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Expanded, Contracted, and Isomeric Porphyrins: Theoretical Aspects John Mack*

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Department of Chemistry, Rhodes University, Grahamstown 6140, South Africa ABSTRACT: The use of cyclic polyene perimeter-model approaches, such as Gouterman’s four-orbital model and Michl’s perimeter model, to analyze trends in the electronic structures and optical properties of expanded, contracted, and isomeric porphyrins is described with an emphasis on the use of magnetic circular dichroism (MCD) spectroscopy to validate the results of TD-DFT calculations. Trends in the electronic structures and optical properties of isomeric porphyrins are examined by comparing the properties of porphycenes, corrphycenes, hemiporphycenes, isoporphycenes, N-confused and neoconfused porphyrins, and norroles, whereas those of ringcontracted porphyrins are examined by comparing the properties of subporphyrins, triphyrins, and vacataporphyrins. The ring-expanded compounds that are examined include cyclo[n]pyrroles, [22]pentaphyrins(1.1.1.1.1), sapphyrins, smaragdyrins, isosmaragdyrins, orangarins, ozaphyrins, [26]hexaphyrins(1.1.1.1.1.1), rubyrins, rosarins, amethyrins, isoamethyrins, bronzaphyrins, and doubly N-confused hexaphyrins.

CONTENTS 1. Introduction 2. Electronic Structures of Porphyrins 2.1. Gouterman’s Four-Orbital Model 2.2. Michl’s Perimeter Model 2.2.1. 4N + 2 Perimeter Model 2.2.2. 4N Perimeter Model 2.3. Mö bius Aromaticity 2.4. Quantitative Prediction of Aromaticity 3. Porphyrins, Corroles, and Norcorroles 4. Isomeric Porphyrins 4.1. Porphycenes 4.2. Corrphycenes and Hemiporphycenes 4.3. Isoporphycenes 4.4. N-Confused Porphyrins 4.5. Neoconfused Porphyrins and Norroles 5. Ring-Contracted Porphyrins 5.1. Subporphyrins 5.2. [14]Triphyrins(2.1.1) 5.3. Vacataporphyrins 6. Ring-Expanded Porphyrins 6.1. Cyclo[n]pyrroles 6.2. Pentaphyrins 6.2.1. [22]Pentaphyrins(1.1.1.1.1) 6.2.2. Sapphyrins 6.2.3. Smaragdyrins and Isosmaragdyrins 6.2.4. Orangarins 6.2.5. Ozaphyrins 6.3. Hexaphyrins 6.3.1. [26]Hexaphyrins(1.1.1.1.1.1) 6.3.2. Rubyrins 6.3.3. Rosarins, Amethyrins, and Isoamethyrins 6.3.4. Bronzaphyrins 6.4. N-Confused Ring-Expanded Porphyrins © 2016 American Chemical Society

6.5. Larger Ring-Expanded Compounds 7. Conclusions Author Information Corresponding Author ORCID Notes Biography Acknowledgments Abbreviations References

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1. INTRODUCTION Porphyrins are macrocyclic tetrapyrrolic ligands with four bridging meso carbons that play a key role in biochemical processes such as photosynthesis and respiration and have heteroaromatic π-systems because of the 18-π-electron system formed on the inner perimeter of the macrocycle (Scheme 1). They can be prepared either as free-base ligands or as metal complexes. Their rich redox chemistry and favorable optical properties have led to an intense research focus on synthetic porphyrins, such as tetraphenylporphyrins and octaethylporphyrins.1 In recent decades, there has been growing interest in the synthesis and properties of their structural analogues such as expanded, contracted, and isomeric porphyrins, because these structural modifications result in marked changes in the optical, redox, and ion-coordination properties, making them potentially suitable for a wide range of applications.2 The goal of this review is to examine studies that have been carried out to describe trends in the optical and redox properties and electronic structures of expanded, contracted, and isomeric Special Issue: Expanded, Contracted, and Isomeric Porphyrins

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Received: August 22, 2016 Published: December 7, 2016 3444

DOI: 10.1021/acs.chemrev.6b00568 Chem. Rev. 2017, 117, 3444−3478

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Scheme 1. Molecular Structures of Free-Base Porphyrin and Porphycene, Corrphycene, Hemiporphycene, the E and Z Isomers of Isoporphycene, the 3H Tautomer of Singly N-Confused Porphyrin, and a Trans Isomer of Doubly N-Confused Porphyrin

Scheme 2. Molecular Structures of Free-Base Porphyrin and Porphycene, Pentaphyrin, Sapphyrin, Smaragdyrin, Isosmaragdyrin, Orangarin, and an Ozaphyrin Model Compound

ward ring-expanded porphyrin analogue structures8 have a single meso carbon bridge between each set of pyrrole rings in a similar manner to the parent porphyrin ligand. Expanded structures with five to eight pyrrole rings are referred to as [22]pentaphyrin(1.1.1.1.1), [26]hexaphyrin(1.1.1.1.1.1), [30]heptaphyrin(1.1.1.1.1.1.1), and [34]octaphyrin(1.1.1.1.1.1.1.1), respectively. In each case, the number in square brackets provides the number of π-electrons on the main macrocyclic

porphyrins by using a molecular orbital (MO) theory approach with a strong focus on Michl’s perimeter model for 4N + 23−6 and 4N7 cyclic polyenes as a conceptual framework for examining the effects of different structural modifications. Ring-expanded and -contracted porphyrins are usually understood to be porphyrin analogues in which there are more and fewer than four pyrrole rings, respectively, in the macrocyclic structure (Schemes 2−4). The most straightfor3445


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Scheme 3. Molecular Structures of Phosphorus Corrole, Nickel Norcorrole, Boron Subporphyrin, [14]Triphyrin(2.1.1),a and Vacataporphyrin {[18]Triphyrin(6.1.1)}a

a

Only one of the possible NH tautomers of each [14]triphyrin(2.1.1)20 and vacataporphyrin21 is shown.

Scheme 4. Molecular Structures of Free-Base Porphyrin and Porphycene, Hexaphyrin, Rubyrin, Rosarin, Amethyrin, a Bronzaphyrin Model Compound, and Cyclo[6]pyrrole

tional protonated pyrrole nitrogen is added to the inner ligand perimeter of corroles to compensate for the loss of a meso carbon, so that the inner ligand perimeter of the macrocycle retain the 18-π-electron system required to retain heteroaromatic properties. In the context of norcorroles, there are no extra pyrrole nitrogens on the inner perimeter, so an antiaromatic 16-π-electron system is formed. In a similar manner, a wide range of ring-expanded and -contracted porphyrin structures have been reported with either no or differing numbers of meso carbon atoms between neighboring pyrrole rings. The simplest set of such structures are the cyclo[n]pyrroles, which are structures with greater than six pyrroles that contain no meso carbon atoms. In the context of pentaphyrins (Scheme 2), research on [22]pentaphyrin(1.1.1.1.0) (sapphyrin),14 [22]pentaphyrin(1.0.1.0.0) (orangarin),15 and [22]pentaphyrin(1.1.0.1.0) (smaragdyrin)16 macrocycles has been

ring, whereas the numbers in parentheses refer to the numbers of meso carbon atoms between each set of neighboring pyrroles. Although pentaphyrins usually retain the planarity of the parent porphyrin structures, hexaphyrins and larger ringexpanded structures often deviate substantially from planarity, and this deviation provides scope for 4N Möbius aromaticity9 and antiaromaticity,10,11 as well as the more conventional 4N + 2 Hückel aromaticity and antiaromaticity (Figure 1).12 The analogous [14]triphyrin(1.1.1) ring-contracted ligands are referred to as subporphyrins,13 and to date, they have been prepared only as boron complexes, because of the small size of the central cavity. Corroles and norcorroles (Scheme 3) are ring-contracted tetrapyrrolic structures in which either one or two of the meso carbons are replaced by direct bonds between the α-carbons of neighboring pyrrole rings to form [18]tetraphyrin(1.1.1.0) and [18]tetraphyrin(1.0.1.0) macrocycles, respectively. An addi3446


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Scheme 5. Molecular Structures of Neoconfused Porphyrin and Norrole

to include the phthalocyanines36 and their ring-expanded or -contracted analogues, such as superphthalocyanines,37,38 subphthalocyanines,39 and the recently reported pentabenzotriazasmaragdyrin,40 which have aza-nitrogens or other heteroatoms at the bridging positions rather than meso carbons. Core-modified porphyrin analogues41 in which the pyrrole nitrogens are replaced with other heteroatoms such as oxygen and sulfur (including ring-expanded structures42) or the pyrrole rings are replaced by other heterocyclic ring moieties including those resulting from fused structures involving more than one pyrrole moiety (e.g., N-fused porphyrins43) or porphyrin ring (e.g., fused porphyrin tapes44) are also not covered, along with the protonation properties of the isomeric, ring-contracted, and ring-expanded porphyrins,45 and their radical anion and cation species.46 The goal is to examine the effect on the electronic structures and optical properties of isomerism, ring contraction, and ring expansion of a porphyrin ligand from a theoretical standpoint by using Michl’s perimeter 4N + 2 and 4N models3−7 as the conceptual framework.

Figure 1. Topologies of structures with Hückel and Mö bius aromaticity, along with the numbers of electrons required for aromatic and antiaromatic properties, and doubly twisted figure-eight structures that have properties similar to those of planar Hückel structures. Reproduced with permission from ref 79. Copyright 2010 American Chemical Society.

particularly noteworthy, whereas research on hexaphyrins (Scheme 4) has largely focused on [26]hexaphyrin(1.1.0.1.1.0) (rubyrin),17 [24]hexaphyrin(1.0.1.0.1.0) (rosarin),17 and [24]hexaphyrin(1.0.0.1.0.0) (amethyrin18) compounds. In the context of ring-contracted porphyrins (Scheme 3), the most important structures are [14]triphyrin[2.1.1]19,20 and [18]triphyrin(6.1.1) (vacataporphyrin)21 ligands. In contrast to the subporphyrins, free-base [14]triphyrin[2.1.1] can be prepared, because only one protonated pyrrole nitrogen is required to form a 14-π-electron conjugation system on the inner perimeter, and a wide range of metal complexes can be formed. The term isomeric porphyrin is normally used to refer to structures in which the meso-carbon substitution patterns of the conventional [18]tetraphyrin(1.1.1.1) porphyrin structure are modified to form [18]tetraphyrin(2.0.2.0) (porphycene),22 [18]tetraphyrin(2.1.0.1) (corrphycene),23 [18]tetraphyrin(2.1.1.0) (hemiporphycene), and [18]tetraphyrin(3.0.1.0) (isoporphycene) structures24 (Scheme 1) and also N-confused, doubly N-confused, and neoconfused porphyrin structures25−30 (Scheme 5) in which a nitrogen atom lies at the α- or β-positions rather than the conventional pyrrole nitrogen position on the inner ligand perimeter. Similar pentaphyrin and hexaphyrin structures can also be prepared (Schemes 2 and 4). Among the most noteworthy in this regard are the [22]pentaphyrin(2.0.2.0.0) (ozaphyrin)31 and [26]hexaphyrin(2.0.0.2.0.0) (bronzaphyrin)32 macrocycles, which can be viewed as ring-expanded porphycenes. There has also been considerable interest in the coordination chemistry of ring-expanded N-confused structures.28,33−35 The scope of this review is restricted to the conventional definition of the term porphyrin, and hence, no attempt is made

2. ELECTRONIC STRUCTURES OF PORPHYRINS Although this has been the subject of some controversy in recent years,47 the electronic structures of tetrapyrrolic porphyrins are conventionally regarded as being derived from an [18]annulene or [16]annulene dianion,48−53 because this explanation readily accounts for the strong aromatic-ringcurrent effect that is observed in their NMR spectra. This approach has long formed the basis of the theoretical understanding of the optical properties of porphyrinoids, and it can readily be extended to their analogues. The obvious starting point for a review of the theoretical treatment of the electronic structures of a series of porphyrin analogues, therefore, is to examine the cyclic polyene approaches that have historically been used to analyze trends in the electronic structures and optical and redox properties of conventional porphyrins and their corrole and norcorrole analogues, because these structures can be viewed as the parent ligands for the expanded, contracted, and isomeric analogues. Although density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations are now in routine use to provide calculated MO energy diagrams and UV−visible absorption spectra, older theoretical approaches that were developed to assign spectroscopic data on the basis of semiempirical calculations continue to play an important role by providing readily accessible conceptual frameworks that can be used to analyze trends in the electronic structures and optical properties of series of structurally related porphyrinoids.58−63 3447


