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. 2021 Oct 29;125(46):9953–9961. doi: 10.1021/acs.jpca.1c06621

Understanding Hyperporphyrin Spectra: TDDFT Calculations on Diprotonated Tetrakis(p-aminophenyl)porphyrin

Jeanet Conradie †,‡,*, Carl C Wamser §,*, Abhik Ghosh †,*
PMCID: PMC8630795  PMID: 34714662

Abstract

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A detailed TDDFT study (with all-electron STO-TZ2P basis sets and the COSMO solvation model) has been carried out on the effect of diprotonation on the UV–vis–NIR spectra of free-base tetraphenylporphyrin and tetrakis(p-aminophenyl)porphyrin. The diprotonated forms have been modeled as their bis-formate complexes, i.e., as so-called porphyrin diacids. The dramatic redshift of the Q-band of the TAPP diacid has been explained in terms of an elevated “a2u” HOMO and lowered LUMOs, both reflecting infusion of aminophenyl character into the otherwise classic Gouterman-type frontier MOs. The exercise has also yielded valuable information on the performance of different exchange–correlation functionals. Thus, the hybrid B3LYP functional was found to yield a substantially better description of key spectral features, especially the diprotonation-induced redshifts, than the pure OLYP functional. Use of the range-separated CAMY-B3LYP functional, on the other hand, did not result in improvements relative to B3LYP.

Introduction

Porphyrins are notorious for leaving stains on glassware. Most tetraphenylporphyrins are dissolved by acid, which transforms their characteristic purple color to a brilliant green. The color change corresponding to diprotonation of tetraphenylporphyrin (H2[TPP]) is associated with modest redshifts of both the Soret and Q bands, from 417 and 646 nm to 443 and 659 nm, respectively.1 Much more dramatic spectral changes are observed for meso-tetrakis(p-aminophenyl)porphyrin (H2[TAPP]), for which protonation of the two unprotonated central nitrogens results in redshifts of the Soret and Q bands, originally at 438 and 669 nm in DMSO, to 467 and 813 nm, respectively (Figure 1).2 In addition to the redshift, the Q-band also dramatically gains in intensity. Martin Gouterman3 and co-workers, using semiempirical calculations, recognized these redshifts as a form of hyperporphyrin character,4 reflecting charge transfer from the meso-aryl groups.5 Modern quantum chemical methods, however, have not been applied to H2[TAPP] and its diprotonated form.6−8

Figure 1.

Figure 1

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UV–vis–NIR spectral changes associated with titration of H2[TAPP] with methanesulfonic acid in DMSO. Adapted with permission from ref (2). Copyright 2014 American Chemical Society.

As it happens, even unprotonated H2[TAPP] exhibits a number of peculiarities. Thus, unlike most para-substituted tetraphenylporphyrins, which exhibit optical spectra that are qualitatively indistinguishable from parent H2[TPP], H2[TAPP] exhibits significantly redshifted Soret and Q bands. Second, the oxidation potential of H2[TAPP] is substantially lower than that predicted on the basis of a Hammett correlation applicable to the great majority of para-substituted tetraphenylporphyrins.2 Taken together, these results suggest that the HOMO of H2[TAPP] is unexpectedly high in energy and that the amino substituent acts differently from other para substituents. Is H2[TAPP] itself to be viewed as an incipient hyperporphyrin?

The above phenomena, while of interest in and of themselves, are relevant to a number of practical applications. As dyes absorbing in the near-infrared (NIR), hyperporphyrins are clearly of interest in photomedicine, for example, as photosensitizers in photodynamic therapy.9−13 Protonated porphyrins have been used as sensors for gases such as ammonia, hydrogen sulfide, and sulfur dioxide,14,15 while H2[TAPP] has also been used as a building block for dye-sensitized solar cells.16−18 Porphyrin protonation has also been used for pH19,20 and anion sensing21 and even for modulating the optical properties of metal–organic frameworks (MOFs).22 Thus, motivated, we sought to shed light on the above spectral shifts via time-dependent (TD) density functional theory (DFT)23 calculations on H2[TPP], H2[TAPP] and their centrally diprotonated forms (Chart 1).24−29 Gratifyingly, the results have led to a host of long-awaited insights and spectral assignments, as recounted below.

Chart 1. Molecules Studied in This Worka.

Chart 1

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a Ball-and-stick diagrams based on OLYP-D3/STO-TZ2P optimized geometries.

