The Dog That Didn’t Bark: A New Interpretation of Hypsoporphyrin Spectra and the Question of Hypsocorroles

Nearly a half-century after Gouterman classified the UV–vis–NIR spectra of porphyrin derivatives as normal, hyper, or hypso, we propose a heretofore unsuspected “mechanism” underlying hypso spectra. Hypsoporphyrins, which exhibit blueshifted optical spectra relative to normal porphyrins (such as Zn porphyrins), typically involve dn transition metal ions, where n > 6. The spectral blueshifts have been traditionally ascribed to elevated porphyrin eg LUMO (lowest unoccupied molecular orbital) energy levels as a result of antibonding interactions with metal dπ orbitals. Herein, we have found instead that the blueshifts reflect a lowering of the a2u HOMO (highest occupied molecular orbital) energy levels. Electronegative metals such as Pd and Pt transfer smaller quantities of electron density to the porphyrin nitrogens, compared to a more electropositive metal such as Zn. With large amplitudes at the porphyrin nitrogens, the a2u HOMOs of Pd(II) and Pt(II) porphyrins accordingly exhibit lower orbital energies than those of Zn(II) porphyrins, thus explaining the hypso effect. Hypso spectra are also observed for corroles: compared with six-coordinate Al(III) corroles, which may be thought of exhibiting normal spectra, Au(III) corroles, for instance, exhibit blueshifted or hypso spectra.


INTRODUCTION
The famous four-orbital model, 1,2 which explained the electronic absorption spectra of simple porphyrins, was devised by Gouterman in the early 1960s, while he was an Assistant Professor at Harvard. According to this model, the two highest occupied molecular orbitals (HOMOs) (a 1u and a 2u under D 4h symmetry) and the two lowest unoccupied molecular orbitals (LUMOs) (e g ) are energetically well-separated from all other occupied and virtual molecular orbitals (MOs). The Q and Soret bands are then explained by transitions between these four MOs, taking configuration interaction into account. Some 15 years later, now on West Coast, he presented an optical taxonomy of porphyrins in a lengthy chapter in Dolphin's multivolume workThe Porphyrins. 3 He classified porphyrins into three major classesnormal, hypso, and hyper. Normal porphyrins exhibit electronic absorption spectra that can be largely accounted for with the four-orbital model. Hypsoporphyrins exhibit blueshifted spectra, typical examples including d n metalloporphyrins for n > 6. In contrast, hyperporphyrins exhibit redshifted optical spectra and/or extra absorption bands above 300 nm. Typical examples include d n metalloporphyrins with n < 6, which in turn include many heme proteins and their intermediates and model compounds. Substituents and other structural perturbations can also lead to hyper spectra. 4 Many, but not all, hypsoporphyrins, especially the noble metal porphyrins, are moderately to strongly phosphorescent. 5−7 Their long-lived triplet states have been exploited for oxygen sensing and photodynamic therapy. 8−12 Gouterman and coworkers famously exploited platinum(II) porphyrins to devise pressure-sensitive paints for airplane wings. 13 30,31 and Au 20,32−35 corroles, have been found to exhibit NIR phosphorescence under ambient conditions, raising the question whether they, or at least some of them, should be described as hypsocorroles.
Remarkably, in spite of their broad importance, few hypso and hyper spectra have been examined by means of modern quantum chemical methods, such as time-dependent density functional theory (TDDFT) calculations, 36 The hypso effect has traditionally been explained in terms of metal(d π )−porphyrin(LUMO) orbital interactions. 3 By engaging in backbonding interactions with the porphyrin e g LUMOs, the d xz and d yz orbitals are stabilized. The corresponding antibonding MOs, that is, the LUMOs, the theory goes, are destabilized, which results in an elevated HOMO−LUMO gap, explaining the hypsochromic shifts of the Q and Soret bands. To our surprise, the present reinvestigation provided no support whatsoever for this long-held picture, suggesting instead an entirely different "mechanism" underlying hypso spectra.