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2.1. Gouterman’s Four-Orbital Model

magnetic moments of the excited states can be derived from (1/+0 ratios, where +0 is the dipole strength of the corresponding band in the electronic absorption spectrum. This approach provided the definitive evidence for the forbidden and allowed natures of the Q and B bands.57 The parent free-base porphyrins have D2h symmetry, so their MCD spectra are dominated by Gaussian-shaped oppositely signed xand y-polarized Faraday )0 terms rather than (1 terms. The Q bands of porphyrins only retain their forbidden character in this context because the 1a1u and 1a2u MOs are accidentally neardegenerate. This enables the cancellation of the electric dipole transition moments of near-equal contributions from the 1a1u → 1eg* and 1a2u → 1eg* one-electron transitions.54 When porphyrin structure is further modified to form structural analogues, such as phthalocyanines (Pcs) that have aza-nitrogen atoms rather than bridging meso carbons, the energies of the 1a1u and 1a2u MOs differ markedly, because the incorporation of electronegative nitrogen atoms leads to a stabilization of the 1a2u MO, and fused-ring expansion with benzene rings destabilizes the 1a1u MO. This leads to a mixing of the forbidden and allowed properties of the Q and B bands, because there are nonequal contributions from the 1a1u → 1eg* and 1a2u → 1eg* one-electron transitions in each case, and in the context of phthalocyanines, this means that the Q band becomes significantly more intense to the point that it dominates the optical spectra.36

64,65

Platt used molecular orbital theory to assign the major spectral bands in the optical spectra of benzene in the late 1940s based on a consideration of the ML = 0, ±1, ±2, 3 angular nodal properties of the π-system MOs, where ML is the magnetic quantum number that describes the orbital angular momentum (OAM) properties of the cyclic polyene π-system. The orbitally degenerate highest occupied molecular orbital (HOMO, ML = ±1) and lowest unoccupied molecular orbital (LUMO, ML = ±2) are linked by allowed ΔML = ±1 and forbidden ΔML = ±3 transitions, because the electric and magnetic vectors of the incident photon rotate at most once every wavelength. In the 1960s, Gouterman and co-workers54−57 demonstrated that the main spectral bands of porphyrins can be assigned in a similar manner using the ML = 0, ±1, ±2, ±3, ±4, ±5, ±6, ±7, 8 sequence in the MOs of a C16H162− parent perimeter species corresponding to the inner ligand perimeter. When the four pyrrole rings are introduced into the structure, the symmetry of a parent 16-atom ring of sp2-hybridized carbon atoms is lowered from D16h to D4h. There is a degenerate LUMO (1eg*) with ML = ±5 angular nodal patterns, and the MOs derived from the ML = ±4 HOMO (1a1u and 1a2u) are nondegenerate (Figure 2). Gouterman’s fourorbital model54−57 (Figure 3) accounts for the presence of allowed and forbidden B and Q bands, due to spin-allowed electronic transitions with ΔML = ±1 and ±9 properties, respectively.

2.2. Michl’s Perimeter Model

2.2.1. 4N + 2 Perimeter Model. Moffitt66,67 reported a perimeter model for cyclic polyenes in the early 1950s that can be used to analyze trends in the electronic structures of cyclic πconjugation systems. Moffitt was able to demonstrate that the relative alignments of the angular nodal planes of the π-MOs of cyclic polyenes are retained even after modifications to the structure lower the molecular symmetry.66,67 The effects of different structural perturbations can be analyzed relative to a parent hydrocarbon perimeter, and such an analysis can be used to qualitatively predict trends in the electronic structures and optical properties of low-symmetry cyclic polyenes. Michl3−6 further developed the perimeter-model approach in the 1970s and used it to rationalize the optical properties of a wide range of aromatic and heteroaromatic π-systems including porphyrinoids in both a qualitative and quantitative manner, through a detailed analysis of the effects that structural perturbations have on the induced excited-state magnetic moments that are associated with Platt’s allowed and forbidden B and L transitions.

Figure 2. Four frontier π-MOs of zinc porphyrin (ZnP) and its C16H162− parent perimeter. Reproduced with permission from ref 58. Copyright 2005 American Chemical Society.

The electronic absorption spectra of metal porphyrin complexes contain intense B (or Soret) bands in the 400− 450-nm region and weaker Q bands in the 500−650-nm region (Figures 3 and 4). The Q and B transitions are x-/y-polarized, because there are nondegenerate 1A1g ground states and orbitally degenerate 1Eu ππ* excited states. Magnetic circular dichroism (MCD) spectroscopy played a key role in confirming the validity of this approach, because derivative-shaped x-/ypolarized (1 terms dominate the MCD spectra. The induced

Figure 3. (Left) Electronic transitions and (right) states associated with the Q and B bands of Gouterman’s four-orbital model.54 Reproduced with permission from ref 58. Copyright 2005 American Chemical Society. 3448


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Figure 5. (Left) Michl’s perimeter model in the context of a C16H162− parent perimeter.3−6 The outer circle provides a diagrammatic depiction of the counterclockwise and clockwise motions of electrons around the 16 2pz atomic orbitals. This generates the value of ML for the wave function of each complex MO. (Right) Magnitudes of the induced magnetic moments plotted diagrammatically based on LCAO calculations that were reported by Michl.3−6 Their alignment with respect to the applied magnetic field can be predicted qualitatively using Ampere’s rule for the flow of conventional current in solenoids. The perspective used is toward the light source. Adapted with permission from ref 3. Copyright 1978 American Chemical Society.

Figure 4. Electronic absorption spectra of isomeric octaethylporphyrins, including porphyrin (OEP), porphycene (OEPc), hemiporphyrazine (OEHPc), and corrphycene (OECn) compounds. Adapted with permission from ref 119. Copyright 2002 Wiley-VCH Verlag GmbH & Co. KGaA.

The parent cyclic perimeter can be described as a series of 2pz atomic orbitals, and complex wave functions can be used to describe the circulation of an electron in either a clockwise or counterclockwise direction when the absorption of an incident photon results in electronic excitation. This is not possible with the more conventional real wave functions that are more typically used to describe π-MOs. In the context of tetrapyrrolic porphyrins, the C16H162− parent perimeter has a series of MOs with degenerate complex wave functions4 (Figure 5). Ψ−N and ΨN MOs, where N refers to the value of the ML quantum number, are generated by circulation of electron density in clockwise and counterclockwise directions, respectively, when the perspective used to define the orientation is along the axis of light propagation toward the light source. The angular nodal patterns of the HOMO and LUMO have ML = ±4 and ±5 properties, respectively. This means that spin-allowed oneelectron excitation causes OAM changes of ΔML = ±1 and ±9, which leads to a fully allowed B band and a forbidden Q band at lower energy, because the electron dipole transition moments of the x- and y-polarized components can either add together or cancel. Although, strictly speaking, the forbidden Q band should be referred to as the L band in the context of Michl’s perimeter model, the Q- and B-band nomenclature of Gouterman has been used by most synthetic chemists who have prepared ring-contracted and -expanded and isomeric porphyrin compounds, so this nomenclature is employed consistently throughout this review. In the context of the high-symmetry parent perimeters, the HOMO and LUMO are orbitally degenerate, and there is no net electron circulation in the ground state, because there are no unpaired electrons. Upon electric-dipole-allowed electronic excitation, an electron is promoted to the LUMO, and its motion on the perimeter is no longer balanced by that of an electron in the MO in the HOMO level that has the opposing handedness. The magnitude and alignment of the induced magnetic dipole transition moments that result can be derived experimentally by measuring MCD spectra, so this specialist spectroscopic technique has played an unusually prominent role in porphyrin analogue research, because it facilitates the

definitive assignment of the main electronic Q and B bands.68 Usually, there is greater OAM associated with the LUMO than with the HOMO. This means that the circulation of the electron is the dominant factor when the OAM of the incident left circularly polarized (lcp) or right circularly polarized (rcp) photon is conserved. When a magnetic field is applied along the axis of light propagation during the MCD measurement, the energetically favored alignment is that associated with the clockwise motion induced by an incident rcp photon, because the positive magnetic dipole is aligned with the applied field (Figure 5). This results in a derivative-shaped signal with a −/+ sign pattern from low to high energy, because, by definition, the signal provided by a CD spectrometer is ΔAl−r. This is referred to as a positive Faraday (1 term, because the sign of the (1 term is defined by the ΔAl−r signal of the higher-energy lobe. (1 terms of this type typically dominate the MCD spectra of high-symmetry radially symmetric porphyrinoids with a 4-fold axis of symmetry. When the symmetry of a porphyrinoid is lowered further so that there is no 3-fold or higher axis of symmetry, as is the case with most isomeric porphyrin structures and corrole-type structures, significant spectral changes are observed. The MOs derived from the HOMO and LUMO of the parent perimeter are no longer degenerate, so the x- and y-polarized components of the Q and B bands split, because they no longer lie at the same wavelength. The forbidden and allowed properties of the Q and B bands mix, because the electric dipole transition moments of the x- and y-polarized components of the Q bands can no longer cancel each other. In the context of porphyrinoids, the relative energy separations of the MOs derived from HOMO and LUMO of the parent hydrocarbon perimeter (referred to as the ΔHOMO and ΔLUMO values in Michl’s terminology) have a significant influence on the observed optical properties. When ΔHOMO ≈ ΔLUMO, the Q band remains forbidden, and most of the intensity observed in the Q-band region is derived through vibrational borrowing from the allowed B transition.54 Cyclic perimeters of this type are referred to as soft MCD chromophores, because the 3449


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observed sign sequences of the Q and B bands can be readily reversed by modifications to the structure. When this is not the case, because either ΔHOMO ≫ ΔLUMO or ΔLUMO ≫ ΔHOMO, a so-called hard MCD chromophore is formed with a fixed observed sign sequence. The intensity of the Q band increases as the value of |ΔHOMO − ΔLUMO|2 increases, as a result of the mixing of the allowed and forbidden properties of the B and Q bands.3−6 The observed sign sequences for the Q and B bands in the MCD spectra of low-symmetry porphyrinoid structures can be used to validate the results of DFT and TD-DFT calculations.58−63 Michl demonstrated that the sign sequences observed in the MCD spectrum are determined by whether the OAM of the incident lcp or rcp photon is conserved by the circulation of the positive hole in the HOMO level or the electron in the LUMO level. When ΔHOMO ≫ ΔLUMO, the OAM associated with the excited electron predominates, and there is a −/+/−/+ ΔAl−r intensity pattern with ascending energy for the Faraday )0 terms associated with the Q and B bands. This matches the sign of the Faraday )0 terms only if the conventions that were recommended by Piepho and Schatz are adopted,69,70 which is not always the case even in the recent literature. In contrast, when ΔLUMO ≫ ΔHOMO, the positive hole circulating in the HOMO level is the main factor, and this means that the alignments of the magnetic moments induced by the absorption of incident lcp and rcp photons are switched over so that the observed ΔAl−r signals for the Faraday )0 terms are +/−/+/− in ascending energy terms. Michl3−6 introduced the terminology a, s, −a, and −s for the MOs that are derived from the parent perimeter’s HOMO and LUMO into the literature (Figure 6), so that porphyrinoid πsystems of different point groups and relative MO orderings can be readily compared without having to consult a correlation table. Where appropriate, this convention is employed throughout this review to facilitate a comparison of trends in the electronic structures of porphyrin analogue compounds with differing symmetries. MOs that have nodal planes aligned with the yz plane are referred to as the a or −a MOs depending on whether they are derived from the HOMO or LUMO, respectively, whereas MOs with large MO coefficients on the yz plane are denoted as the s and −s MOs. When the angular nodal planes and the antinodes of the π-system are clearly defined on this basis for each of the frontier π-MOs, the effects of different structural perturbations can be readily predicted, and a consideration of the relative sizes of the ΔHOMO and ΔLUMO values and their effect on the HOMO−LUMO gap can be used to rationalize the main trends that are observed in the optical properties. 2.2.2. 4N Perimeter Model. Michl developed a detailed perimeter model for 4N π-systems7 in the 1990s so that trends in the electronic structures and optical spectra of antiaromatic π-systems can also be analyzed both qualitatively and quantitatively with reference to a parent hydrocarbon perimeter.71−75 There are six rather than four π-MOs involved with this model that are derived from the HOMO, the singly occupied molecular orbital (SOMO), and the LUMO of the parent perimeter. In the context of lower-symmetry compounds, these three levels lose their degeneracy, and the six MOs are referred to as h−, h+, s−, s+, l−, and l+ (Figure 7), with h, s, and l referring to those derived from the HOMO, SOMO, and LUMO, respectively, of the parent perimeter, and − and + referring to the MOs of lower and higher energy,