Results

a. The Theoretical Model

The term “theoretical model” emphasizes the assumptions underlying our study and encompasses a number of aspects. A key aspect, obviously, concerns the exact chemical nature of the molecules studied, especially of the diprotonated forms of the porphyrins. Here we have modeled them as highly symmetric (D2d) bis-formate adducts. These adducts, also known as porphyrin diacids,30,31 are experimentally well-known and have been structurally characterized. These models also have the advantage of being charge-neutral, which should help stave off spurious transitions that may result in the presence of unbalanced charges (a relatively common issue in TDDFT calculations).

A second, related aspect concerns solvation, which also helps deter spurious transitions in TDDFT calculations. The results quoted below all refer to the COSMO32 solvation model and dichloromethane as solvent. Experimentally, both DMSO and dichloromethane have been used.1,2,8 We also examined the PCM33 model (with the Gaussian program) and found that it does not make much of a difference relative to COSMO.

Finally, the choice of the exchange–correlation functional turned out to be important. We began our study using OLYP34,35-D3,36 OLYP being a generalized gradient approximation that has been extensively calibrated in our laboratory. The calculations indeed yielded valuable insights and assignments but also evinced a number of shortcomings that we wished to improve upon. Thus, OLYP predicted excessively large redshifts for the Q bands of the porphyrin diacids (Figure 2 andTable 2). The same calculations also predicted an intense transition (at 628 nm) between the main Soret and Q features of TAPP diacid, for which there does not appear to be an experimental counterpart (Figure 1).

Figure 2.

Figure 2

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Calculated TDDFT UV–vis–NIR spectra in dichloromethane (COSMO) as a function of the exchange–correlation functional.

Table 2. OLYP/STO-TZ2P TDDFT Results, Including Transition Energies (E) and Wavelengths (λ), Oscillator Strengths (f), MO Compositions, and Excited State Symmetries.

          MO composition
    
compound peak E (eV) λ (nm) f from to weight (%) state symmetry
H2[TPP] Q 1.986 624.2 0.157 HOMO LUMO 79.6 B2
          HOMO–1 LUMO+1 19.5 B2
    2.092 592.6 0.202 HOMO LUMO+1 78.3 B1
          HOMO–1 LUMO 20.4 B1
  Soret 2.630 471.5 1.669 HOMO–1 LUMO+1 76.6 B2
          HOMO LUMO 17.3 B2
    2.641 469.5 1.749 HOMO–1 LUMO 76.4 B1
          HOMO LUMO+1 19.1 B1
{H4[TPP]}(HCO2)2 Q 1.723 719.7 0.394 HOMO LUMO 88.9 E
          HOMO–1 LUMO 8.7 E
  Soret 2.503 495.4 1.165 HOMO–1 LUMO 75.6 E
          HOMO–7 LUMO 9.8 E
    2.742 452.2 0.323 HOMO–7 LUMO 89.2 E
          HOMO–1 LUMO 7.0 E
H2[TAPP] Q 1.686 735.4 0.439 HOMO LUMO 92.3 B2
    1.761 704.0 0.581 HOMO LUMO+1 92.4 B1
  Soret 2.150 576.6 0.117 HOMO–1 LUMO 75.0 B1
          HOMO–4 LUMO 24.4 B1
    2.181 568.4 0.419 HOMO–1 LUMO+1 82.3 B2
          HOMO–4 LUMO+1 16.7 B2
    2.451 505.8 0.402 HOMO–5 LUMO 47.1 B2
          HOMO–4 LUMO+1 43.6 B2
          HOMO–1 LUMO+1 7.8 B2
    2.488 498.3 0.739 HOMO–4 LUMO 54.6 B1
          HOMO–5 LUMO+1 27.8 B1
          HOMO–1 LUMO 15.0 B1
    2.734 453.5 0.681 HOMO–5 LUMO 48.3 B2
          HOMO–4 LUMO+1 31.9 B2
          HOMO–7 LUMO 6.1 B2
          HOMO–1 LUMO+1 5.9 B2
    2.789 444.5 0.695 HOMO–5 LUMO+1 66.4 B1
          HOMO–4 LUMO 14.7 B1
          HOMO–1 LUMO 6.9 B1
          HOMO LUMO+1 5.5 B1
    3.044 407.3 0.147 HOMO–7 LUMO+1 95.4 B1
    3.053 406.1 0.315 HOMO–7 LUMO 89.6 B2
{H4[TAPP]}(HCO2)2 Q 1.331 931.4 0.731 HOMO LUMO 96.1 E
  Soret 1.972 628.6 0.526 HOMO–1 LUMO 98.1 E
    2.450 506.1 0.664 HOMO–4 LUMO 77.0 E
          HOMO–9 LUMO 18.7 E
    2.741 452.4 0.217 HOMO–9 LUMO 67.2 E
          HOMO–2,3 LUMO+2 12.7 E
          HOMO–4 LUMO 10.2 E
    2.931 423.0 0.164 HOMO–11 LUMO 89.0 E
          HOMO–2,3 LUMO+2 9.4 E
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The above problems were largely solved with B3LYP37,38 and its range-separated counterpart CAMY-B3LYP.39−41 Thus, both these functionals yielded Q-band redshifts that agreed well with experiment. Somewhat surprisingly, CAMY-B3LYP did not lead to improved results relative to B3LYP. We speculate that adjusting the amount of exchange in the B3LYP functional may well result in even better agreement between theory and experiment. Be that as it may, the present results, in our view, are entirely satisfactory and allow clear assignments for the protonation-induced spectral changes of H2[TPP] and H2[TAPP].

b. Molecular Orbital (MO) Energy Level Diagrams

A comparative Kohn–Sham molecular orbital (MO) energy level diagram (Figure 3) provides substantial insight into the observed spectral shifts and the hyperporphyrin effect and nicely sets the stage for a discussion of spectral assignments. The relevant MOs are depicted in Figure 4.

Figure 3.

Figure 3

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CAMY-B3LYP/STO-TZ2P Kohn–Sham MO energy (eV) level diagram for the four species studied, in dichloromethane modeled with COSMO.

Figure 4.

Figure 4

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Key CAMY-B3LYP (COSMO) frontier MOs, along with their irreps and orbital energies, relevant to Figure 3.

Of the four species examined, only H2[TPP] conforms strictly to the Gouterman four-orbital model;42,43 i.e., the two HOMOs are energetically close and the two LUMOs are essentially degenerate and these 4 MOs are energetically well-separated from all other MOs. That said, we shall see that the main optical transitions of all four species do conform to a largely Gouterman-type four-orbital composition. Below, although we will generally describe key MOs in terms of their actual irreducible representations (irreps), on occasion we will also use the well-known D4h irreps, within quotation marks, to facilitate allusion to the four-orbital model.

For strongly saddled TPP diacid, the “a2u” HOMO (which transforms as b2 under D2d) drops marginally in energy relative to H2[TPP] (Figures 3 and 4). The drop appears to be associated with a slightly greater delocalization of the MO onto the phenyl groups relative to parent H2[TPP]. The LUMOs undergo a sharper drop, reflecting substantial delocalization onto the phenyl groups. These orbital energy shifts result in a significant contraction of the HOMO–LUMO gap, qualitatively explaining the Q-band redshift observed (11−13 nm, depending on the solvent; Table 1) upon protonation of H2[TPP]. The “a1u” HOMO (transforming as b1) also drops sharply, away from the “a2u” HOMO (Figure 3). These changes in orbital energy are best viewed as the combined effects of protonation, the resulting strong saddling, and enhanced porphyrin-phenyl conjugation as a result of the latter; it is unclear whether the individual effects of the three factors can be rigorously dissected into separate, additive contributions.

Table 1. Comparison of TDDFT and Experimental2,8 Absorption Maxima (nm).

          experiment
molecule band OLYP B3LYP CAMY-B3LYP CH2Cl2 DMSO
H2[TPP] Q 624.2 593.0 594.7 646 646
    592.6 558.5 553.6    
  Soret 471.5 417.1 439.3 416 417
    469.5 412.4 439.1    
{H4[TPP]}(HCO2)2 Q 719.7 657.3 660.0 657 659
  Soret 495.4 445.0 447.6 438 443
H2[TAPP] Q 735.4 649.0 641.8 655 669
    704.0 612.5 598.8    
  Soret 576.6 447.9 448.3 427 438
    568.4 436.6 448.1    
{H4[TAPP]}(HCO2)2 Q 931.4 792.5 809.1 725 813
  Soret 506.1 490.0 445.1 460 466
      450.1      
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Compared with H2[TPP], H2[TAPP] exhibits a slight rise in the LUMO energy levels and a sharper rise in the energy of the “a2u” HOMO (Figure 3), understandably, given the large amplitudes of the latter MO at the meso positions (Figure 4). The result is again a contraction of the HOMO–LUMO gap, coincidentally to about the same value as for TPP diacid.

