C(subscript)S Point-Group Symmetry in Compound(s) I: Role of Overlap of Thiolate 3p(z) AO and Porphyrin a2u MO

These diagrams show the bent angle of the sulfur-iron "bond(s)" [the bond comprises the various molecular orbitals (MOs) that allow for pi-type bonding interactions between the sulfur 3p(x) and 3p(y) AOs with the 3d(xz) and 3d(yz) AOs of iron (or, rather, the MOs of non-protein-bound heme that those AOs of iron contribute to the formation of)] and sigma-type interactions (I'd define a sigma-type interaction, in this context, as being "overlap of quasi-cylindrical symmetry about the S-Fe axis," or something like that) of the 3p(z) AO of sulfur with the 3d(z2) AO of iron (or, rather, the MOs of heme that the 3d(z2) AO of iron has already participated in the formation of) and the a2u MO of heme [see Ogliaro et al., 2001: (http://www.ncbi.nlm.nih.gov/pubmed/11948872); Harris, 2001: (http://www.ncbi.nlm.nih.gov/pubmed/11738185)]. The bent angle of protein-cysteine-liganded heme and also in nitrosylhemes (Porphyrin-Fe-N=O) and in iron(II)-hemes bound to O2 (unless the Fe is bound to both oxygens of O2, in which case it's C2v symmetry, I think) causes those heme species to be assigned to the Cs point group, in which the only possible symmetry operations are the identity operation and the reflection about a sigma(h) plane of symmetry (I think I've drawn it correctly) [for a depiction of the bent angles of the Fe-N and N=O bonds, away from the traditionally-assigned z-axis that is perpendicular to the plane of the porphyrin ring, that characterize Cs point-group symmetry, see Novozhilova et al., 2006, p. 2100, Figs. 6 and 7: (http://www.ncbi.nlm.nih.gov/pubmed/16464112)(http://harker.chem.buffalo.edu/group/publication/370.pdf)]. The only other characteristic of Cs point group symmetry is that it's "abelian," and I forget what that is or maybe don't understand it. I'd need some more math to understand the symmetry stuff fully [for the point-group character tables, see: (http://www.webqc.org/symmetrypointgroup-cs.html)]. One begins with a flow chart and then goes from there. The angle is bent, in part, "because" the angle allows for the constructive overlap of the sulfur's 3p(z) AO with the a2u molecular orbital of heme.

The other main point is that there's potential for confusion in the nature of the interaction of sulfur's 3p(z) orbital with the a2u orbital, on the one hand, and, on the other hand, with the 3d(z2) AO of iron. I don't have time, at the moment, to get into this and refer to various articles, but one might say that one "reason" that the sulfur's "ungerade" 3p(z) AO's can exhibit constructive overlap with the "ungerade" a2u MO of heme [this would be symmetry-forbidden in the planar, isolated porphyrin ring that exhibits D4h point-group symmetry, by virtue of its nitrogen atoms being coplanar with the rest of the porphyrin ring (rather than "domed" out of the plane of the porphyrin ring, as in Cs and C4v point-group symmetries)], for example, is that the a2u MO of heme cease to really be "ungerade" in Cs point-group symmetry (and also in the C4v point group). The 3d(z2) AO and other AOs of the isolated ferryl moiety are "gerade," but those AOs and the a2u MO are neither gerade nor ungerade in Cs point-group symmetry, given that there's no inversion point in Cs point-group symmetry (there's a center of mass of heme, but no inversion point is assigned to it). They're all either a' or a'', in the Cs point group. Anyway, the change in the Fe-S bonding angle changes the symmetry point group that one assigns heme to and, more importantly, changes many of the interactions of the porphyrin-localized MOs of heme with the MOs of heme that are predominantly-localized to the FeO moiety, & it's interesting.

These are the conventions, evidently [conventions that few researchers actually follow, evidently, given that it seems like it would become problematic in computer models of MOs (http://vitalii.chemicalblogs.com/2_computational_chemistry/archive/40_conventions_for_symmetry_notations.html)] for the assignment of the principal axis (a C1 axis that makes the molecule nonaxial, given that one ends up back where one started after rotating the molecule 360 degrees, or 2pi radians, about the z-axis). The z-axis that I've drawn intersects 2 atoms (the maximum number), and the x-axis is perpendicular to the plane of the isolated, nonsubstituted porphyrin ring. The sigma(h) plane is a horizontal reflection plane, and the "lines" or axes of the Fe-S and Fe=O bonds are in the same plane (those lines are coplanar, and their plane is coplanar with the sigma(h) plane). The molecule is symmetric upon reflection through the sigma(h) plane but has no other axes of symmetry or planes of reflection. The assignment of a molecule to a point group is not determined by x, y, or z-axis assignments, but one has to assign x, y, and z axes (and, ultimately, a spherical coordinate system) in order to superimpose 3-dimensional plots of MO probability density functions (the orbital "shapes" are dictated by the probability that an electron will be within the region that is defined by the surface of the orbital at any given instant) onto the "coordinate-system-independent" C2, C3, etc., symmetry axes and planes of reflection. Evidently, that's part of the reason there can be confusion, as far as orbital symmetry assignments go. Researchers assign different coordinate systems, and that can, apparently, alter the MO symmetry assignments, across different articles, even when different groups of researchers are referring to precisely the same molecule, in precisely the same electronic state.



The reverse face of heme is shown in the second diagram: