Jun-ichi Aihara*ab and Masakazu Makinob
aDepartment of Chemistry, Faculty of Science, Shizuoka University, Oya, Shizuoka 422-8529, Japan. E-mail: scjaiha@yahoo.co.jp
bInstitute for Environmental Sciences, University of Shizuoka, Yada, Shizuoka 422-8526, Japan
First published on 15th October 2009
For some porphyrinoids, such as orangarin and amethyrin, the main route of macrocyclic π-circulation is different from the main macrocyclic conjugation pathway predicted by porphyrin chemists. Our analytical theory of ring-current diamagnetism allows us to predict the main macrocyclic conjugation pathway from the ring current distribution. We can now interpret macrocyclic aromaticity and macrocyclic circulation consistently within the same theoretical framework.
Macrocyclic aromaticity and macrocyclic circulation are two different manifestations of macrocyclic conjugation in porphyrinoids.1-6 A ring current distribution in a polycyclic π-system, however, is strongly dependent on molecular geometry, so that information on global and macrocyclic aromaticity cannot be extracted directly from it. For some expanded porphyrins, such as orangarin and amethyrin, the main stream of π-circulation8,9 deviates from the so-called main macrocyclic conjugation pathway5,10 even if the direction of the macrocyclic ring current might be predicted from the annulene picture. In this paper, we propose a general theoretical method for extracting information on the main macrocyclic conjugation pathway from the ring current distribution, and interpret macrocyclic conjugation and macrocyclic circulation within the same theoretical framework.
Fig. 1 Non-identical circuits in porphine (1). |
The term macrocycle is used to represent a planar or quasi-planar polycyclic π-system with a large inner cavity. Porphyrins and kekulene are such macrocyclic compounds. A macrocyclic circuit is any large circuit that surrounds the inner cavity (e.g., circuits c–k in Fig. 1), also being referred to as a conjugation pathway in the macrocycle. This is distinguished from a local circuit located in each five-membered ring (e.g., circuits a and b in Fig. 1). All macrocyclic circuits constitute macrocyclic conjugation.5-7Macrocyclic aromaticity and macrocyclic circulation are the aromaticity and π-circulation associated with macrocyclic circuits, respectively. Superaromatic stabilization energy (SSE) represents an extra ASE due to macrocyclic conjugation.5-7,15,16 Thus, the term superaromaticity is a synonym of macrocyclic aromaticity.
Our theory of ring-current diamagnetism19–22 is nothing other than an exact or analytical reformulation of Hückel–London theory.23,24 It allows a decomposition of the ring current induced in a polycyclic π-system, G, exactly into individual circuit contributions. A current induced in each circuit may be termed a circuit current, the intensity of which is given in the form:20–22
(1) |
Hückel heteroatom parameters proposed by Van-Catledge30 were employed. In addition, all nitrogen atoms coordinated to a metal ion were dealt with as imine (N–) nitrogens. This assumption is fully consistent with the geometry of magnesium porphine (2) and with the ring current distribution in it. Fig. 2 shows the molecular geometry of magnesium porphine calculated by Cyrański et al.31 at the B3LYP/6-31G* level of theory,32–34 where all outer C–C bonds in pyrrole rings behave as formal double bonds.35 As will be seen later, the ring current distribution we calculated for magnesium porphine is very similar to the current density map reported by Steiner and Fowler,36,37 in which the current flowing along the inner cross is slightly stronger than the one flowing along the 20-membered outer periphery. Hückel parameters we employed for the nitrogen atoms reasonably reproduce these aspects of metalloporphyrins. There are two extra π-electrons in the inner ring, formally making a 16-membered aromatic dianion.
Fig. 2 Bond lengths (in Å) in magnesium porphine (2, M = Mg). Values in parentheses are Hückel π-bond orders. |
Realistic molecular geometries are necessary to evaluate the intensities of ring and circuit currents. Geometries used for 1–6 are those obtained by Jusélius and Sundholm38,39 at the resolution-of-the-identity density-functional theory (RI-DFT) level40 using the Becke–Perdew (B–P) parametrization41-43 as implemented in TURBOMOLE.44 We optimized molecular geometries of 7–9 at the B3LYP/6-31G** level of theory33,34 using a GAUSSIAN 03 program.32 For the optimized geometries of 7–9, see the ESI†. These geometries were used to calculate the areas enclosed by the circuits.
Fig. 3 Main macrocyclic conjugation pathways and BREs in nine porphyrinoids. |
BREs for all non-identical π-bonds in 1–9 are graphically summarized in Fig. 3. For porphyrinoids with positive SSEs (1–6, 8), the main macrocyclic conjugation pathway can be traced by choosing a π-bond with a larger BRE at every bifurcation of the π-network.5,6 Those in free-base porphyrins 1, 3, 5, and 8 are aromatic [4n+2]annulene pathways, which are all conjugated circuits in Randić's termonology.47 For metal complexes 2, 4, and 6, π-bonds with larger BREs constitute the innermost, shortest possible, [16]annulene pathway along which 18 π-electrons formally reside. All π-bonds located along these conjugation pathways are intensified, with larger positive BREs than those located along the bypasses.
There are no such aromatic annulene pathways in orangarin (7) and amethyrin (9), because they have negative SSEs. Another type of macrocyclic pathways can instead be traced by choosing a π-bond with a smaller BRE at every bifurcation of the π-network.5,6 Main macrocyclic pathways thus determined for 7 and 9 are antiaromatic [4n]annulene pathways, which are also conjugated circuits in Randić's sense.47 These pathways will also be referred to as main macrocyclic conjugation pathways, because they are closely associated with macrocyclic antiaromaticity. All π-bonds located along these antiaromatic pathways are weakened, with smaller BREs than those located along the bypasses. Macrocyclic annulene pathways proposed by porphyrin chemists can thus be justified in terms of BREs.1-7
Next, let us examine the geometric patterns of macrocyclic circulation in porphyrinoids. Steiner and Fowler8,9,36,37 carried out ring-current calculations on 1–3 and 7–9 with the 6-31G** basis by means of coupled Hartree–Fock theory within the ipsocentric48,49 CTOCD-DZ (continuous transformation of origin of current density diamagnetic zero) formulation.50,51 They noted that all these porphyrinoids give clearly dominant macrocyclic currents; intense diamagnetic currents are induced along the macrocycles of 1–3 and 8, whereas the macrocycles of 7 and 9 sustain intense paramagnetic currents.8,9 The occurrence of paramagnetic ring currents in 7 and 9 may be due partly to the absence of substituents. Sessler et al. reported that polysubstituted forms of 7 and 9 are 20π- and 24π-electron nonaromatic macrocycles, respectively.10
Main streams of Steiner–Fowler macrocyclic currents in porphine (1)36 and sapphyrin (8)8 follow the main macrocyclic conjugation pathways shown in Fig. 3. In metalloporphine (2) and chlorin (3), however, no distinct main stream is observable in the Steiner–Fowler current density maps;36,37π-currents of comparable intensity flow along the outer C–C and inner C–N bonds of one or more pyrrole rings. On the other hand, orangarin (7) and amethyrin (9) are predicted to sustain intense paramagnetic currents along the inner periphery, but not along the conventional annulene pathways.8,9 The main streams of these paramagnetic currents necessarily pass through all nitrogen atoms including all amine nitrogens.
Global ring current patterns we calculated for 1–9 are shown as 1a–9a in Fig. 4. Here, counterclockwise and clockwise circulations represent diatropic and paratropic ring currents, respectively. As far as 1–3 and 7–9 are concerned, our Hückel-London calculations reproduce well the global ring current patterns obtained by Steiner and Fowler.8,9,36,37 Main streams of macrocyclic circulation in free bases 1, 5, and 8 follow the main conjugation pathways, whereas those in the other species do not always follow the main conjugation pathways. In 2–4 and 6, π-currents of comparable intensity flow along the outer CC and inner CN bonds of one or more pyrrole rings. Therefore, no distinct main streams are observable in these species. As noted by Steiner and Fowler,8,9 the main streams of macrocyclic ring currents in 7 and 9 runs along the inner periphery. These aspects of macrocyclic circulation do not conform to the annulene picture of porphyrinoids.
Fig. 4 Decomposition of ring currents induced in 1–9 (1a–9a) into macrocyclic (1b–9b) and local (1c–9c) circuit contributions. All current intensities are given in units of the benzene value. |
Although our ring current distributions for 7 and 9 indeed are similar to Steiner and Fowler's current density maps,8,9 it seems that our simpler calculations somewhat overestimate the intensities of macrocyclic paramagnetic currents. This kind of drawback is possibly due to the neglect of bond-length alternation and/or deformation that might occur along the antiaromatic annulene pathways. Note that many porphyrinoid macrocycles with [4n]annulene pathways do not exhibit antiaromatic ring current effects and have been regarded as nonaromatic ones.2–6 This experimental fact implies that macrocyclic antiaromaticity tends to be suppressed significantly by structural modifications. Steiner–Fowler current density maps for 7 and 98,9 can be reproduced formally by assigning a resonance integral of ca. 0.8β to all π-bonds that link adjacent pyrrolic rings. However, such a modification of the π-system does not affect the discussion below.
As has been seen above, at least for 7 and 9, the main macrocyclic conjugation pathway is never the same as the main stream of macrocyclic circulation.6,8,9 We then describe how to extract information on the main macrocyclic conjugation pathway from the ring current distribution. Note that local circulations within individual pyrrolic rings are superposed on macrocyclic circulation, both constituting the global current distribution.7 Local circulations in the pyrrolic rings of 1–9 are always diamagnetic in nature. In the case of porphyrinoids with positive SSEs, a diamagnetic current is induced along the macrocycle; it is bifurcated when it runs across every pyrrole ring. Both diamagnetic macrocyclic and diamagnetic local currents flow in the same direction on the outer C–C bonds of the pyrrole rings. However, both currents totally or partially cancel each other out on the inner C–N bonds, because both currents flow in opposite directions there. Thus, local circulations may obscure the location of the main macrocyclic circulation pathway.