TAPP diacid exhibits LUMO energy levels slightly higher than those of TPP diacid, but the energy of the “a2u” HOMO (transforming, again, as b2) is considerably higher (Figures 3 and 4), reflecting the combined effects of protonation, strong saddling, and para-amino substitution. The HOMO–LUMO gap accordingly is dramatically contracted, qualitatively consistent with the extremely redshifted Q-band of TAPP diacid. Interestingly, although the “a1u” MO has approximately the same energy as that in TPP diacid, it corresponds to HOMO–4/HOMO–5 in TAPP diacid, depending on the functional. Between the “a2u” and “a1u” HOMOs, lie 2–3 aminophenyl-based MOs, disrupting the simple four-orbital model.

c. Spectral Assignments

Tables 2–4 present the detailed TDDFT data, including the MO-to-MO composition of key transitions for OLYP, B3LYP, and CAMY-B3LYP. Although the three functionals tell the same broad story, the reader may readily verify that the latter two functionals yield excitation energies (wavelengths) in significantly better agreement with experiment (Figure 1 and Table 1).

Table 4. CAMY-B3LYP/STO-TZ2P TDDFT Results, Including Transition Energies (E) and Wavelengths (λ), Oscillator Strengths (f), MO Compositions, and Symmetries.

          MO composition
    
molecule peak E (eV) λ (nm) f from to weight (%) symmetry
H2[TPP] Q 2.08 594.7 0.08 HOMO LUMO 69 B2
          HOMO–1 LUMO+1 29 B2
    2.24 553.6 0.11 HOMO LUMO+1 67 B1
          HOMO–1 LUMO 31 B1
  Soret 2.82 439.3 2.16 HOMO–1 LUMO+1 70 B2
          HOMO LUMO 28 B2
    2.82 439.1 2.18 HOMO–1 LUMO 67 B1
          HOMO LUMO+1 31 B1
{H4[TPP]}(HCO2)2 Q 1.88 660.0 0.42 HOMO LUMO 85 E
          HOMO–1 LUMO 13 E
  Soret 2.77 447.6 1.70 HOMO–1 LUMO 84 E
          HOMO LUMO 13 E
H2[TAPP] Q 1.93 641.7 0.34 HOMO LUMO 82 B2
          HOMO–1 LUMO+1 14 B2
    2.07 598.8 0.47 HOMO LUMO+1 84 B1
          HOMO–1 LUMO 14 B1
  Soret 2.77 448.3 2.10 HOMO–1 LUMO+1 83 B2
          HOMO LUMO 15 B2
    2.77 448.1 1.91 HOMO–1 LUMO 83 B1
          HOMO LUMO+1 14 B1
{H4[TAPP]}(HCO2)2 Q 1.53 809.1 0.93 HOMO LUMO 94 E
          HOMO–4 LUMO 3 E
  Soret 2.79 445.1 1.59 HOMO–4 LUMO 86 E
          HOMO–1 LUMO 7 E
    3.082 402.2 0.096 HOMO–1 LUMO 86.5 E
          HOMO–4 LUMO 7.2 E
    3.200 387.4 0.024 HOMO–2,3 LUMO 97.7 E
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As expected, the Q and Soret transitions of H2[TPP] exhibit a classic Gouterman four-orbital composition (Table 1). Thus, the two near-degenerate Q features (Qx and Qy) may be described as primarily HOMO → LUMO and HOMO → LUMO+1 transitions, while the two Soret features may be described as primarily HOMO–1 → LUMO and HOMO–1 → LUMO+1 transitions, respectively. In terms of composition, the Q and Soret bands of TPP diacid are also similar: the Q bands are thus essentially HOMO → LUMO (e), while the Soret bands are essentially HOMO–1 → LUMO (e), noting that the LUMOs are exactly degenerate in the D2d diacids. The calculations generally do a good job of reproducing the protonation-induced redshifts of the Soret bands (experimentally about 22–26 nm, depending on the solvent) but somewhat overestimate the Q-band redshifts (with OLYP significantly worse than B3LYP and CAMY-B3LYP).

The two Q and Soret bands of H2[TAPP] are compositionally very similar to those of H2[TPP], i.e., being essentially HOMO → LUMO/LUMO+1 and HOMO–1 → LUMO/LUMO+1, respectively. The B3LYP and CAMY-B3LYP calculations do a good job of reproducing the modest redshifts of Q and Soret bands (experimentally about 11–21 nm, depending on the solvent) relative to H2[TPP]. Once again, OLYP greatly overestimates these observed redshifts.