Figure 6. Angular nodal patterns for the a, s, −a, and −s MOs of zinc porphyrin at an isosurface value of 0.04 au. Michl3−6 introduced this nomenclature to describe whether nodal planes (a and −a) or antinodes (s and −s) are aligned with the y axis. The alignment of the nodal planes is determined by the molecular symmetry, and it can be used to qualitatively assess how structural modifications will affect the relative energies of the frontier π-MOs and, hence, the optical and redox properties, as the MO energies are determined by the relative sizes of the MO coefficients at different positions on the cyclic polyene perimeter.

respectively, in each case. In Figure 7, a C24H244− cyclic perimeter provides the parent perimeter for a bimetallic AuIII hexaphyrin.35 The HOMO, SOMO and LUMO have ML = ±6, ±7, ±8 nodal patterns, respectively. When the symmetry of a C24H244− perimeter is lowered to form the bimetallic hexaphyrin shown in Figure 7, the h−, h+, s−, s+, l−, and l+ MOs are nondegenerate, but the ML = ±6, ±7, ±8 nodal patterns are retained, in a manner analogous to what happens in the context of Michl’s 4N + 2 model. Michl introduced new terminology to describe compounds with 4N perimeters.7 The term antiaromatic is supposed to be used in this context only for compounds that have clear biradical properties as a result of the s− and s+ MOs being close in energy. When there is a large energy gap between these MOs, so that there is an electron pair in the s− MO, the compounds are described instead as “unaromatic”. Subsequently, however, most porphyrinoid researchers have not used this terminology, and compounds of this type are usually said to be nonaromatic. An intrashell s− → s+ transition between the two MOs derived from the SOMO gives rise to the lowest-energy S band of the 4N perimeter model (Figure 7), which usually has nearzero intensity despite being magnetic-dipole-allowed.72 There are four other intershell transitions that involve one-electron electric-dipole-allowed transitions with HOMO → SOMO and SOMO → LUMO character (Figure 7), and this results in two relatively weak (N1, N2) and two more intense (P1, P2) bands, which can be viewed as being broadly analogous to the Q and B bands of the 4N + 2 model. The N1 and P1 bands result from the mixing between the h+ → s+ and s− → l− one-electron transitions through configuration interaction, and their intensities differ because there can be either cancellation or addition of their electron-dipole transition dipole moments. Similarly, the N2 and P2 bands are associated with the h− → s+ and s− → l+ one-electron transitions (Figure 7). 3450


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Figure 7. Angular nodal patterns of the frontier π-MOs with arbitrary sets of nodal lines, relative MO energies, and symmetry labels for an antiaromatic C24H244− cyclic perimeter and the unaromatic electronic structure of a bimetallic AuIII hexaphyrin.35 The s− and s+ MOs correspond to the HOMO and LUMO, respectively. Reproduced with permission from ref 35. Copyright 2009 Wiley-VCH Verlag GmbH & Co. KGaA.

first example of a Möbius-aromatic compound in 2003.77 Subsequently, expanded porphyrinoid structures with far stronger ring currents and aromatic properties that are unambiguously Möbius in character were reported. The first example of a porphyrinoid with Möbius aromaticity, A,D-di-pbenzihexaphyrin, was reported by the Latos-Grażyński group in 200778,79 (Figure 8), and compounds with Möbius antiaromaticity were also subsequently reported.10,11 In recent years, a number of ring-expanded and ring-contracted structures have been reported to exhibit Mö bius aromaticity, including vacataporphyrins,10,80 hexaphyrins,81−85 N-confused hexaphyrins,33 octaphyrins,86−89 decaphyrins,90 and dodecaphyrins.91 The optical spectroscopy of these Möbius-aromatic systems remains broadly analogous to that of their Hückel-aromatic counterparts, because the parent perimeters in both cases have a doubly degenerate HOMO and a doubly degenerate LUMO.53

The perimeter-model approach is most useful when the Q and B bands are the dominant spectral features and there is limited configurational interaction with higher-energy ππ* states, which can become significant for structural analogues in which there is peripheral fused-ring expansion of the pyrrole moieties.58,63 Michl’s (4N + 2)3−6 and 4N7 perimeter models can be most readily applied to free-base porphyrins and complexes that are formed with main-group elements and d10 metals. This means that a perimeter-model approach is applicable to most of the structures that are considered in this review, because, in most cases, there has been comparatively little research on open-shell transition-metal complexes, which have more complex spectra that also contain metal-to-ligand and ligand-to-metal charge-transfer bands. 2.3. Mö bius Aromaticity

In normal planar annulenes such as benzene, the 4N + 2 electrons in the delocalized π-system give the molecule an overall stability associated with a closed-shell Hü c kel occupancy. In contrast, if 4N electrons are present, there is an open-shell electron configuration. The properties of these πsystems, such as their higher reactivity and lower stability compared to aromatic compounds, are referred to as antiaromaticity. Möbius aromaticity has been reported for cyclic polyenes that adopt a Möbius-strip-type conformation with a half-twist to form a nonorientable structure (Figure 1).9 It has been demonstrated that, in Möbius-strip-type structures, 4N pathways are aromatic, whereas 4N + 2 are antiaromatic, which is the reverse of what is normally observed for planar Hückel aromaticity. In contrast, when the structure is doubly twisted to form a figure-eight structure rather than a Mobius strip (Figure 1), the conventional 4N + 2 aromaticity and 4N antiaromaticity Hückel aromaticity rules are restored.12 The existence of Möbius aromaticity was first predicted by Edgar Heilbronner in the 1960s.76 The Herges group reported the

2.4. Quantitative Prediction of Aromaticity

Because aromaticity lies at the core of the study of porphyrin analogues, it is often important to adopt a quantitative approach to determine whether a macrocycle is aromatic or antiaromatic. Although the theoretical treatment of porphyrinoids tends to focus on the comparison of calculated and observed electronic absorption spectra as a way to determine the accuracy of predictions of the electronic structure, predictions of the ring current generated on the macrocycle and comparisons of the geometries of X-ray and optimized geometries are also important. In spectroscopic terms, comparison of the macrocyclic ring current associated with NMR spectroscopy and the associated shielding and deshielding effects is the most obvious approach to adopt. One approach that has been developed in the context of theoretical calculations is to measure nucleus-independent chemical shift (NICS) values to determine the absolute magnetic shielding at 3451


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Figure 8. Three structural topologies that are available for A,D-di-p-benzihexaphyrin. T0, T1, and T2 refer to the numbers of half-twists and, hence, denote planar Hückel, half-twisted Möbius strip, and twisted Hückel topologies, respectively. The T0 and T2 topologies are double-sided, whereas there is an interlocking of the two lobes of the 2pz orbitals in the T1 Möbius strip topology. Reproduced with permission from ref 78. Copyright 2007 Wiley-VCH Verlag GmbH & Co. KGaA.

study the aromatic and antiaromatic properties of porphyrinoids and other cyclic polyene systems. AICD and GIMIC calculations can provide quantitative information about the flow of current along chemical bonds in a manner that facilitates the identification of aromatic conjugated pathways based on a theoretical study of the magnetically induced current density, because the scalar field can be plotted in a manner similar to isosurfaces for π-system MOs (Figure 9). In recent years, the use of AICD plots to determine whether novel core-modified ring-expanded porphyrinoid π-systems have aromatic or antiaromatic properties has been particularly noteworthy.100,108

the center of the macrocyclic ring, by inserting a dummy atom into a DFT calculation.92 The values are reported with the opposite sign from the shielding value provided by the calculation to fit the chemical-shift conventions of NMR spectroscopy. Negative NICS values indicate aromaticity, whereas positive values are consistent with antiaromaticity. Values determined at the core of the macrocycle are referred to as NICS(0) values, whereas NICS(1) values are determined at a point 1 Å above the plane of the π-system. The NICS(0) value provides the average of the three components of the tensors of the chemical shift; however, because the component of the tensor that is most clearly related to the π-system lies perpendicular to the xy plane of the ring, the NICS(0) value understates its effect. In recent years, the NICS(1) value has gained prominence, because it does not contain contributions from in-plane tensor components that depend on the σbonding framework and, hence, are not related to aromaticity.93,94 NICS calculations have proven to be particularly useful in the context of ring-expanded porphyrins.95,96 Another approach that has been used is the harmonic oscillator model of aromaticity (HOMA),97 which provides a normalized sum of the squared values of the bond-length deviations from the value that would be obtained for a fully aromatic system. A fully aromatic ring has a HOMA value of unity, whereas fully nonaromatic compounds have a value of zero. The Herges9,98−100 and Sundholm84,101−107 groups developed anisotropy of the induced current density (AICD) and gauge including magnetically induced current (GIMIC) software to

Figure 9. AICD isosurface plots for free-base porphyrin at isosurfaces of (a) 0.003 and (b) 0.005. Adapted with permission from ref 106. Copyright 2016 American Chemical Society. 3452


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3. PORPHYRINS, CORROLES, AND NORCORROLES Throughout this review, the optical spectroscopy of the ringexpanded and -contracted and isomeric structural analogues of porphyrins, corroles, and norcorroles (Scheme 3) are described in detail using Michl’s perimeter model as the conceptual framework to rationalize trends in their electronic structures and optical properties. In the context of porphyrin complexes with 4-fold major axes of symmetry, the −a and −s MOs are degenerate, because the ML = ±5 nodal patterns are rotated by 90° with respect to each other along either the x or y axis (Figure 2). Although the ΔLUMO value is zero, a nonzero ΔHOMO value is anticipated, because the degeneracy of the a1u and a2u MOs of Gouterman’s four-orbital model energy is lifted because the angular nodal planes lie on two sets of eight alternating atoms (Figure 2). When the symmetry of the C16H162− parent perimeter is lowered to D4h through the introduction of the four pyrrole rings, the s MO is stabilized, because there are large MO coefficients on the pyrrole nitrogen heteroatoms, whereas these atoms lie on the nodal planes of the a MO and, therefore, have very little effect on its energy. The effect of the addition of bridging groups to the perimeter, which is related to the incorporation of fused pyrrole rings, is determined by whether the phases of the 2pz MOs at the points of attachment result in an interaction that is bonding or antibonding. When peripheral substituents or bridging groups are added to a position on a perimeter that corresponds to a

Figure 10. Angular nodal patterns of the frontier MOs of ZnIITPP and BIIIsubP and their relative energies. Reproduced with permission from ref 159. Copyright 2007 American Chemical Society.

Figure 11. Angular nodal patterns and MO energies of a series of isomeric porphyrins predicted at the B3LYP/6-31G(d) level of theory during geometry optimizations with the Gaussian software package.237 When the ΔHOMO and ΔLUMO values from Michl’s perimeter model vary significantly, an intensification of the Q band is anticipated. 3453


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nodal plane, or a heteroatom is introduced at these positions, minimal changes in the MO energy are anticipated. The four C2H2 bridges are added on nodal planes where the s MO is concerned, and hence, there is no significant change in its energy, whereas there is a significant stabilization of the a MO because there are bonding interactions at the points of attachment. The net effects of the introduction of pyrrole nitrogens and C2H2 bridges on the energies of the a and s MOs are very similar, and these MOs are hence said to be neardegenerate. As a result, weak forbidden Q bands are observed in the visible region, because ΔHOMO ≈ ΔLUMO ≈ 0. If the main C4 axis is replaced with a 3-fold axis through the removal of one of the pyrrole rings and meso carbons or if it is replaced by a 5-fold axis of symmetry through the incorporation of an extra porphyrin ring and meso carbon, the ΔHOMO value is unlikely to change significantly from near zero in the absence of another structural perturbation (Figure 10), because the alignment of the nodal planes of the a and s MOs will remain almost unchanged, and the ΔLUMO value will remain zero for symmetry reasons. This means that the electronic structure and optical properties of radially symmetric ring-expanded and -contracted analogues are often broadly similar to those of the parent porphyrin ligand. When the major C4 symmetry axis is removed through symmetry-lowering modifications, the alignments of the angular nodal planes of the a, s, −a, and −s MOs can still be readily defined based on the molecular symmetry if one or more mirror planes lie perpendicular to the π-conjugation system. For example, free-base porphyrins have two planes of symmetry that run through the two oppositely aligned sets of pyrrole nitrogens. The a MOs have nodal planes on the pyrrole nitrogens, whereas the s MOs have antinodes (Figure 11), and the −a and −s MOs have either nodes or antinodes. The introduction of inner NH protons along the y axis leads to a slight lifting of the degeneracy of the −a and −s MOs, because the sizes of the MO coefficients on the different sets of pyrrole nitrogens are no longer equivalent. This leads to a splitting of the Q and B bands into x- and y-polarized components.54 Analyses of the bond lengths in the X-ray structures of porphyrins and other tetrapyrrolic compounds with four meso carbons have consistently shown that trans NH tautomers are favored energetically, as would be anticipated for steric reasons.109 The two possible trans tautomers interconvert through a stepwise trans−cis−trans process.110 In contrast, when corroles are formed through the removal of one of the meso carbons and the formation of a direct pyrrole− pyrrole bond, the observed spectral changes are more significant than is the case for free-base porphyrins. The electronic structures of corroles (Scheme 3) can be analyzed through a consideration of the effects of structural perturbations that are made to the MOs of the parent C15H153− perimeter, which have an ML = 0, ±1, ±2, ±3, ±4, ±5, ±6, ±7 sequence. Because the HOMO and LUMO have ML = ±4 and ±5 properties (Figure 12), this leads to allowed and forbidden B and Q bands by analogy with Gouterman’s fourorbital model111 (Figure 3). In contrast to porphyrin complexes, there is a significant splitting of the −a and −s MOs (Figure 13), because there are markedly different structures along the x and y axes, given that there are only 15 atoms on the inner ligand perimeter. There is a smaller effect on the energies of the a and s MOs, because the nodal planes still lie in broadly similar alignments to what is observed with porphyrins. Because ΔLUMO > ΔHOMO, a hard MCD

Figure 12. MO energies of the frontier π-MOs of P(O) corrole and P(O) 5,10,15-triphenylcorrole model complexes and their angular nodal patterns at the B3LYP/6-31G(d) level of theory and an isosurface value of 0.03 au. The a, s, −a, and −s nomenclature is derived from Michl’s perimeter model3−6 (Figure 6). Reproduced with permission from ref 111. Copyright 2014 American Chemical Society.

Figure 13. Relative energies of the four frontier π-MOs of P(O) corrole and P(O) triphenylcorrole model complexes and phosphorus(V) 5,10,15-tris(4-methoxycarbonylphenyl)corrole (1). The a, s, −a, and −s nomenclature is derived from Michl’s perimeter model3−6 (Figure 6). Red squares are used to plot values for the HOMO−LUMO gaps against a secondary axis. Reproduced with permission from ref 111. Copyright 2014 American Chemical Society.

chromophore is formed with enhanced intensity in the Q-band region (Figure 14). When, as is usually the case, phenyl substituents are added at the three meso carbons, there is a narrowing of the HOMO−LUMO gap due to a relative destabilization of the s MO that is related to the large MO coefficients on the meso carbons (Figures 6 and 12). This causes a significant red shift of the major spectral bands (Figures 4 and 14), but the Q bands are relatively weak when compared to those of the analogous corrolazine compounds,112 because the |ΔHOMO − ΔLUMO|2 values are still relatively small in the absence of the significant splitting of the a and s MOs that is predicted for phthalocyanine analogues. In contrast with free-base porphyrins, free-base corroles have three inner 3454


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Figure 14. Electronic absorption and MCD spectra of phosphorus(V) 5,10,15-tris(4-methoxycarbonylphenyl)corrole. Inset: Fluorescence intensity associated with the Q band. Adapted with permission from ref 111. Copyright 2014 American Chemical Society.

Figure 15. MO energies predicted for the B3LYP-optimized structures of free-base (1) porphyrin and (2) porphycene, (3) corrphycene, (4) hemiporphycene, (5) E-isoporphycene, (6) Z-isoporphycene, the (7) 3H and (8) 2H isomers of singly N-confused porphyrin, and the (9) trans and (10) cis isomers of doubly N-confused porphyrin comparable to those shown in Figure 21, and neoconfused (11) porphyrin and (12) norrole at the B3LYP/6-31G(d) level of theory. Only the dominant NH tautomer is shown in each case (Scheme 1). Blue circles and red triangles are used for the a/−a and s/−s MOs, respectively, of Michl’s four-orbital model (Figure 11). Small black diamonds are used to highlight occupied MOs. Green diamonds are used to plot the HOMO−LUMO gap values against a secondary axis.

stimulated when Ghosh et al. reported that DFT calculations predicted that norcorrole rings should be stable based on having a bis(dipyrrin) polyene structure.116 Subsequently, the Bröring group successfully prepared an Fe(III) complex, which could not be isolated because of its rapid dimerization.117 More recently, Kobayashi and co-workers successfully prepared a stable Ni(II) norcorrole through a facile gram-scale synthesis process involving the formation of a Ni(II) complex with two α,α′-dibromodipyrrins.118 The MCD spectroscopy was found to be consistent with Michl’s 4N perimeter model for antiaromatic compounds, and the NMR spectroscopy provided

NH protons to compensate for the loss of a meso carbon, and this means that two tautomers are possible, with the nonprotonated nitrogen atom either adjacent to or opposite the direct pyrrole−pyrrole bond. These tautomers were reported to be energetically favored in solvents with differing polarities in a manner that leads to solvatochromic properties.113 More recent results suggest that the solvent-dependent optical properties can also be caused by deprotonation in polar solvents.114,115 Interest in norcorroles (Scheme 3), which have two oppositely arranged direct pyrrole−pyrrole bonds, was 3455


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Figure 16. Derivation of the four frontier π-MOs of porphyrin and porphycene from a C20H202+ parent perimeter corresponding to the outer perimeter of the porphyrin macrocycle. The relative sizes of the ΔHOMO and ΔLUMO values can be predicted quantitatively through an inspection of the sizes of the MO coefficients at the points of attachment of the bridging nitrogen atoms when the porphycene ligand is formed. Reproduced with permission from ref 127. Copyright 1991 American Chemical Society.

hemiporphycene (OEHPc), are compared (Figure 4),119 the trends observed spectroscopically follow what would be anticipated based on a perimeter-model approach. The intensities of the bands in the Q-band region (450−700 nm) follow the trend anticipated based on the predicted |ΔHOMO − ΔLUMO|2 values (Figure 11). More intense Q bands are observed in the absorption spectra of OEPc and OEHPc, which have larger ΔLUMO values, than in the spectra of OEP and OECn (Figure 4).

evidence of a paratropic ring-current effect, but no detailed theoretical treatment was attempted.

4. ISOMERIC PORPHYRINS Over the past couple of decades, there has also been a growing focus on the chemistry of isomeric porphyrins (Scheme 1). Interest initially focused on compounds with differing mesocarbon substitution patterns, such as porphycenes, hemiporphycenes, corrphycenes, isoporphycenes, and N-confused structures in which the pyrrole nitrogen is rotated out to one of the peripheral β-positions of the pyrrole ring. When B3LYP optimizations are carried out for these isomeric structures, the perimeter approach can be used to identify several key trends in the electronic structures (Figure 15). A large ΔLUMO value is introduced when the meso-carbon pattern is changed from (1.1.1.1) to (2.0.2.0) to form porphycene, because the effects of the structural perturbation differ markedly along the x and y axes and, hence, the effects on the −a and −s MOs also differ. The Q bands are thus split into well-resolved x- and y-polarized components (Figure 4). A smaller ΔLUMO value is predicted for hemiporphycene, and much smaller splittings are predicted for corrphycene and the E and Z isomers of isoporphycene, where the structural perturbations are almost identical along the x and y axes. When the optical spectra of a series of octaethyl isomeric porphyrin compounds, including porphyrin (OEP), porphycene (OEPc), corrphycene (OECn), and

4.1. Porphycenes

The porphycenes120,121 were the first constitutional isomers of the porphyrins to be reported. They were first prepared by the Vogel group in 1986122 and have subsequently became the focus of considerable research interest.22,123 Their structures have oppositely arranged direct pyrrole−pyrrole bonds and two meso-carbon-atom bridges (Scheme 1). Waluk and co-workers used the 4N + 2 perimeter model and MCD spectroscopy to analyze trends in their electronic structures (Figure 16)124−127 and also studied their NH tautomerism properties.128−133 The presence of trans tautomers is normally assumed for theoretical analyses of the optical properties of porphycenes.124−127,134 The tautomerization processes differ markedly from those of porphyrins and are extremely rapid and complex.133 The (2.0.2.0) meso-carbon pattern causes a large ΔLUMO value (Figures 11 and 16), because the porphycene structure differs significantly along the x and y axes. This leads to an 3456


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Figure 17. (Top) Molecular structures of a porphycene model structure, dibenzoporphycene (H2BHPc), and tetrabenzoporphycene (H2BPc) and (bottom) their calculated TD-DFT spectra, along with the electronic absorption and MCD spectra of a cyclo(2.2.2)butadiene-fused porphycene (H2THPc), H2BHPc, and H2BPc. Adapted with permission from ref 134. Copyright 2009 Wiley-VCH Verlag GmbH & Co. KGaA.

|ΔHOMO − ΔLUMO|2 ≈ 0, so-called soft MCD chromophores are formed, and trends such as those described in the MCD spectra of benzo-substituted porphycenes can be used to validate the accuracy of DFT descriptions of the electronic structures.

intensification and red shift of the Q(0,0) bands (Figure 4) in a manner that is potentially useful for applications, along with a marked splitting of the x- and y-polarized components. It should be noted that Waluk and co-workers used an older set of definitions for the intensity mechanisms of the Faraday terms,68 so the stated sign sequence of the )0 terms in this work was opposite to the observed +/−/+/− sequences in ascending energy terms in the Δεmax values of the MCD spectra. Fused-ring expanded porphycenes have also been studied. For example, Yamada and co-workers prepared free-base diand tetrabenzoporphycenes and their metal complexes134 by carrying out retro-Diels−Alder reactions of bicyclo[2.2.2]octadiene-fused porphycenes. The addition of adjacent benzene rings to form dibenzoporphycene (BHPc) and tetrabenzoporphycene (BPc) led to a red shift of the Q and B bands (Figure 17). A +/− sign sequence was observed in ascending energy terms in the Q-band region because ΔLUMO > ΔHOMO (Figures 11 and 16). In contrast, in the B-band region, −/+ sign sequences can clearly be observed in the H2BHPc and H2BPc spectra, but not in the spectrum of a bicyclo(2.2.2)octabutadine-fused porphycene (THPc). Djerassi and coworkers 135,136 demonstrated that, when |ΔHOMO − ΔLUMO|2 ≈ 0 in the context of chlorins, opposite sign sequences are often observed in the Q- and B-band regions of the MCD spectra, because changes to the structure initially have a larger effect in the Q-band region, because of the larger induced excited-state magnetic dipoles. The Q(0,0) bands of BHPc and BPc are significantly weaker than those of THPc (Figure 17), because the |ΔHOMO − ΔLUMO|2 values are lowered when fused benzene rings are added, as benzo substitution leads to a larger ΔHOMO value because the a MO is destabilized by antibonding interactions at the points of attachment on the pyrrole β-position carbon atoms.134 When

4.2. Corrphycenes and Hemiporphycenes

In 1994, Sessler and co-workers reported the first synthesis of corrphycenes (Scheme 1).137 The ΔHOMO and ΔLUMO values were predicted to be similar (Figure 11), because the structures are similar along the x and y axes because of the (2.1.0.1) meso-carbon pattern. Waluk and co-workers subsequently reported a perimeter-model analysis of the electronic structure and optical properties (Figure 18).138 In 1997, Sessler and co-workers reported the synthesis of hemiporphycenes,139 and Waluk and co-workers analyzed their electronic structures (Figure 19).124 In contrast with the results for corrphycenes, the ΔLUMO values were predicted to be significantly greater than the ΔHOMO values, because the structures differed significantly along the x and y axes as a result of the (2.1.1.0) meso-carbon pattern. This results in a marked intensification of the Q bands (Figure 4). Waluk and co-workers recently used theoretical calculations, X-ray structures, and IR spectral data to demonstrate that the trans NH tautomers of alkyl-substituted corrphycene are more stable than the corresponding cis structures and are likely to always be dominant both in solution and in the solid state.140 4.3. Isoporphycenes

In 1999, Vogel and co-workers reported the first synthesis of isoporphycene as a fourth constitutional isomer of porphyrin.24,141,142 DFT calculations demonstrated that E and Z diastereomers can be formed (Scheme 1). Octaethylisoporphycene was studied, because of its enhanced solubility. This 3457


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Figure 19. Derivation of the four frontier π-MOs of hemiporphycene from a C20H202+ parent perimeter corresponding to the outer perimeter of the porphyrin macrocycle. The sizes of the ΔHOMO and ΔLUMO values can be predicted quantitatively through an inspection of the sizes of the MO coefficients at the points of attachment of the bridging nitrogen atoms when the hemiporphycene ligand is formed. Reproduced with permission from ref 124. Copyright 2002 Elsevier.