On the other hand, porphyrinoids with negative SSEs sustain a paramagnetic current along the macrocycle. The current is bifurcated when it runs across every pyrrole ring. Apart from this, a strong diamagnetic current is induced in every five-site circuit. In this case, both paramagnetic macrocyclic and diamagnetic local currents flow in opposite directions on the outer C–C bonds of the pyrrole rings and so totally or partially cancel each other out there. However, both currents flow in the same direction on the inner C–N bonds. As a result, the intensified current is observed on all inner C–N bonds. This must be the main reason why 7 and 9 appear to sustain strong paramagnetic circulations along the inner peripheries.
Therefore, if one wants to trace macrocyclic circulation only, the motion of π-electrons along the macrocycle only must be extracted from the global current distribution. Fortunately, our analytical theory of ring-current diamagnetism20-22 allows us to decompose the ring current distribution exactly into individual circuit contributions. As shown in Fig. 4, the entire ring current in each porphyrinoid species can then be decomposed exactly into the contributions of macrocyclic and local five-site circuits. For example, the entire ring current induced in porphine (1a) can be partitioned into the contributions of macrocyclic (1b) and local five-site (1c) circuits; 1b and 1c consist of currents induced in 16 macrocyclic circuits (circuits c–k in Fig. 1) and 4 five-site ones (circuits a and b in Fig. 1), respectively. It is 1b that represents the net macrocyclic circulation induced in 1. Comparison of 1a with 1b reveals that the main stream of macrocyclic circulation in 1a remains unchanged in 1b, which indicates that the main macrocyclic circulation pathway is the same as the main stream of circulation in the entire π-system. Both agree with the main macrocyclic conjugation pathway exactly. The same is true for two other free-base porphyrinoids 5 and 8. Here, we tacitly assumed that the areas of all macrocyclic circuits are roughly of comparable magnitude, being much larger than those of local five-site circuits. This possibly is a fairly reasonable assumption for all porphyrinoids studied.
The entire ring current in orangarin (7a) can be decomposed into the contributions of macrocyclic (7b) and local five-site (7c) circuits; 7b and 7c consist of currents induced in 32 macrocyclic and 5 five-site circuits, respectively. Likewise, the entire ring current in amethyrin (9a) can be decomposed into the contributions of 64 macrocyclic (9b) and 6 five-site (9c) circuits. That is, 7b and 9b represent net macrocyclic circulations induced in 7 and 9, respectively. One sees that the main circulation pathways in 7b and 9b are different from the main streams of global circulation in 7a and 9a, respectively, but are identical with the main macrocyclic conjugation pathways in Fig. 1. As differences between the intensities of currents that flow on the outer C–C and inner C–N bonds are sizeable in 7b and 9b, there is no doubt that strong macrocyclic currents are induced along the conventional annulene pathways.
As stated above, 2–4 and 6 exhibit a current distribution pattern in which the π-currents of similar intensity flow along the outer C–C and inner C–N bonds in one or more pyrrole rings. These ring current patterns can be analyzed in the same manner. If we exclude local circulations in pyrrole rings from the ring current distribution as in 2b–4b and 6b, we can discern the same annulene pathways as predicted from the BREs. Thus, for all of 1–9, authentic main macrocyclic conjugation pathways are clearly discernible in the macrocyclic current distributions (1b–9b) in which local circulations are missing. We can now safely say that, as far as porphyrinoid macrocycles are concerned, the main macrocyclic circulation pathway is identical with the main macrocyclic conjugation pathway. All main macrocyclic conjugation pathways pass through imine (N–) nitrogens but avoid amine (–NH–) nitrogens.
Finally, one might have noted that some five-site or pyrrole circuits, such as those in 7c and 9c, sustain much larger diamagnetic currents than those in other porphyrinoids. It may be interesting to see that highly antiaromatic and aromatic circuits coexist in 7 and 9. In such polycyclic π-systems, both the aromaticity of aromatic circuits and the antiaromaticity of antiaromatic circuits are often enhanced appreciably; paramagnetic and diamagnetic circuit currents induced in these circuits are necessarily intensified simultaneously. This is why all five-site circuits in 7 and 9 sustain large diamagnetic currents. Similar intensification of circuit currents was observed in many charged polycyclic benzenoid hydrocarbons.52
Footnote |
† Electronic supplementary information (ESI) available: B3LYL/6-31G**-optimized geometries of orangarin (7), sapphyrin (8), and amethyrin (9). See DOI: 10.1039/b910521b |
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