The calculated, degenerate Q transitions of TAPP diacid may be described as essentially pure “a2u” → LUMO (e) transitions. The strongly redshifted position of the transition appears 2-fold in origin, an elevated “a2u” HOMO and lower-energy e LUMOs, relative to H2[TAPP]; both effects reflect infusion of aminophenyl character into the classic Gouterman-type frontier MO in question. The “a1u” HOMO of TAPP diacid, in contrast, is lower in energy, relative to H2[TAPP], which explains a modest protonation-induced redshift for the Soret band. Interestingly, while B3LYP does a good job of reproducing the observed Soret redshift, CAMY-B3LYP predicts a small blueshift instead.

A major difference between B3LYP and CAMY-B3LYP concerns the Soret region of TAPP diacid. Thus, while B3LYP predicts two Soret-like features at 459.6 and 501.6 nm (Figure 2 and Table 3), CAMY-B3LYP predicts a unique, dominant Soret maximum at 445.1 nm (Figure 2 and Table 4). As indicated in Table 3, the 501.1 nm peak with B3LYP is a degenerate pair of aminophenyl → LUMO (e) transitions. Such transitions also occur with CAMY-B3LYP, but with much weaker intensities and on the higher-energy side of the major Soret peak (Table 4).

Table 3. B3LYP/STO-TZ2P TDDFT Results, Including Transition Energies (E) and Wavelengths (λ), Oscillator Strengths (f), MO Compositions, and Symmetries.

          MO composition
    
molecule peak E (eV) λ (nm) f from to weight (%) symmetry
H2[TPP] Q 2.10 590.2 0.14 HOMO LUMO 76 B2
          HOMO–1 LUMO+1 23 B2
    2.23 556.8 0.17 HOMO LUMO+1 75 B1
          HOMO–1 LUMO 25 B1
  Soret 2.75 451.2 1.99 HOMO–1 LUMO+1 75 B2
          HOMO LUMO 22 B2
    2.75 451.0 2.02 HOMO–1 LUMO 74 B1
          HOMO LUMO+1 24 B1
{H4[TPP]}(HCO2)2 Q 1.86 665.3 0.47 HOMO LUMO 89 E
          HOMO–1 LUMO 10 E
  Soret 2.68 463.1 1.51 HOMO–1 LUMO 87 E
          HOMO LUMO 10 E
H2[TAPP] Q 1.88 657.9 0.46 HOMO LUMO 90 B2
          HOMO–1 LUMO+1 8 B2
    1.99 623.7 0.61 HOMO LUMO+1 92 B1
          HOMO–1 LUMO 8 B1
  Soret 2.64 469.7 1.72 HOMO–1 LUMO+1 82 B2
          HOMO LUMO 7 B2
    2.67 463.5 1.45 HOMO–1 LUMO 86 B1
          HOMO LUMO+1 7 B1
{H4[TAPP]}(HCO2)2 Q 1.48 837.3 0.91 HOMO LUMO 97 E
          HOMO–4 LUMO 2 E
  Ar → LUMO 2.47 501.6 0.76 HOMO–1 LUMO 94 E
          HOMO–4 LUMO 5 E
    2.54 487.4 0.009 HOMO–2,3 LUMO 100 B2
  Soret 2.70 459.6 0.72 HOMO–4 LUMO 85 E
          HOMO–5 LUMO 6 E
          HOMO–1 LUMO 5 E
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Conclusion

A first TDDFT study of tetraphenylporphyrin and tetrakis(p-aminophenyl)porphyrin diacids has afforded substantial insight into the origin of their hyperporphyrin spectra.45 In short, multiple effects account for hyperporphyrin spectra.

Two different effects are primarily responsible for the Q-band redshifts. For diacid formation, the major contributor to the Q-band redshifts is a lowering of the LUMOs as a result of infusion of meso-aryl character. Elevation of the “a2u” HOMO also plays a role, albeit a smaller one. In contrast, the redshifted Q-band of H2[TAPP] relative to H2[TPP] reflects destabilization of the “a2u” HOMO via interaction with aminophenyl-based occupied MOs, while the LUMOs remain energetically relatively unperturbed.

Beyond the Q bands (i.e., for the Soret bands as well as certain pre-Soret and post-Soret bands), the transitions of the diacid forms are compositionally more complex. In these, meso-aryl → LUMO character mixes in with classic Gouterman “a1u” → LUMO transitions. Indeed, some of these transitions may be described as primarily meso-aryl or aminophenyl-based; the intensities of these transitions appear to vary significantly with the exchange–correlation functional.