Figure 18. Derivation of the four frontier π-MOs of corrphycene from a C20H202+ parent perimeter corresponding to the outer perimeter of the porphyrin macrocycle. The sizes of the ΔHOMO and ΔLUMO values can be predicted quantitatively through an inspection of the sizes of the MO coefficients at the points of attachment of the bridging nitrogen atoms when the corrphycene ligand is formed. Reproduced with permission from ref 125. Copyright 2002 American Chemical Society.

stabilizes the E diastereoisomer, resulting in an E/Z ratio of 49:1.24 The optical spectroscopy is relatively similar to that of the parent porphyrin (Figure 20), as would be anticipated based on the relatively small ΔHOMO and ΔLUMO values (Figure 15). A red shift of the Q and B bands is predicted due to a narrowing of the HOMO−LUMO gap. Subsequently, the redox properties of hemiporphycenes and isoporphycenes were investigated by Sessler and Vogel.143 The authors concluded that the remaining unprepared constitutional isomers of porphyrin would be considerably higher in energy than the relatively labile isoporphycene, making isoporphycene the probable limit for the stability of meso-carbon-based porphyrin isomers. Bremm et al.144 carried out a molecular modeling study on nickel isoporphycenes and demonstrated that peripheral substituents can have a significant impact on the relative stabilities of the E and Z diastereomers. 4.4. N-Confused Porphyrins

Figure 20. Electronic absorption spectrum of the E-stereoisomer of octaethylisoporphycene overlaying the spectra of the analogous porphyrin, porphycene, hemiporphycene, and corrphycene compounds that are shown in Figure 2. Adapted with permission from ref 24. Copyright 1999 Wiley-VCH Verlag GmbH & Co. KGaA.

In 1994, the Furuta and Latos-Graży ń s ki groups 25,26 independently reported the synthesis of N-confused porphyrin in which one of the pyrrole moieties is rotated145 so that a carbon atom sits at one of the four positions on the inner perimeter and a nitrogen atom lies at one of the β-pyrrole positions (Scheme 1).25,26 The tautomerism of N-confused porphyrins (NCPs) involves protonation of both the inner and peripheral nitrogen atoms. Studies have demonstrated that the favored tautomer in this regard changes based on solvent polarity.146,147 In nonpolar solvents, the inner 3H tautomer dominates, whereas in polar solvents, the inner 2H tautomer is

more stable, resulting in a significant solvent dependence of the optical spectroscopy. DFT calculations by the Furuta group on all 96 possible N-confused isomer and tautomer structures predicted a destabilization of ca. 18 kcal.mol−1 for each confused ring moiety in the structure.148,149 Nemykin and coworkers studied the MCD spectroscopy of singly N-confused porphyrins and demonstrated that a +/−/+/− sign sequence is observed because of a large ΔLUMO value.150,151Cis and trans doubly N-confused porphyrins were subsequently synthesized in the form of Cu(III) complexes,152,153 which were used by 3458


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Figure 23. UV−visible absorption spectra of the neoconfused porphyrin shown in the inset (R = CO2Me and R1, R2 = ethyl). A red line is used for the free-base ligand in CH2Cl2, whereas a blue line is used for a monocation species formed in the presence of 5 equiv of TFA, and a purple line is used for a dication species generated in 1% TFA-CH2Cl2. Adapted with permission from ref 29. Copyright 2014 American Chemical Society.

Kobayashi and co-workers to demonstrate that a conventional four-orbital approach can be used to analyze the optical spectra and electronic structures.154 A large ΔLUMO value is predicted for the cis and trans structures (Figure 21) because of the effects that introducing electronegative nitrogen atoms at different positions on the pyrrole moieties have on the energies of the a, s, −a, and −s MOs (Figure 4). When the nitrogen atoms are moved to the β-pyrrole positions of the y-axis pyrrole rings, there is a marked destabilization of the s and −s MOs (Figure 22), which have large MO coefficients at the four core positions, whereas a stabilization is anticipated for the a and −a MOs, which have large MO coefficients on the β-pyrrole carbon atoms where the electronegative confused nitrogen atom is incorporated.

Figure 21. Isosurface plots of the a, s, −a, and −s MOs of zinc porphyrin (ZnPor, 2) and the cis and trans doubly N-confused complexes (cis-1′ and trans-1′) obtained at the HF/6-31G(d) level of theory. Adapted with permission from ref 154. Copyright 2008 Elsevier.

4.5. Neoconfused Porphyrins and Norroles

In 2011, the latest addition to the class of isomeric porphyrins, neoconfused porphyrin (Scheme 5), was reported by the Lash group,29,30 shortly after the Furuta group had reported the corresponding corrole analogues, which are usually referred to as norroles.155 The neoconfused porphyrins have a nitrogen atom at one of the α-carbon positions, rather than at the peripheral β-positions, as is the case for their N-confused counterparts (Schemes 1 and 5). Theoretical calculations were used to demonstrate that the energetically favored tautomer for these compounds has an internal NH that lies opposite the neoconfused moiety, because this minimizes steric and lone pair−lone pair interactions.156 In a manner similar to that observed with NCPs, the s and −s MOs are destabilized, because an electronegative nitrogen atom on the y axis with a large MO coefficient is replaced by a carbon atom (Figure 11). In contrast, the a MO is significantly stabilized, because the αpyrrole carbons of porphyrins, where an electronegative nitrogen atom is introduced, have large MO coefficients. This causes a large ΔHOMO value, but in contrast with phthalocyanines, the Q band does not become the dominant spectral feature (Figure 23), because the low-symmetry also results in a large ΔLUMO value, as the structures of the πconjugation system are markedly different along the x and y axes, resulting in a relatively low |ΔHOMO − ΔLUMO|2 value

Figure 22. Schematic representation of the perturbation of the a, s, − a, and −s MOs after pyrrole inversion. Adapted with permission from ref 154. Copyright 2008 Elsevier. 3459


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Figure 24. Electronic absorption and MCD spectra of a series of BIIIsubP compounds with three 4-methoxyphenyl (MO), tolyl (TL), phenyl (Ph), 4-pyridyl (4py), and 3-pyridyl (3py) meso aryl rings. Adapted with permission from ref 159. Copyright 2007 American Chemical Society.

Figure 25. (Bottom) MCD and electronic absorption spectra of [14]triphyrin(2.1.1) and [14]benzotriphyrin(2.1.1) compounds at 298 K in CHCl3 and (top) the angular nodal patterns of the a, s, −a, and −s MOs of a [14]triphyrin(2.1.1) model compound. Adapted with permission from ref 20. Copyright 2008 American Chemical Society.

(Figure 11). AbuSalim and Lash recently used a series of theoretical calculations to explore whether five doubly neoconfused porphyrin structures and 54 neoconfused N-confused porphyrin tautomers are likely to be synthetically accessible and concluded that the most stable neoconfused N-confused

porphyrin tautomers might prove to be, because they have stabilities comparable to those of their doubly N-confused counterparts.157 As is the case with porphyrins and corroles, the alignments of the angular nodal planes of the a, s, −a, and −s MOs of norroles remain largely unchanged relative to those of 3460


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components,155 but the MCD spectroscopy of these compounds and their norrole analogues, which would definitively identify the main electronic origins of the Q and B transitions, has yet to be reported.

5. RING-CONTRACTED PORPHYRINS Although the synthesis of the analogous tetraaza compounds, boron subphthalocyanines (BsubPcs), was reported as far back as 1972,158 similar progress on boron subporphyrins159 (BsubPs) and boron subtribenzoporphyrins160 was not reported until 2006. Detailed analyses of the optical spectroscopy and electronic structures of ring-contracted triphyrin compounds have demonstrated that a perimeter-model approach can be used to understand key trends in their properties.54,161 5.1. Subporphyrins

The optical spectroscopy of subporphyrins (Scheme 3) can be readily understood in terms of a C12H122− perimeter with an ML = 0, ±1, ±2, ±3, ±4, ±5, 6 sequence in the MO energies. In contrast with tetrapyrrole porphyrins, there is a C3 symmetry axis. The MOs derived from the HOMO of the parent perimeter have ML = ±3 nodal properties and are neardegenerate in a manner similar to what is predicted for the a and s MOs of porphyrins (Figures 2, 6, and 10), whereas the MOs derived from the LUMO have ML = ±4 nodal patterns and remain degenerate (Figure 10). Figure 24 displays the optical spectra of a series of subPs with different meso aryl substituents and a μ-oxo dimer compound. The intense band in the 370−380-nm region can be assigned to the B transition (Figure 10), whereas the weaker absorption bands in the 400− 540-nm region can be readily assigned as Q bands, because the relative intensification that is observed in this region of the MCD spectrum is consistent with the larger ΔML = ±7 induced magnetic moment that would be anticipated by analogy with Gouterman’s four-orbital model for conventional porphyrins.54 TD-DFT calculations provided further support for these assignments.159

Figure 26. Series of vacataporphyrin stereoisomers (VPH2-n)H that were obtained at the B3LYP/6-31G** level of theory. The projections shown emphasize the differences among the conformations. Reproduced with permission from ref 10. Copyright 2008 American Chemical Society.

the parent porphyrin structure when a meso carbon is removed (Figure 11). There is a significant narrowing of the HOMO− LUMO gap and a marked red shift of the Q and B bands relative to what is predicted and observed for neoconfused porphyrin (Figure 15), due primarily to a destabilization of the s MO that is related to the loss of the meso carbon atom. The large ΔHOMO and ΔLUMO values appear to result in Q and B bands that are split into well-separated x- and y-polarized

Figure 27. MO energies predicted for free-base (1) porphyrin and (2) porphycene, (3) [22]pentaphyrin(1.1.1.1.1), (4) sapphyrin, (5) smaragdyrin, (6) isosmaragdyrin, (7) ozaphyrin, (8) [26]hexaphyrin(1.1.1.1.1.1), (9) rubyrin, and (10) bronzaphyrin at the B3LYP/6-31G(d) level of theory using the Gaussian software package.237 Only the dominant NH tautomer is shown in each case (Schemes 2 and 4). Blue circles and red triangles are used for the a/−a and s/−s MOs, respectively, of Michl’s four-orbital model (Figures 28 and 29). Small black diamonds are used to highlight occupied MOs. The HOMO−LUMO gap values are plotted against a secondary axis and are denoted by green diamonds. 3461


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Figure 28. Angular nodal patterns and MO energies of a series of pentaphyrins predicted at the B3LYP/6-31G(d) level of theory using the Gaussian software package.237 When the ΔHOMO and ΔLUMO values from Michl’s perimeter model vary significantly, an intensification of the Q band is anticipated when there is a large |ΔHOMO − ΔLUMO|2 value.3−6

Figure 29. Angular nodal patterns and MO energies of a series of hexaphyrins predicted at the B3LYP/6-31G(d) level of theory using the Gaussian software package.237 When the ΔHOMO and ΔLUMO values from Michl’s perimeter model vary significantly, an intensification of the Q band is anticipated when there is a large |ΔHOMO − ΔLUMO|2 value.3−6

large substituents effects are observed at shorter wavelengths because subporphyrins are soft MCD chromophores with ΔHOMO ≈ 0 and ΔLUMO ≈ 0 (Figure 10). In the B-band region, subPs with electron-donating meso phenyl groups such

It is noteworthy that the MCD spectra of subPs differ markedly depending on the properties of aryl rings that are introduced at the three meso positions (Figure 24). Although a −/+ sequence is consistently observed in the Q-band region, 3462


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Scheme 6. Molecular Structures of Cyclo[8]pyrrole, Cyclo[4]naphthobipyrrole, Cyclo[8]isoindole, and Cyclo[8]acenaphthopyrrole

as 4-methoxyphenyl (MOsubP) and tolyl (TLsubP) rings (Figure 24) exhibit intense −/+ sign sequences in ascending energy terms. In contrast, a +/− pattern is observed in the spectra of complexes with electron-withdrawing meso phenyl rings, such as 3-pyridyl (3pysubP), 4-pyridyl (4pysubP), and (4-trifluoromethyl)phenyl (TFsubP) groups. The higherenergy positive lobe of the B band of MOsubP becomes less intense in the cases of TLsubP and PhsubP (Figure 24), so that only a negative lobe is observed in the spectrum of PhsubP. Subsequently, there is positive MCD intensity at lower energy in the spectrum of 3PysubP, which further intensifies in the TFsubP and 4PysubP spectra (Figure 24) until the positive and negative lobes have almost equal intensities in the spectrum of the latter. The s MO has large MO coefficients on the meso carbons (Figure 11), so the ΔHOMO value can change with respect to the ΔLUMO value. A detailed theoretical analysis that focused on the magnitudes of the induced magnetic moments of the excited states was reported by Ceulemans and co-workers,162 who suggested that the Q band of subporphyrins should be referred to as the S band based on shichi, the Japanese word for seven, because of a belief that the Q-band terminology used by Gouterman for tetraphyrins had originally been inspired by the use of the Japanese word for nine, kyuu, by a Japanese co-worker. This anecdote might have been apocryphal, however, as the Q-band terminology was already in use by Platt in the mid-1950s prior to Gouterman’s work,65 with the explanation for its adoption being that the properties of the porphyrin Q excited state are very different from those of the analogous L excited state of benzene64 in terms of their behavior toward structural modifications such as peripheral substitution. 5.2. [14]Triphyrins(2.1.1) Figure 30. MO energies and angular nodal patterns at an isosurface value of 0.04 au for the four frontier π-MOs of cyclo[8]pyrrole, cyclo[8]isoindole, and two isomers of two different isomeric structures of cyclo[8]acenaphthopyrrole in TD-DFT calculations at the B3LYP/ 6-31G(d) level of theory. Reproduced with permission from ref 190. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