COMPUTATIONAL METHODS
All calculations were carried out with the ADF 44 2018 program with all-electron ZORA-STO-TZ2P basis sets, fine meshes for numerical integration of matrix elements, and adequately tight convergence criteria for both SCF and geometry optimization cycles. Molecular geometries were optimized with OLYP 45,46 -D3, 47 with D 4h and C 2v symmetry constraints for the porphyrin and corrole derivatives, respectively. These optimized geo-    41,42 Interestingly, the lowest-energy Q band of Pt IV [TPP]Cl 2 appears to pose a peculiar challenge for some of the functionals. Thus, the calculated lowest-energy transition for this compound (experimental value:570 nm 42 ) is not a true Q band but a HOMO(a 2u ) → LUMO(a 1g ) transition, where the a 1g LUMO corresponds to the empty d z2 orbital of the Pt(IV) center. Table  1 shows that while OLYP unduly redshifts this feature, CAMY-B3LYP results in an undue blueshift, whereas B3LYP-D3 and B3LYP* perform just about right.
3.2. MO Analysis. A first step toward understanding the hypsoporphyrin effect is to examine the MO composition of the various calculated spectral features. This information is provided in Table 2 for the B3LYP-D3 functional, while key MOs are depicted in Figure 3   The Journal of Physical Chemistry A pubs.acs.org/JPCA Article flies in the face ofand indeed invalidatesthe conventional explanation for the hypsoporphyrin effect, namely, that a πantibonding interaction with the metal d π orbitals is responsible for an elevation of the orbital energies of the e g LUMOs. A comparative study of the frontier MO energy levels ( Figures  5 and 6) came to our rescue. While the LUMO energy levels were found to be almost identical across all the porphyrin (or corrole) derivatives studied, the hypsoporphyrins examined exhibit lower orbital energies for the a 2u HOMOs (or for the topologically similar b 1 HOMOs of corroles). This, then, appears to be the new explanation for the hypsoporphyrin effect.
3  2 ]. An examination of the atomic Mulliken and Hirschfeld charges, as well as of the nitrogen 1s orbital energies (Table 3), suggests a plausible explanation. Hypsoporphyrins appear to involve less electropositive metals that transfer less electron density to the porphyrin/corrole ligands as a whole and specifically to the macrocycle nitrogens.
Thus, both the macrocyclic ligands as a whole and their central nitrogens carry less negative Hirschfeld charges in the case of the hypsoporphyrins, relative to the normal porphyrin Zn II [TPP]. As a result, the nitrogen 1s orbital energies are also relatively more negative, which would translate to higher XPS ionization potentials, for the hypsoporphyrins. Given that the a 2u HOMO has large amplitudes on the macrocycle nitrogens, it follows that hypsoporphyrins should also exhibit lower a 2u orbital energies, which accounts for the hypsoporphyrin effect.
The above argument might suggest that a Pt(IV) porphyrin would exhibit a stronger hypsochromic shift than a Pt(II) porphyrin. As shown in Table 1, the opposite is observed. A recent, combined X-ray absorption spectroscopy and density functional theory (DFT) study has shown that a Pt(IV) porphyrin entails substantial oxidation of the porphyrin ligand as a whole. 54 That systemic oxidation results in a lowering of not only the a 2u HOMO, but also an even greater lowering of the e g LUMOs, which explains the lack of a hypsoporphyrin spectrum for Pt IV [TPP]Cl 2 .

CONCLUSIONS
DFT and TDDFT calculations indicate that the hypsoporphyrin effect (blueshifted Q and Soret bands) does not result from elevated porphyrin LUMO (e g ) energy levels as a result of antibonding interactions with metal d π orbitals. Instead the observed blueshifts reflect a lowering of the a 2u HOMO energy level. Electronegative metals such as Pd and Pt transfer smaller quantities of electron density to the porphyrin nitrogens, compared to a more electropositive metal such as Zn. As a result, the nitrogens in Pd and Pt porphyrins exhibit higher electrostatic potentials, more negative N 1s orbital energies, and higher N 1s ionization potentials. With large amplitudes at the porphyrin nitrogens, the a 2u HOMOs of Pd(II) and Pt(II) porphyrins also exhibit lower orbital energies (mirroring the behavior of the N 1s     Figure 5. B3LYP-D3 MO energy level diagrams for key TPP derivatives studied. Figure 6. B3LYP-D3 MO energy level diagrams for key TPC derivatives. The Journal of Physical Chemistry A pubs.acs.org/JPCA Article orbitals) than Zn(II) porphyrins, thus explaining the hypsoporphyrin spectra. The hypsoporphyrin concept also appears to extend to corroles. With blueshifted spectral features relative to sixcoordinate Al(III) corroles, Au(III) corroles appear to be justifiably described as hypsocorroles. It may be recalled that examples hypercorroles, likewise, have also been documented in the literature. 55 The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.1c08425.