An important finding, from a methodological point of view, is that the hybrid functionals B3LYP and CAMY-B3LYP perform much better than the pure functional OLYP. Use of the range-separated CAMY-B3LYP functional, however, does not appear to confer any significant advantage relative to classic B3LYP. Additional functionals, as well as solvent effects, are being examined in our laboratory. Overall, the above study has led to straightforward insights into an important class of hyperporphyrin spectra, which, we believe, should significantly aid in the design of a variety of porphyrin-based functional materials such as phototherapeutics, sensors, and solar dyes.

Computational Methods

All calculations were carried out with the ADF44 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 OLYP34,35-D336 with appropriate symmetry constraints (as indicated in Chart 1e); these optimized geometries were then used for TDDFT calculations with the OLYP-D3, B3LYP,37,38 and CAMY-B3LYP39 functionals. The COSMO32 solvation model (with dichloromethane as solvent) was used throughout.

Acknowledgments

This work was supported by grant nos. 262229 and 324139 of the Research Council of Norway (AG) and grant nos. 129270 and 132504 of South African National Research Foundation (JC).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.1c06621.

  • Optimized Cartesian coordinates (PDF)

The authors declare no competing financial interest.

Supplementary Material

jp1c06621_si_001.pdf (149.2KB, pdf)

References

  1. Wasbotten I. H.; Conradie J.; Ghosh A. Electronic Absorption and Resonance Raman Signatures of Hyperporphyrins and Nonplanar Porphyrins. J. Phys. Chem. B 2003, 107, 3613–3623. 10.1021/jp014417i. [DOI] [Google Scholar]
  2. Weinkauf J. R.; Cooper S. W.; Schweiger A.; Wamser C. C. Substituent and Solvent Effects on the Hyperporphyrin Spectra of Diprotonated Tetraphenylporphyrins. J. Phys. Chem. A 2003, 107, 3486–3496. 10.1021/jp022046f. [DOI] [Google Scholar]
  3. For a recent biography of Martin Gouterman, see:; Ghosh A. An Exemplary Gay Scientist and Mentor: Martin Gouterman (1931–2020). Angew. Chem., Int. Ed. 2021, 60, 9760–9770. 10.1002/anie.202012840. [DOI] [PubMed] [Google Scholar]
  4. Vitasovic M.; Gouterman M.; Linschitz H. J. J. Porphyrins Phthalocyanines 2001, 5, 191–197. 10.1002/jpp.309. [DOI] [Google Scholar]
  5. It is worth noting that the intermediate protonation stages (+3 to + 5) of H2[TAPP] show some hyperporphyrin character, but the spectrum of the +6 state looks much like plain TPP diacid.
  6. Chen D.-M.; Liu X.; He T.-J.; Liu F.-C. Density functional theory investigation of porphyrin diacid: electronic absorption spectrum and conformational inversion. Chem. Phys. 2003, 289, 397–407. 10.1016/S0301-0104(03)00088-0. [DOI] [Google Scholar]
  7. Štěpánek P.; Andrushchenko V.; Ruud K.; Bouř P. Porphyrin Protonation Studied by Magnetic Circular Dichroism. J. Phys. Chem. A 2012, 116, 778–783. 10.1021/jp2105192. [DOI] [PubMed] [Google Scholar]
  8. Wang C.; Wamser C. C. Hyperporphyrin Effects in the Spectroscopy of Protonated Porphyrins with 4-Aminophenyl and 4-Pyridyl Meso Substituents. J. Phys. Chem. A 2014, 118, 3605–3615. 10.1021/jp501398g. [DOI] [PubMed] [Google Scholar]
  9. Bonnett R.Chemical Aspects of Photodynamic Therapy; CRC Press, 2000. [Google Scholar]
  10. Pandey R. K.; Kessel D.; Dougherty T. J.. Handbook of photodynamic therapy: updates on recent applications of porphyrin-based compounds; World Scientific, 2016. [Google Scholar]