Shen and co-workers reported the serendipitous synthesis of free-base [14]triphyrin(2.1.1) in 2008 (Scheme 3).20 The key difference between [14]triphyrin(2.1.1) and subporphyrins is that there is an extra meso carbon atom, which facilitates the formation of the free-base ligand, because a 14-π-electron system can be formed in the presence of a single NH proton. The electronic properties can be rationalized through a comparison with a C14H14 parent perimeter with MOs arranged in an ML = 0, ±1, ±2, ±3, ±4, ±5, ±6, 7 sequence.19,20 The angular nodal patterns of the a, s, −a, and −s MOs are similar to those of BsubPs (Figures 10 and 25). The MCD spectra of [14]triphyrins(2.1.1) contain coupled pairs of Gaussian-shaped Faraday )0 terms of opposite signs that are similar to those that

have been reported in the spectra of low-symmetry porphyrin and phthalocyanine analogues,19,20 because the addition of an extra meso carbon means that there is no 3-fold or higher axis of symmetry. The electronic absorption spectra of free-base [14]triphyrin(2.1.1) and its benzo-fused analogue (Figure 25) contain intense B bands at 370 and 414 nm, respectively, along with less intense Q bands between 500 and 600 nm.19,20 In 3463


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Figure 33. UV−visible absorption and fluorescence emission spectra of [22]pentaphyrin(1.1.1.1.1), sapphyrin, isosmaragdyrin, and orangarin compounds in CH2Cl2. Adapted with permission from ref 169. Copyright 2008 American Chemical Society. Figure 31. UV−visible absorption spectra of cyclo[8]pyrrole, cyclo[8]isoindole, and cyclo[8]acenaphthopyrrole with TD-DFT calculations at the B3LYP/6-31G(d) level of theory plotted against a secondary axis. Adapted with permission from ref 190. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

recent years, Michl’s 4N + 2 perimeter model has been used to analyze the properties of a series of metal complexes.163−165 5.3. Vacataporphyrins

Vacataporphyrin is the trivial name that has been adopted for [18]triphyrin(6.1.1) structures (Scheme 3). In 2002, the LatosGrażyński group21 reported the formation of 5,10,15,20tetraaryl-21-vacataporphyrin through the subtraction of a tellurium atom from the corresponding 5,10,15,20-tetraaryl21-telluraporphyrin, which can be viewed as an annulene− porphyrin hybrid that forms an [18]triphyrin(6.1.1) structure. The optical spectroscopy of these vacataporphyrin compounds can be readily understood in terms of Q and B bands, because there is an 18-π-electron macrocycle. The properties of metal coordination complexes of vacataporphyrins were comprehensively reviewed by Latos-Grażyński and co-workers.166 The palladium complexes are particularly noteworthy, because they have been demonstrated to adopt both Hückel and Möbius aromaticity based in part on the use of NICS calculations obtained using the gauge-including atomic orbitals (GIAO)B3LYP method for a series of free-base vacataporphyrin stereoisomer structures (Figure 26). The Hückel-aromatic (VPH2-1)H and (VPH2-3)H structures were found to have NICS(0) values of −13.6 and −7.7 ppm,10 respectively, comparable to the −16.5 ppm value predicted for porphyrin,167 whereas the Möbius-antiaromatic (VPH2-4)H and (VPH2-5)H conformers had values of +6.0 and +4.0 ppm, respectively, which are comparable to the value of +5.0 ppm reported previously for 22-hydroxybenziporphyrin.168

Figure 32. MO energies of cyclo[8]pyrrole, cyclo[8]isoindole (2), and two isomeric structures of cyclo[8]acenaphthopyrrole (1a and 1b) in TD-DFT calculations at the B3LYP/6-31G(d) level of theory. Light gray lines are used to highlight the MOs that are associated with the πMOs of the parent C24H246− cyclic perimeter, and the relevant ML values are provided on the left. The MOs that are offset to the right are associated with the SO42− anion in the central cavity. The MO energy values and angular nodal patterns of the four frontier π-MOs with ML = ±7, ±8 properties are provided in Figure 30. Adapted with permission from ref 190. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA.

6. RING-EXPANDED PORPHYRINS In recent years, there has been considerable interest in the synthesis of ring-expanded porphyrin analogues, because their properties are markedly different from those of tetrapyrrolic porphyrins and there are a number of potential applications. 3464


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terparts, there is a narrowing of the HOMO−LUMO gap as a result of the extension of the π-conjugation system, and hence, a red shift of the main spectral bands is anticipated. This has been observed experimentally, with the main B band shifting from ca. 420 nm for porphyrins to ca. 480 nm for [22]pentaphyrin(1.1.1.1.1)169 and ca. 570 nm for [26]hexaphyrin(1.1.1.1.1.1)81 and the main Q band shifting from 550−650 nm for porphyrin (Figure 4) to 750−850 nm for [22]pentaphyrin(1.1.1.1.1)169 and ca. 780 and 1020 nm for [26]hexaphyrin(1.1.1.1.1.1).81 In a manner similar to that observed for the corroles, the introduction of one or two direct pyrrole−pyrrole bonds into the structures of [22]pentaphyrin(1.1.1.1.1) and [26]hexaphyrin(1.1.1.1.1.1) leads to the formation of sapphyrins, smaragdyrins, isosmaragdyrins, and rubyrins, which retain 4N + 2 aromatic properties through the addition of extra inner NH protons (Schemes 2 and 4). In contrast, the introduction of three or four direct pyrrole−pyrrole bonds leads to the formation of orangarins, rosarins, and amethyrins with 4N antiaromatic properties in a manner analogous to those observed for the norcorroles (Scheme 5), because the addition of extra NH protons is disfavored for steric reasons. Coremodified ozaphyrin and bronzaphyrin compounds with structures analogous to those of porphycenes have also been reported (Schemes 2 and 4), and cyclo[n]pyrrole structures with six or more pyrroles and no meso carbons can be stabilized by complexing a negative anion. Generally, steric considerations determine the dominant tautomer of neutral free-base pentaphyrins and hexaphyrins (Schemes 2 and 4), and their spectroscopic properties have been analyzed on this basis,14−18,170−174 using an approach similar to that used for isomeric porphyrins.124−127,134,137 Rapid tautomerization processes are likely to occur in solution, however, as is the case with porphyrins and their isomeric analogues (Scheme 1). For example, Sessler et al. used low-temperature 1H NMR spectroscopy to study the inner NH tautomerism of free-base

Figure 34. Optical spectra in (CH2Cl2) of (A) (···) free-base and () dication octamethylporphyrin in the presence of trifluoroacetic acid and (B) (···) free-base and () dication decamethylsapphyrin in the presence of trifluoroacetic acid. Reproduced with permission from ref 193. Copyright 1983 American Chemical Society.

When B3LYP optimizations are carried out for Hückelaromatic pentaphyrins and hexaphyrins, several key trends observed in the MO energies and nodal patterns of the four frontier π-MOs can be readily identified by using a perimetermodel approach (Figures 27−29). Upon moving from conventional free-base porphyrins to their [22]pentaphyrin(1.1.1.1.1) and [26]hexaphyrin(1.1.1.1.1.1) coun-

Figure 35. Derivation of the four frontier π-MOs from a C24H242+ parent perimeter corresponding to the outer perimeter of the sapphyrin ligand. The sizes of the ΔHOMO and ΔLUMO values can be predicted quantitatively through an inspection of the sizes of the MO coefficients at the points of attachment of the bridging nitrogen atoms and the four meso carbon positions when the sapphyrin and tetraphenylsapphyrin ligands are formed. Reproduced with permission from ref 171. Copyright 2002 Wiley-VCH Verlag GmbH & Co. KGaA. 3465


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Figure 36. (Bottom) Absorption and (middle) MCD spectra of a protonated 16,20-dibutyl-2,3,6,7,10,11,15,21-octamethyl-isosmaragdyrin species in acetonitrile at 293 K. (Top) Calculated INDO/S spectrum for the energies and intensities of Faraday )0 terms. The −B scale is used here so that an older set of MCD intensity unit definitions matches the signs of the observed CD signal. Adapted with permission from ref 196. Copyright 2001 American Chemical Society.

Figure 38. MO energy diagrams for (a) sapphyrin and (b) orangarin. The nodal patterns shown on the right-hand side are consistent with Michl’s 4N perimeter model. Reproduced with permission from ref 172. Copyright 2004 Royal Society of Chemistry.

years. In 2002, Sessler and co-workers reported that cyclo[8]pyrrole can be formed through an oxidative coupling of 2,2′bipyrrole with FeCl3.178,179 The main structural difference from conventional porphyrins is that there are no meso carbon atoms.180−184 A key difference from conventional porphyrins is that the ligands bind anions, such as SO42−, through hydrogenbonding interactions with protonated pyrrole nitrogens. The anion-binding,180,181 liquid-crystal,182 and photophysical properties185 of cyclo[n]pyrroles (n = 6−8) have been studied, and trends in their electronic structures have been analyzed.183,186 More recently, research on cyclo[n]pyrroles has tended to focus on fused-ring-expanded compounds, such as cyclo[8]isoindoles,187 cyclo[4]naphthobipyrroles,188,189 and cyclo[8]and cyclo[10]acenaphthopyrroles (Scheme 6),190,191 which have different ring moieties added at the β-positions. This tends to result in nonplanarity due to the steric effects between adjacent peripheral fused rings. For example, an X-ray structure for cyclo[4]naphthobipyrrole188 exhibits a saddle-type conformation in which the pyrrole nitrogen atoms exhibit a small mean deviation from the core plane. Trends in the optical properties and TD-DFT calculations of cyclo[8]pyrrole, cyclo[8]isoindole, and cyclo[8]acenaphthopyrrole190 (Figure 31) can be readily understood with reference to a parent C24H246− hydrocarbon that has MOs arranged in an ML = 0, ±1, ±2, ..., ±10, ±11, 12 sequence. The a and s MOs have ML = ±7 nodal properties (Figure 30), whereas ML = ±8 nodal patterns are observed for the −a and − s MOs. In a manner analogous to Gouterman’s four-orbital model for conventional porphyrins,54 this leads to allowed and forbidden B and Q bands with ΔML = ±1 and ±15 properties, respectively. There is a marked red shift and relative intensification of the main band in the visible region upon annulation with fused acenaphthalene rings (Figure 31), as a result of the larger ΔLUMO values of cyclo[8]acenaphthopyrrole (Figure 30). A red shift of both the Q and B bands is observed, because there is a narrower HOMO−

Figure 37. Total π-current density maps for (a) sapphyrin and (b) orangarin. The blue and red colors distinguish diamagnetic and paramagnetic ring currents, respectively. The intensity of color represents the relative magnitude of current density. Reproduced with permission from ref 172. Copyright 2004 Royal Society of Chemistry.

decaalkylated sapphyrins and concluded that a complex equilibrium is involved even at cryogenic temperatures.175 When the macrocycles are expanded to form hexaphyrins and larger rings, there is greater scope for nonplanar structures and the formation of structures with Möbius-aromatic properties. The spectroscopic properties and Hückel and Möbius aromaticity of ring-expanded porphyrins have been reviewed several times in recent years.8,12,78,176,177 In 2011, LatosGrażyński and co-workers published a comprehensive review of the various possible topologies that are involved.12 This review focuses instead on the applications of the perimeter-model approach that have been carried out by various different research groups to study trends in their electronic structures and optical properties. 6.1. Cyclo[n]pyrroles

Cyclo[n]pyrroles, such as cyclo[8]pyrrole {[30]octaphyrin(0.0.0.0.0.0.0.0)} (Scheme 6) and its smaller cyclo[6]pyrrole and cyclo[7]pyrrole and larger cyclo[9]pyrrole analogues, are a class of ring-expanded porphyrinoids that has been the subject of considerable research interest in recent 3466


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Figure 39. Planar Hückel and Möbius twist topologies adopted by (a) [26]hexaphyrin(1.1.1.1.1.1) and (b) [28]hexaphyrin(1.1.1.1.1.1) compounds. Reproduced with permission from ref ref 81. Copyright 2008 American Chemical Society.

