html)(http://www.ncbi.nlm.nih.gov/pubmed/8824241)] is useful and shows that nitroxide compounds can exert antioxidant effects by serving as one-electron reductants of ferryl heme to ferric heme, and a key point is that the ferryl-to-ferric step can be rate-limiting in the maintenance of the catalase activity of protein-bound hemes. Drugs that contain hydroxamate groups are oxidized to their nitroxide radical species by their reactions with peroxyl radicals, and then the nitroxide form of the drug could reduce ferryl heme to ferric heme, without generating the superoxide that would usually be formed through the reduction of ferryl heme by hydrogen peroxide, and yield the oxo-ammonium cation form of the hydroxamate-containing drug. The oxo-ammonium cation species generally tend to exert superoxide-dismutase-mimetic effects by (reacting with superoxide and) forming O2, and that regenerates the nitroxide species that is likely to be the key species, in the absence of free iron, for example. But the acceleration of the rate of reduction of ferryl heme to ferric heme, via the reduction of ferryl heme by the nitroxide species, can, evidently, accelerate the two-electron catalase or "hydroperoxidase" activity of the perferryl-to-ferric heme reduction step. The redox cycling, via the reduction of the oxoammonium species by reduced glutathione, for example, of nitroxide-oxoammonium-hydroxylamine species is actually thought to be necessary for the so-called "catalytic" antioxidant mechanisms (as opposed to stoichiometric antioxidant mechanisms) by which nitroxides or hydroxamate-based drugs that are serving as "nitroxide prodrugs" can act. The nitroxide-oxoammonium cycling is "catalytic" because the species aren't consumed or inactivated through the cycling. And the SOD-mimetic effect may also be an important element, particularly since that mechanism can regenerate the nitroxide species. Anyway, it's too late to put up a sketch, but one reduction mechanism (for the reduction of ferryl heme to ferric heme by a nitroxide radical) is very similar to the reduction by H2O2.

Electrophilicity of the Oxene Oxygen of Tetravalent Hemes; Proton-Coupled Electron Transfer Mechanisms in Heme Reduction Reactions

These are some articles about, among other things, proton-coupled electron transport in hydrogen abstraction/hydrogen transfer reactions [Cheng and Li, 2007: (http://pubs.acs.org/doi/abs/10.1021/cr040077w); Sligar et al., 1980: (http://www.pnas.org/content/77/3/1240.full.pdf)(http://www.ncbi.nlm.nih.gov/pubmed/6929480); Guallar et al., 2003: (http://www.ncbi.nlm.nih.gov/pubmed/12771375)(http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=165819); Stubbe et al., 2003: (http://pubs.acs.org/doi/abs/10.1021/cr020421u); Reece et al., 2006: (http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1647304)(http://www.ncbi.nlm.nih.gov/pubmed/16873123); Sutcliffe et al., 2000: (http://www.ncbi.nlm.nih.gov/pubmed/10973049)]. One of the reasons the articles on the cycling of ferryl and perferrryl and ferric heme are confusing is that the iron-oxygen "double" bond is depicted in a manner that makes the polarity of the bond appear to be similar to the polarity of a carbonyl C=O double bond. In fact, the oxygen can be treated as if it has a formal charge of +2, given that the oxygen, in the p(pi)-d(pi) overlap of the oxygen's pi orbitals with the d(xy) and d(yz) orbitals of iron (and also with a mess of empty or half-filled antibonding d-orbitals or hybrid orbitals of iron), only winds up, effectively, with six valence electrons (Sligar et al., 1980). The oxygen has the electron configuration of an oxene oxygen, which is "atomic oxygen." That's the number of electrons that "atomic oxygen" has, in its ground-state electron configuration. The +2 is the formal charge and is calculated [6-(1/2(4))-2] in the same way any other formal charge calculation is calculated [(ground state valence electrons) - 1/2(shared) - (unshared)], even though the reality is that it's a mess of d-orbitals and all of that and is probably 8/3rds or something crazy like that. I think another example of an "oxene" compound is that short-lived, unsaturated ethylene epoxide compound (an unsaturated, three-membered oxirane). I'm not sure of another good example of a true oxene-like compound, but it's really unusual. It means that the Fe=O bond polarity (in ferryl and perferryl hemes) is reversed, in comparison to the polarity of a C=O bond. The oxygen is electrophilic (electron-deficient), and I've drawn it as such in these "electrophilic loser" diagrams. But anyway, that's helpful to me. Many articles describe the iron-oxo moieties of perferryl and ferryl heme as being something like [Por-Fe(4+)=O(2-)]2+, but a better way to abbreviate the structure might be to write something like this: [Por-Fe=O(+)(+)]2+. It's really necessary to know that oxygen has, effectively, six valence electrons.