  11. Amos-Tautua B. M.; Songca S. P.; Oluwafemi O. S. Molecules 2019, 24, 2456. 10.3390/molecules24132456. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Lin Y.; Zhou T.; Bai R.; Xie Y. Chemical approaches for the enhancement of porphyrin skeleton-based photodynamic therapy. J. Enzyme Inhib. Med. Chem. 2020, 35, 1080–1099. 10.1080/14756366.2020.1755669. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Tian J.; Huang B.; Nawaz M. H.; Zhang W. Recent advances of multi-dimensional porphyrin-based functional materials in photodynamic therapy. Coord. Chem. Rev. 2020, 420, 213410. 10.1016/j.ccr.2020.213410. [DOI] [Google Scholar]
  14. Tuerdi G.; Nizamidin P.; Kari N.; Yimit A.; Wang F. Optochemical properties of gas-phase protonated tetraphenylporphyrin investigated using an optical waveguide NH3 sensor. RSC Adv. 2018, 8, 5614–5621. 10.1039/C7RA11643H. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Maimaiti A.; Abdurahman R.; Kari N.; Ma Q.-r.; Wumaier K.; Nizamidin P.; Abliz S.; Yimit A. Highly sensitive optical waveguide sensor for SO2 and H2S detection in the parts-per-trillion regime using tetraaminophenyl porphyrin. J. Mod. Opt. 2020, 67, 507–514. 10.1080/09500340.2020.1758817. [DOI] [Google Scholar]
  16. Walter M. G.; Rudine A. B.; Wamser C. C. Porphyrins and phthalocyanines in solar photovoltaic cells. J. Porphyrins Phthalocyanines 2010, 14, 759–792. 10.1142/S1088424610002689. [DOI] [Google Scholar]
  17. Walter M. G.; Wamser C. C. Synthesis and Characterization of Electropolymerized Nanostructured Aminophenylporphyrin Films. J. Phys. Chem. C 2010, 114, 7563–7574. 10.1021/jp910016h. [DOI] [Google Scholar]
  18. Day N. U.; Wamser C. C.; Walter M. G. Porphyrin polymers and organic frameworks. Polym. Int. 2015, 64, 833–857. 10.1002/pi.4908. [DOI] [Google Scholar]
  19. Thyagarajan S.; Leiding T.; Årsköld S. P.; Cheprakov A. V.; Vinogradov S. A. Highly non-planar dendritic porphyrin for pH sensing: observation of porphyrin monocation. Inorg. Chem. 2010, 49, 9909–9920. 10.1021/ic100968p. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Fagadar-Cosma E.; Vlascici D.; Birdeanu M.; Fagadar-Cosma G. Novel fluorescent pH sensor based on 5-(4-carboxy-phenyl)-10,15,20-tris(phenyl)-porphyrin. Arabian J. Chem. 2019, 12, 1587–1594. 10.1016/j.arabjc.2014.10.011. [DOI] [Google Scholar]
  21. Zhang Y.; Li M. X.; Lü M. Y.; Yang R. H.; Liu F.; Li K. A. Anion Chelation-Induced Porphyrin Protonation and Its Application for Chloride Anion Sensing. J. Phys. Chem. A 2005, 109, 7442–7448. 10.1021/jp050516a. [DOI] [PubMed] [Google Scholar]
  22. Zhao Y.; Cai X.; Zhang Y.; Chen C.; Wang J.; Pei R. Porphyrin-based metal-organic frameworks: protonation induced Q band absorption. Nanoscale 2019, 11, 12250–12258. 10.1039/C9NR02463H. [DOI] [PubMed] [Google Scholar]
  23. For a comprehensive introduction to TDDFT, see: Ullrich C. A.Time-Dependent Density-Functional Theory: Concepts and Applications; Oxford University Press, 2011; 526 pp, 10.1093/acprof:oso/9780199563029.001.0001. [DOI] [Google Scholar]
  24. To our knowledge, there are no reasonably comprehensive reviews on TDDFT calculations on porphyrin-type molecules. Major earlier studies include refs (25−29).
  25. Baerends E. J.; Ricciardi G.; Rosa A.; van Gisbergen S. J. A. A DFT/TDDFT interpretation of the ground and excited states of porphyrin and porphyrazine complexes. Coord. Chem. Rev. 2002, 230, 5–27. 10.1016/S0010-8545(02)00093-0. [DOI] [Google Scholar]
  26. Ricciardi G.; Rosa A.; Baerends E. J.; van Gisbergen S. A. J. Electronic Structure, Chemical Bond, and Optical Spectra of Metal Bis(porphyrin) Complexes: A DFT/TDDFT Study of the Bis(porphyrin)M(IV) (M = Zr, Ce, Th) Series. J. Am. Chem. Soc. 2002, 124, 12319–12334. 10.1021/ja020554x. [DOI] [PubMed] [Google Scholar]
  27. Alemayehu A.; Conradie J.; Ghosh A. A First TDDFT Study of Metallocorrole Electronic Spectra: Copper meso-Triarylcorroles Exhibit Hyper Spectra. Eur. J. Inorg. Chem. 2011, 2011, 1857–1864. 10.1002/ejic.201001026. [DOI] [Google Scholar]
  28. Venkataramanan N. S.; Suvitha A.; Nejo H.; Mizuseki H.; Kawazoe Y. Electronic structures and spectra of symmetric meso-substituted porphyrin: DFT and TDDFT-PCM investigations. Int. J. Quantum Chem. 2011, 111, 2340–2351. 10.1002/qua.22519. [DOI] [Google Scholar]
  29. Parker S. M.; Rappoport D.; Furche F. Quadratic Response Properties from TDDFT: Trials and Tribulations. J. Chem. Theory Comput. 2018, 14, 807–819. 10.1021/acs.jctc.7b01008. [DOI] [PubMed] [Google Scholar]
  30. Stone A.; Fleischer E. B. The Molecular and Crystal Structure of Porphyrin Diacids. J. Am. Chem. Soc. 1968, 90, 2735–2748. 10.1021/ja01013a001. [DOI] [Google Scholar]
  31. Cheng B.; Munro O. Q.; Marques H. M.; Scheidt W. R. An Analysis of Porphyrin Molecular Flexibility – Use of Porphyrin Diacids. J. Am. Chem. Soc. 1997, 119, 10732–10742. 10.1021/ja9716214. [DOI] [Google Scholar]
  32. Klamt A.; Schüürmann G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and Its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 799–805. 10.1039/P29930000799. [DOI] [Google Scholar]
  33. Tomasi J.; Mennucci B.; Cammi R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999–3094. 10.1021/cr9904009. [DOI] [PubMed] [Google Scholar]
  34. Handy N. C.; Cohen A. J. Left-right correlation energy. Mol. Phys. 2001, 99, 403–412. 10.1080/00268970010018431. [DOI] [Google Scholar]
  35. Lee C.; Yang W.; Parr R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785–789. 10.1103/PhysRevB.37.785. [DOI] [PubMed] [Google Scholar]
  36. Grimme S.; Antony J.; Ehrlich S.; Krieg H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. 10.1063/1.3382344. [DOI] [PubMed] [Google Scholar]
  37. Becke A. D. Density-functional exchange-energy approximation with correct asymptotic behaviour. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098–3100. 10.1103/PhysRevA.38.3098. [DOI] [PubMed] [Google Scholar]
  38. Miehlich B.; Savin A.; Stoll H.; Preuss H. Results Obtained with the Correlation Energy Density Functionals of Becke and Lee, Yang and Parr. Chem. Phys. Lett. 1989, 157, 200–206. 10.1016/0009-2614(89)87234-3. [DOI] [Google Scholar]
  39. Seth M.; Ziegler T. Range-Separated Exchange Functionals with Slater-Type Functions. J. Chem. Theory Comput. 2012, 8, 901–907. 10.1021/ct300006h. [DOI] [PubMed] [Google Scholar]
  40. Note that CAMY-B3LYP is the Yukawa form of CAM-B3LYP41 with a = 0.19 Å and b = 0.46 Å (and g = 0.34) but with the Yukawa potential as the switching function, as opposed to the Coulomb potential attenuated by the complementary error function.
  41. Yanai T.; Tew D. P.; Handy N. C. A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51–57. 10.1016/j.cplett.2004.06.011. [DOI] [Google Scholar]
  42. Gouterman M.; Wagniére G. H.; Snyder L. C. Spectra of Porphyrins Part II. Four-Orbital Model. J. Mol. Spectrosc. 1963, 11, 108–115. 10.1016/0022-2852(63)90011-0. [DOI] [Google Scholar]
  43. Gouterman M.Optical Spectra and Electronic Structure of Porphyrins and Related Rings. In The Porphyrins; Dolphin D., Ed.; Academic Press: New York, 1978; Vol. III, Part A, pp 1–165. [Google Scholar]
  44. Ghosh A.; Conradie J.. The Dog That Didnt Bark: A New Interpretation of Hypsoporphyrin Spectra and the Question of Hypsocorroles. J. Phys. Chem. A, DOI: 10.1021/acs.jpca.1c08425. [DOI] [PMC free article] [PubMed] [Google Scholar]
  45. te Velde G.; Bickelhaupt F. M.; Baerends E. J.; Fonseca Guerra C.; van Gisbergen S. J. A.; Snijders J. G.; Ziegler T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931–967. 10.1002/jcc.1056. [DOI] [Google Scholar]

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