Figure 41. (a) MCD and absorption spectra of a [28]hexaphyrin(1.1.1.1.1.1) compound measured in CH2Cl2 at room temperature. (b) ZINDO/S absorption spectra calculated using the (top) Möbius strip and (bottom) planar Hückel B3LYP-optimized structures in the insets. Adapted with permission from ref 81. Copyright 2008 American Chemical Society.

Figure 40. (a) MCD and absorption spectra of a [26]hexaphyrin(1.1.1.1.1.1) compound measured in CH2Cl2 at room temperature. (b) ZINDO/S absorption spectrum calculated using the B3LYP-optimized structure in the inset. Adapted with permission from ref 81. Copyright 2008 American Chemical Society.

LUMO band gap (Figure 32), due to a significant stabilization of the LUMO relative to cyclo[8]isoindole that is related to differences in the interactions between the cyclo[8]pyrrole core and the peripheral fused benzene and acenaphthalene rings. When peripheral rings are added, the effect on the MO energies is determined primarily by the magnitude and relative phases of the MO coefficients at points of attachment, because they determine whether there is a destabilizing antibonding or stabilizing bonding interaction.6 The LUMO of cyclo[8]isoindole has significant MO coefficients at the points of

attachment (Figure 30), so the sign change in the phases leads to a marked destabilization relative to cyclo[8]pyrrole. In contrast, the first atoms of the acenaphthylene moieties of cyclo[8]acenaphthopyrrole lie on or close to nodal planes in the LUMO, so there is no such destabilization. 6.2. Pentaphyrins

6.2.1. [22]Pentaphyrins(1.1.1.1.1). There has been comparatively little interest in [22]pentaphyrin(1.1.1.1.1) compounds (Scheme 2) in recent decades. Kim and co3467


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Figure 42. Cycloreversion reaction of the dithienylethene moiety and the structures of the rubyrins with the “open form” (left, compound O-1) and the “closed form” (right, compound C-1) of dithienylethene. Reproduced with permission from ref 108. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.

workers169 reported an NICS(0) value of −16.2 ppm for a fully protonated [22]pentaphyrin(1.1.1.1.1) trication species at the B3LYP/6-31G* level of theory, so the aromaticity is predicted to be comparable to that of conventional porphyrins. The ΔHOMO value of [22]pentaphyrin(1.1.1.1.1) is predicted to be significantly larger than the ΔLUMO value (Figures 27 and 28), and this leads to a moderately intense Q band at ca. 800 nm (Figure 33).169 In recent years, there has been interest in the two-photon absorption169 and 1O2 photosensitizer170,192 properties of [22]pentaphyrin(1.1.1.1.1) compounds. 6.2.2. Sapphyrins. In the 1960s, the first reported example of a ring-expanded porphyrin was initially discovered serendipitously by Woodward and co-workers, although its detailed analysis was not reported until the 1980s.193 Sapphyrin (Scheme 2) was adopted as a trivial name because the compound forms dark blue crystals. A similar color-based trivial nomenclature was later adopted for other ring-expanded macrocycles. Sapphyrins have [22]pentaphyrin(1.1.1.1.0) structures and an extra inner proton NH, so the heteroaromatic πsystem is maintained. Kim and co-workers169 reported an NICS(0) value of −14.9 ppm for a fully protonated sapphyrin dication species at the B3LYP/6-31G* level of theory. The Q and B bands lie about 80 nm to the red of those of the analogous octamethylporphyrin (Figure 34), as a result of the narrowing of the HOMO−LUMO gap upon ring expansion (Figure 27).193 Because the ΔHOMO and ΔLUMO values are predicted to be almost identical (Figures 27 and 28), sapphyrins are expected to be soft MCD chromophores with weak Q bands (Figure 33) and hence, to have MCD sign sequences that change when the structure is modified. In 2002, Waluk and co-workers reported a perimeter-model approach to the optical spectroscopy and electronic structures of sapphyrins (Figure 35)171 and demonstrated that the addition of four meso phenyl rings results in the observed MCD sign sequence changing from +/−/+/− to −/+/−/+, because the ΔHOMO value becomes greater than the ΔLUMO value. 6.2.3. Smaragdyrins and Isosmaragdyrins. In 1972, Grigg, and co-workers reported the synthesis of a new type of [22]pentaphyrin(1.1.0.1.0) macrocycle with two direct pyrrole−pyrrole bonds, which they referred to as norsapphyrins but which are now generally referred to as smaragdyrins

(Scheme 2).194 The ΔHOMO and ΔLUMO values of the free base are predicted to be roughly comparable (Figures 27 and 28), so a soft MCD chromophore is anticipated. In 1998, Sessler and co-workers successfully prepared the first example of a [22]pentaphyrin(1.1.1.0.0) macrocycle that is generally referred to as isosmaragdyrin.195 Waluk and co-workers subsequently reported an in-depth study of its optical spectroscopy as well as theoretical calculations.196 The authors demonstrated that, although the optical properties initially appear to be very different from those of conventional tetrapyrrolic porphyrins, a four-orbital model approach can be readily be used to analyze their spectral properties so that the major bands can be assigned to the Q and B transitions. In contrast with what is predicted for smaragdyrin (Figure 27), there is a relatively intense Q band (Figures 33 and 36) because of the large |ΔHOMO − ΔLUMO|2 value (Figure 28). The ΔLUMO value is significantly greater than the ΔHOMO value, because the structure differs significantly along the x and y axes (Scheme 2). Kim and co-workers169 reported an NICS(0) value of −14.1 ppm for a protonated isosmaragdyrin cation species at the B3LYP/6-31G* level of theory. 6.2.4. Orangarins. In 1990, Sessler and co-workers reported the formation of a novel [20]pentaphyrin(1.0.1.0.0) macrocycle with three direct pyrrole−pyrrole bonds197 (Scheme 2) that was referred to as orangarin because of its bright orange color. Because orangarins have only three inner NH protons, a 4N π-system is anticipated. As expected, no Q band is observed in the UV−visible absorption spectrum (Figure 33). Theoretical studies by Steiner and Fowler demonstrated that orangarins generate the anticipated paramagnetic ring current172 (Figure 37). Because of the low symmetry, a large gap is predicted between the s− and s+ MOs derived from the doubly degenerate SOMO of the parent C20H20 perimeter (Figure 38). Kim and co-workers169 reported an NICS(0) value of +42.9 ppm at the B3LYP/6-31G* level of theory for a fully protonated dication species, which is consistent with a very strong paratropic ring current. 6.2.5. Ozaphyrins. In 1993, Ibers and co-workers reported the synthesis of an ozaphyrin (Scheme 2).31 Subsequent attempts to prepare the parent non-core-modified structure were unsuccessful, so the electronic structures of the [22]3468


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(Figure 39). An analysis of semiempirical ZINDO/S calculations and MCD spectra (Figure 40), along with NICS and HOMA calculations, provided definitive evidence that the Q bands of [26]hexaphyrin(1.1.1.1.1.1) compounds lie at ca. 770 and 1020 nm and the B band lies at ca. 570 nm. A similar approach (Figure 41) demonstrated that the optical spectra of the [28]hexaphyrin(1.1.1.1.1.1) compounds that were studied were consistent with a Möbius-strip topology, rather than those predicted for an antiaromatic Hückel structure, with Q- and Btype bands arising from transitions among the four frontier MOs derived from the HOMO and LUMO of a parent C28H28 Möbius perimeter. 6.3.2. Rubyrins. In 1991, Sessler et al. reported the preparation of the deprotonated form of [26]hexaphyrin(1.1.0.1.1.0) (rubyrin) (Scheme 4), resulting in the formation of a planar heteroaromatic ligand.17 Subsequently, rubyrins have tended to be prepared as core-modified compounds with heteroatoms such as sulfur replacing the protonated pyrrole nitrogens.42,198 Although there has been no perimeter-model-type study of the parent rubyrin compound, Shen and co-workers108 recently reported a study of the electronic structure and electronic properties of a core-modified N2S4-type rubyrin with embedded dithienylethene moieties (Figure 42), with either a closed dithienylethene moiety (C-1) or both an open and a closed dithienylethene moiety (O-1). The properties of the C-1 and O-1 structures were found to be consistent with Michl’s 4N + 23−6 and 4N7,71−75 perimeter models when AICD and TD-DFT calculations were carried out (Figures 43 and 44). A strong diatropic ring current is

Figure 43. AICD plots of (a) C-1 and (b) O-1 with the isosurfaces set at 0.065 (Figure 41). A magnetic field is applied orthogonally to the plane of the macrocycle so that its vector points out of the page. The green lines and red conic sections plotted on the isosurface provide the current density vectors. Reproduced with permission from ref 108. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA.

pentaphyrin(2.0.2.0.0) parent compounds have yet to be explored in depth. A large |ΔHOMO − ΔLUMO|2 value is predicted for ozaphyrin (Figures 27 and 28), as there is a large ΔLUMO value similar to that of porphycenes because of the [22]pentaphyrin(2.0.2.0.0) structure, which results in significant structural differences along the x and y axes. 6.3. Hexaphyrins

6.3.1. [26]Hexaphyrins(1.1.1.1.1.1). Although [26]hexaphyrin(1.1.1.1.1.1) compounds can adopt Hückel-aromatic structures in a manner similar to porphyrins and [22]pentaphyrin(1.1.1.1.1), Osuka and co-workers81 demonstrated that Möbius structures can also be accessed upon two-electron reduction to form [28]hexaphyrin(1.1.1.1.1.1) compounds

Figure 44. UV−visible absorption spectra of C-1 (1c) and O-1 (2o) (Figure 41) and calculated TD-DFT oscillator strengths of the X-ray structure of C-1 and a B3LYP geometry of O-1 plotted against a secondary vertical axis. Red diamonds are used to highlight the Q and B or S, N1/2, and P1/2 bands from the 4N + 23−6 and 4N7 perimeter models. Reproduced with permission from ref 108. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA. 3469


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Figure 45. Electronic absorption, MCD, and TD-DFT spectra of aromatic and unaromatic bismetallic AuIII hexaphyrin species (Au2-N and Au2-R; Figure 7). Reproduced with permission from ref 35. Copyright 2009 Wiley-VCH Verlag GmbH & Co. KGaA.

predicted for C-1, whereas the AICD plot for O-1 is consistent with nonaromaticity (Figure 43). The intensities of the MCD bands of O-1 are weaker than those observed for C-1 by an order of magnitude, because there are very weak induced magnetic moments for the excited states as a result of the absence of a complete π-conjugation pathway.108 6.3.3. Rosarins, Amethyrins, and Isoamethyrins. In 1992, Sessler and co-workers reported the formation of a nonaromatic [24]hexaphyrin(1.0.1.0.1.0) macrocycle that, upon analysis of its NMR spectroscopy, was found to lack a significant ring current.173 Waluk and co-workers subsequently demonstrated that a six-orbital approach consistent with Michl’s 4N perimeter model has to be employed to describe the electronic structures and optical properties of rosarins (Scheme 4).199 In 1995, Sessler et al. reported the synthesis of a [24]hexaphyrin(1.0.0.1.0.0). These compounds are normally referred to as amethyrins (Scheme 4), as amethus is the Greek word for purple.15 Amethyrin represented the first ringexpanded porphyrin to be reported to have multiple modes of cation complexation and the first in which the in-plane coordination of two cations was unambiguously established. Sessler and co-workers also subsequently reported the synthesis of [24]hexaphyrin(1.0.1.0.0.0) compounds, which are referred to as isoamethyrins and can be oxidized through complexation with actinide ions to form aromatic [22]hexaphyrin(1.0.1.0.0.0) species.200 In a manner similar to that used to investigate orangarins,172 theoretical calculations were used by Steiner and

Fowler to study the ring currents of amethyrins and to demonstrate that their electronic structures are not Hückel aromatic.174 6.3.4. Bronzaphyrins. In 1992, Ibers and co-workers reported the formation of a [26]hexaphyrin(2.0.0.2.0.0) macrocycle (Scheme 4) that contains two thiophene moieties between two sets of direct thiophene−pyrrole bonds.32 Subsequent attempts to form the parent structure with six pyrrole rings proved unsuccessful,201 so the electronic structures of the [26]hexaphyrin(2.0.0.2.0.0) parent compounds have yet to be explored in depth. However, in a manner analogous to the porphycenes, a very large ΔLUMO value is anticipated (Figure 27), which would be expected to result in a very intense Q band in the near-IR range, making these compounds potentially suitable for applications that require strong absorption in this region of the spectrum. 6.4. N-Confused Ring-Expanded Porphyrins

In recent years, there have been many reports of N-confused ring-expanded porphyrin structures.202 Of particular interest have been the preparation of singly N-confused sapphyrins203,204 and the ability of doubly N-confused hexaphyrins34,205−210 to complex two central metal ions. Relatively few detailed theoretical analyses have been carried out on these compounds to identify trends in the electronic structures in a systematic manner, but a perimeter-model approach can still be used as a conceptual framework for studying trends in the 3470


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electronic structures and optical properties. A good example of the type of analysis that could be carried out is provided by the AuIII complexes of meso-hexakis(pentafluorophenyl)-substituted hexaphyrin(1.1.1.1.1.1),34,35 which have multiple gold−carbon bonds. Two-electron reduction of the 26-π-electron aromatic AuIII hexaphyrins (Au2-N) leads to a reduced 28-π-electron species (Au2-R). Kobayashi and co-workers demonstrated that the absorption spectrum is dramatically changed in this context, because the electronic structure of the Au2-R species is unaromatic in the context of Michl’s terminology (Figure 7). The key difference is that the bands that are observed in the near-IR region of the Au2-N spectrum are absent in the Au2-R spectrum (Figure 45). The MCD spectra were found to be consistent with the results of TD-DFT calculations,35 because the optical spectra of Au2-N and Au2-R can be assigned to the Q and B and S, N1/2, and P1/2 bands of Michl’s 4N + 23−6 and 4N7,71−75 perimeter models, respectively.

aromaticity, such as three-dimensional aromaticity due to the stacking of planar antiaromatic structures.214,215 The recent examples provided for how a perimeter-model approach can be used to identify the effects of core modification and fused-ring expansion on the electronic structures and optical properties of rubyrins108 and cyclo[n]pyrroles190,191 highlight that the analysis of a far wider range of structures will be possible when further modifications are made to the basic set of isomeric, expanded, and contracted structures that were covered from a theoretical standpoint in this review. Of particular significance in this regard will be the core modification of porphyrin analogues;16,216−224 the formation of N-fused43,202,225−229 and neo-fused230,231 structures; ringexpanded compounds with nonpyrrole moieties, such as the texaphyrins;232,233 and C-fused234 and benzonorroles.235,236

6.5. Larger Ring-Expanded Compounds

Corresponding Author

AUTHOR INFORMATION *E-mail: [email protected]. Tel.: +27-46-603-7234.

Considerably less research has been carried out to predict trends in the electronic structures and optical properties of larger ring-expanded compounds with more than six pyrrole rings from a perimeter-model standpoint, because the flexibility of the structures often results in nonaromatic structures with relatively weak macrocyclic ring currents. For example, the [40]decaphyrin(1.0.1.0.0.1.0.1.0.0) compounds, trivially named turcasarins, that were reported by Sessler and co-workers211 adopt a pair of dissymmetric figure-eight conformations. There is clearly still considerable scope for studies on the larger ringexpanded porphyrin analogues using an analysis based on the perimeter-model approach and MCD spectral measurements, however, given the recent reports of a tetraprotonated stable Hückel-aromatic [50]dodecaphyrin(1.1.0.1.1.0.1.1.0.1.1.0) species with a narrow intense B band at 906 nm and Q bands at 1346 and 1600 nm91 and the twisted Hückel-aromatic and antiaromatic structures of Ni(II) [40]- and [42]nonaphyrin(1.1.1.1.1.1.1.1.1) complexes.212 Octaphyrin,86−89 decaphyrin,90 and dodecaphyrin91 structures were also recently reported to exhibit Möbius aromaticity, and hence, strong induced excited-state magnetic moments would be anticipated for their Q- and B-type transitions, resulting in relatively intense MCD bands, similar to those in the spectra of Möbius-aromatic [28]hexaphyrin(1.1.1.1.1.1) compounds reported by Osuka and co-workers.81

ORCID

John Mack: 0000-0002-1345-9262 Notes

The author declares no competing financial interest. Biography John Mack, born in Edinburgh, Scotland (1966), received his Bachelor’s degree from the University of Aberdeen and his Doctoral degree from the University of Western Ontario under the direction of Professor Martin J. Stillman. His graduate research focused on the MCD spectroscopy of phthalocyanine anion radical species. He carried out postdoctoral research in the laboratories of Martin J. Stillman and James R. Bolton at the University of Western Ontario and Nagao Kobayashi at Tohoku University in Japan. He was an Assistant Professor at Tohoku University and currently works as a Senior Researcher at Rhodes University in South Africa. His research interests are focused on studying trends in the electronic structures and optical spectroscopy of porphyrinoids and BODIPY dyes to guide the rational design of novel compounds for use in nanotechnology applications.

ACKNOWLEDGMENTS Financial support was provided by the National Research Foundation of South Africa for financial support through a CUSR grant (uid: 93627). Theoretical calculations were carried out at the Centre for High Performance Computing in Cape Town, South Africa.

7. CONCLUSIONS Structural modifications to the porphyrin ligand result in changes to the optical and redox properties that can be readily predicted on a theoretical basis through a consideration of their effects on the energies of the frontier π-MOs. Whereas ring contraction and isomerism normally result in ligands with conventional 4N + 2 Hückel aromaticity that can be readily analyzed using conventional theoretical frameworks such as Gouterman’s four-orbital model and Michl’s perimeter model, ring expansion to form pentaphyrins, hexaphyrins, and other larger ring-expanded structures provides access to a much wider range of structures, because the enhanced conformational flexibility facilitates the formation of structures with 4N Möbius and 4N + 2 twisted Hückel figure-eight aromaticity,12,213 in addition to the conventional planar 4N + 2 Hückel structures that are usually observed with isomeric and contracted porphyrin analogues. This is likely to provide scope for further breakthroughs in the years ahead regarding novel forms of

ABBREVIATIONS 3pysubP subporphyrin with 3-pyridyl meso substituents 4pysubP subporphyrin with 4-pyridyl meso substituents AICD anisotropy of the induced current density BHPc dibenzoporphycene BPc tetrabenzoporphycene BsubPcs boron subphthalocyanines BsubPs boron subporphyrins DFT density functional theory ΔHOMO energy gap between the a and s MOs ΔLUMO energy gap between the −a and −s MOs GIMIC gauge including magnetically induced current HOMA harmonic oscillator model of aromaticity HOMO highest occupied molecular orbital lcp left circularly polarized 3471


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(15) Sessler, J. L.; Weghorn, S. J.; Hiseada, Y.; Lynch, V. Hexaalkyl Terpyrrole - A New Building-Block for the Preparation of Expanded Porphyrins. Chem. - Eur. J. 1995, 1, 56−67. (16) Pareek, Y.; Ravikanth, M.; Chandrashekar, T. K. Smaragdyrins: Emeralds of Expanded Porphyrin Family. Acc. Chem. Res. 2012, 45, 1801−1816. (17) Sessler, J. L.; Morishima, T.; Lynch, V. Tetrathia- and Tetraoxarubyrins: Aromatic, Core-Modified, Expanded Porphyrins. Angew. Chem., Int. Ed. Engl. 1991, 30, 977−980. (18) Hannah, S.; Seidel, D.; Sessler, J. L.; Lynch, V. New Chemistry of Amethyrin. Inorg. Chim. Acta 2001, 317, 211−217. (19) Xue, Z.; Mack, J.; Lu, H.; Zhang, L.; You, X. Z.; Kuzuhara, D.; Stillman, M. J.; Yamada, H.; Yamauchi, S.; Kobayashi, N.; et al. The Synthesis and Properties of Free-Base [14]Triphyrin(2.1.1) Compounds and the Formation of Subporphyrinoid Metal Complexes. Chem. - Eur. J. 2011, 17, 4396−4407. (20) Xue, Z.-L.; Shen, Z.; Mack, J.; Kuzuhara, D.; Yamada, H.; Okujima, T.; Ono, N.; You, X.-Z.; Kobayashi, N. A Facile One-Pot Synthesis of meso-Aryl-Substituted [14]Triphyrin(2.1.1). J. Am. Chem. Soc. 2008, 130, 16478−16479. (21) Pacholska, E.; Latos-Grażyński, L.; Ciunik, Z. A Direct Link between Annulene and Porphyrin Chemistry - 21-Vacataporphyrin. Chem. - Eur. J. 2002, 8, 5403−5406. (22) Sánchez-García, D.; Sessler, J. L. Porphycenes: Synthesis and Derivatives. Chem. Soc. Rev. 2008, 37, 215−232. (23) Sessler, J. L.; Brucker, E. A.; Weghorn, S. J.; Kisters, M.; Schäfer, M.; Lex, J.; Vogel, E. Corrphycene: A New Porphyrin Isomer. Angew. Chem., Int. Ed. Engl. 1994, 33, 2308−2312. (24) Vogel, E.; Scholz, P.; Demuth, R.; Erben, C.; Bröring, M.; Schmickler, H.; Lex, J.; Hohlneicher, G.; Bremm, D.; Wu, Y. D. Isoporphycene: The Fourth Constitutional Isomer of Porphyrin with an N(4) Core-Occurrence of E/Z Isomerism. Angew. Chem., Int. Ed. 1999, 38, 2919−2923. (25) Chmielewski, P. J.; Latos-Grażyński, L.; Rachlewicz, K.; Głowiak, T. Tetra-p-Tolylporphyrin with an Inverted Pyrrole Ring: A Novel Isomer of Porphyrin. Angew. Chem., Int. Ed. Engl. 1994, 33, 779−781. (26) Furuta, H.; Asano, T.; Ogawa, T. ″N-Confused Porphyrin″: A New Isomer of Tetraphenylporphyrin. J. Am. Chem. Soc. 1994, 116, 767−768. (27) Harvey, J. D.; Ziegler, C. J. Developments in the Metal Chemistry of N-Confused Porphyrin. Coord. Chem. Rev. 2003, 247, 1− 19. (28) Furuta, H.; Maeda, H.; Osuka, A. Confusion, Inversion, and Creation - A New Spring from Porphyrin Chemistry. Chem. Commun. 2002, 1795−1804. (29) Li, R.; Lammer, A. D.; Ferrence, G. M.; Lash, T. D. Synthesis, Structural Characterization, Aromatic Characteristics, and Metalation of Neo-Confused Porphyrins, a Newly Discovered Class of Porphyrin Isomers. J. Org. Chem. 2014, 79, 4078−4093. (30) Lash, T. D.; Lammer, A. D.; Ferrence, G. M. Neo-Confused Porphyrins, a New Class of Porphyrin Isomers. Angew. Chem., Int. Ed. 2011, 50, 9718−9721. (31) Miller, D. C.; Johnson, M. R.; Becker, J. J.; Ibers, J. A. Synthesis and Characterization of the New 22-π Aromatic Furan-Containing Macrocycle, “Ozaphyrin. J. Heterocycl. Chem. 1993, 30, 1485−1490. (32) Johnson, M. R.; Miller, D. C.; Bush, K.; Becker, J. J.; Ibers, J. A. Synthesis and Characterization of a New 26.Pi.-Aromatic ThiopheneContaining Macrocyclic Ligand. J. Org. Chem. 1992, 57, 4414−4417. (33) Toganoh, M.; Furuta, H. Theoretical Study on the Conformation and Aromaticity of Regular and Singly N-Confused [28]Hexaphyrins. J. Org. Chem. 2013, 78, 9317−9327. (34) Mori, S.; Osuka, A. Aromatic and Antiaromatic Gold(III) Hexaphyrins with Multiple Gold−Carbon Bonds. J. Am. Chem. Soc. 2005, 127, 8030−8031. (35) Muranaka, A.; Matsushita, O.; Yoshida, K.; Mori, S.; Suzuki, M.; Furuyama, T.; Uchiyama, M.; Osuka, A.; Kobayashi, N. Application of the Perimeter Model to the Assignment of the Electronic Absorption

LUMO MCD MO MOsubP

lowest unoccupied molecular orbital magnetic circular dichroism molecular orbital subporphyrin with 4-methoxyphenyl meso substituents NCP N-confused porphyrin NICS nucleus-independent chemical shift OAM orbital angular momentum OECn octaethylcorrphycene OEHPc octaethylhemiporphycene OEP octaethylporphyrin OEPc octaethylporphycene Pc phthalocyanine PhsubP subporphyrin with phenyl meso substituents rcp right circularly polarized SOMO singly occupied molecular orbital TD-DFT time-dependent density functional theory TFsubP subporphyrin with (4-trifluoromethyl)phenyl meso substituents THPc bicyclo[2.2.2]octadiene-fused porphycene TLsubP subporphyrin with tolyl meso substituents

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