Anyway, it's interesting that the hydrogen abstraction reactions, such as the one shown below, are thought to be more like proton-coupled/proton-assisted electron transfer reactions than they are like run-of-the-mill homolytic cleavage reactions. I've shown the reduction of ferryl heme by an unsaturated lipid, to form an alkyl radical, and that can then rearrange and react with molecular oxygen and then epoxidize or participate in other reactions that mediate lipid peroxidation. In proton-coupled electron transport, the electron essentially is transferred to the oxidant, which is the electrophilic oxene oxygen on ferryl or perferryl heme, and the hydrogen atom (with its one electron) may not be transferred at all but is transferred "after" the electron is transferred. Sutcliffe et al. (2000) discussed that concept in a more popular forum (the "Trends" journals) and discussed the way that's thought to be the underlying, core mechanism for enzyme catalysis, in the sense that electron tunneling or "quantum tunneling" allows the enzyme to go "through" the activation free-energy barrier through vibration-associated electron tunneling. The electron can be transferred from one residue to another through the protein's single bonds, in effect, or via proton transfers, etc. The math describes or models enzyme catalysis in terms of quantum mechanical vibrational energy of different parts of the enzyme (http://scholar.google.com/scholar?hl=en&q=enzyme+activation+energy+barrier+quantum+mechanical+vibrational&as_ylo=&as_vis=0), but it's as if the enzyme as a whole, instead of just the active site and other discrete sites, participates in the catalysis and "cheats" the activation energy barrier. Here are the initiation reactions for heme-dependent lipid peroxidation [Fe(IV)=O(2+) + LH--->L(e-) + Fe(III)-OH(+)]. I actually botched the product--it's supposed to contain an Fe-O "single bond," but I'm not going to change it:

This is a mechanism, discussed by Reece et al. (2006), by which the perferryl species can undergo reduction to ferric heme by a long-range, "hard-wired" (Reece et al., 2006, p. 1355) proton transfer mechanism. The cytochrome P450 enzyme creates a "water channel" that allows for proton-coupled electron transfer. I've drawn only the deprotonations (fast proton transfers), but the overall reaction is also a two-electron reduction of perferryl heme to ferric heme. There's probably some way to draw it, but I think the idea, as discussed by Guallar et al. (2003) in another proton-coupled-electron-transfer reduction of perferryl heme, is that the proton transfer allows the electrons to be donated through the hydrogen bonds between the carboxylate groups of the alkyl substituents of the heme species (I haven't shown them on the porphyrin ring) and amino acid residues that they form the hydrogen bonds with (I've shown hydrogen bonds, between water molecules, as being dotted lines, but I haven't shown the carboxylate-containing substituents of heme or the hydrogen bonds they can form with amino acid residues on proteins, etc.). So it's like oxygen donates two electrons in its protonation, and two electrons are tunneled through the enzyme and the porphyrin ring to heme. I've drawn the two-electron transfer as if it's coming from the oxygen to the iron, and maybe Reece et al. (2006) was saying that the electrons would be transfered through the water and not the enzyme. That could be the case in the CYP450 case (Reece et al., 2006), because the water molecules are essentially "locked in" as part of the enzyme. The overall idea is that electrons can be transferred through hydrogen bonds and allow for these mind-bending, catalytic mechanisms for electron donation, such as to heme species, in enzymes. The electrons "sweep" up through....No, that's a little joke:

This is the product: