Three Contra-Rotating Currents from a Rational Design of Polycyclic

Article pubs.acs.org/JPCA

Three Contra-Rotating Currents from a Rational Design of Polycyclic Aromatic Hydrocarbons: altan-Corannulene and altan-Coronene Guglielmo Monaco* and Riccardo Zanasi Dipartimento di Chimica e Biologia, Università di Salerno, Fisciano, 84084 (SA), Italy S Supporting Information *

ABSTRACT: Both the ab initio expression of the current density within the ipsocentric approach and conjugated circuit models indicate that placing an unsaturated hydrocarbon inside a [4n]annulene, in such a way that outgoing C−H bonds are substituted by C−C bonds to alternating carbon atoms of the annulene, leads to an homologue altan-molecule whose perimeter is expected to preserve the paratropic circulation of the parent annulene. Computations of current on the novel altan-corannulene and altan-coronene revealed unprecedented patterns of three contra-rotating paratropic/diatropic/paratropic circulations. Graph-theoretical methods have been used to highlight the peculiar topology of these altan-molecules.

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INTRODUCTION Ring currents attract considerable enough attention on the ground that they enable the interpretation of the chemical shifts of aromatic hydrocarbons1 and they are used to define aromaticity according to the magnetic criterion.2,3 The prediction of the patterns of magnetically induced currents can be problematic even in highly symmetrical polycyclics, where the number of possible patterns is greatly reduced, as exemplified by the wrong prediction of diatropic currents on both the hub and rim of corannulene, based on the so-called annulene-within-anannulene (AWA) model.4,5 Actually, in both corannulene and coronene, the circulation on hubs is paratropic, leading to contrarotating circulations.6,7 Later on, the investigation of the yet unsynthesized family of [2n,5]coronenes showed patterns of current in agreement with the AWA picture.8,9 The interpretation of these different behaviors benefitted from the spectral decomposition10,11 of the current density within the ipsocentric CTOCD-DZ method.12−14 According to that decomposition, the current J stems from a double sum over occupied and virtual orbitals and each Ji→m contribution arises from two terms Jti→m r and Ji→m , which are nonvanishing only if the i → m transition is translationally or rotationally allowed, respectively. Translational contributions generate only diatropic circulations, while rotational contributions generate mainly11,15 paratropic circulations. The identification of the nature of the transitions can be simplified by symmetry. This is the case of Cn-symmetric systems, whose eigenfunctions can be labeled by an integer known as quasi-angular momentum m;16−18 character tables then readily show that rotationally and translationally allowed transitions are characterized by Δm = 0 and Δm = ±1, respectively.19 The quasiangular momentum m is easily inferred either from the symmetry labels (for a Cn group, the E1 and E2 terms have quasi-angular momenta m equal to their subscripts, the A term has m = 0, and the B term, only present for even n, has m = n/2) or by inspection, because it is equal to half of the azimuthal node count © 2012 American Chemical Society

(HANC). Besides preserving occupied and virtual spaces and thus allowing a symmetry classification of virtual transitions much similar to those typical of optical spectroscopy, much of the usefulness of the ipsocentric method is due to the fact that generally only few orbitals close to the Fermi level appear to be relevant, at odds with what happens with different choices of the gauge.20,21 Therefore, a localized HOMO or LUMO can be expected to cause some localization of the pattern.11 This happens indeed in [2n,5]coronenes, which all have [4n]annulenes as rims. The degenerate HOMOs of isolated [4n]annulenes in their lowest triplet state are singly occupied and localized on alternating carbon atoms along the ring (Figure 1 shows the HOMOs of

Figure 1. The two degenerate singly occupied tight-binding orbitals of triplet [16]annulene, with m = 4.

triplet [16]annulene). These two orbitals have the same quasiangular momentum m = n, and if just one of them is occupied, a strong rotational contribution is expected. If the annulene is bonded only through a single set of its carbon atoms to another moiety, the orbital localized on that set will be stabilized and will keep two electrons, while the other one will become a virtual orbital localized on the annulene. Received: March 19, 2012 Revised: August 9, 2012 Published: August 14, 2012 9020

dx.doi.org/10.1021/jp302635j | J. Phys. Chem. A 2012, 116, 9020−9026

The Journal of Physical Chemistry A

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of 2, for which a larger plot with transparency is given in the Supporting Information. Circuit resonance energies have been first computed for the reference set of ref 35 (including 2) and then for 1, altan-1, and altan-2. In the case of altan-1 and altan-2, circuits obtained by fusion of no more than 6 rings were considered.

Noteworthy, besides this discussion based on molecular orbitals, the bonding of an alternant Kekulean system through only one set of its atoms is also a sufficient condition to have factorizability of the Kekulé count, which is mostly associated to separate domains in the current density pattern.22 According to these peculiar features, [4n]annulenes can be expected to be useful tools for the design of localized current patterns. Any molecule with outgoing C−H bonds can bring to a homologue altan-molecule by substituting the C−H bonds with C−C bonds to alternating carbon atoms of an annulene. This corresponds to substituting the hydrogen atoms with acetylenic groups (Figure 2) and properly bonding the added groups; if the

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RESULTS AND DISCUSSION We obtained bowl-shaped minima of C5 and C6 symmetry for altan-1 and altan-2, respectively. The angle of departure ϑ of the C−H bonds from the plane of the hub is larger in altan-1 (63°) than in altan-2 (50°), consistently with the bowl-shaped and planar geometries of the parent fragments corannulene and coronene. The bond length alternation along the middle loop (bonds c, d, and e) observed in 1 and 2 is very much preserved passing to the altan homologues (Table 1). As for the novel bonds of the altan Table 1. Selected Bond Lengths in Å and the Out-of-Plane Angles ϑ of the C−H Bonda

Figure 2. The structural modification needed to build an altan-molecule.

outgoing C−H bonds are even and the resulting strain is acceptable, one will end with a novel structure with a peripheral [4n]annulene expected to hold a paratropic circulation. As a first test of this statement, we considered enlargement of corannulene 1 and coronene 2 to yield altan-corannulene and altan-coronene, to be named hereafter altan-1 and altan-2 (Scheme 1). Scheme 1

a

1

altan-1

2

altan-2

a b c d e f g h i j k

1.417 1.385 1.448 1.389 1.448

1.438 1.416 1.419 1.394 1.419 1.462 1.440 1.392 1.461 1.455 1.404

1.427 1.422 1.424 1.372 1.424

1.440 1.441 1.402 1.374 1.403 1.462 1.444 1.394 1.461 1.463 1.408

ϑ (deg)

19

63

0

50

Bond labels as in Scheme 1.

molecules, bonds f and i (which are fixed single bonds) are the longest ones and there is a considerable amount of alternation along the outer loop (bonds g, h, j, and k). This bond alternation can occur in two different ways corresponding to two enantiomers, which appear to easily interconvert via Cnv transition states (energy barriers at the B3LYP/6-31G(d,p) level are 1.0 and 0.9 kcal mol−1 for altan-1 and altan-2, respectively). We computed the current density on one of the degenerate energy minima. To visualize ring currents, getting rid of the strong currents close to the atoms, we have plotted the current on a surface with the same shape as the molecule but displaced by 1 au.9,15 As can be seen in Figure 3a,b for both molecules an unprecedented pattern of three contra-rotating paratropic/ diatropic/paratropic loops is apparent. The reference arrow drawn in the top left corner represents the magnitude of the maximum value of the π current density in benzene, thus showing that the studied systems sustain quite considerable currents. We tried to identify π descendant orbitals, selecting the orbitals with lower value of the electron density along the bonds. As can be seen in Figure 3c,d, those quasi-π orbitals are responsible for much of the total current, although the quasi-σ orbitals also give an important contribution, particularly for the middle loop. In agreement with design expectation, the outer paratropic circulation in 1 and 2 is mainly due to a single rotational contribution, as in [4n]annulenes. As the special decoupling for the LUMO of altan-1 and altan-2 is not shared by the other molecular orbitals, which are delocalized on the three loops,

Quite remarkably, although altan-1 and altan-2 have not been synthesized yet as isolated molecules, altan-1 is found in many endohedral fullerenes; e.g., it forms both caps of Sc3N@D5h− C80,23 Sc3N@Ih−C80,24 and La2@C100,25 one of the two caps in Sc@C2v−C82,26 and in cages with nonisolated pentagons such as Gd3N@C78,27 Gd3N@Cs−C82,28 and [email protected] Indeed, altan-1 can be recognized as a fragment of the most stable forms of C6− 80 and of three out of four of its energetically preferred close homologues.30

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COMPUTATIONAL METHODS Geometries have been optimized at the B3LYP/6-31G(d) level using Gaussian 09.31 Current density patterns have been computed by SYSMO32 at the widely adopted CTOCD-DZ CPHF/6-31G(d,p) level.20 Previous studies have shown that these patterns are grossly unchanged by the introduction of density functional approaches.33 Orbitals have been analyzed with GaussView 4.0,34 using the standard isovalue 0.02 au and, in the case of unclear determination of the HANC, decreasing the isovalue down to 0.001 au. Orbitals plotted in Figures 4 and 5 are sufficient to determine HANCs on inspection but for an orbital 9021



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Figure 4. Orbitals of altan-1 close to the Fermi level, labeled with their symmetry and HANCs. When orbitals are largely localized on one or two loops, their HANCs have been marked in bold, while loops with negligible density have a sign ⌀ in place of their quasi-angular momentum. Translationally (rotationally) allowed virtual transitions are indicated by arrows with a plain (round) start. The width of arrows is proportional to the intensity of the transition as determined by the Γ coefficient of ref 11, premultiplied by an average distance of 10 au from the symmetry axis in the case of translationally allowed transitions.

Figure 3. Current density maps for altan-1 (left) and altan-2 (right) plotted on a surface having the molecular shape at 1 au inside the molecular bowls. The plots are drawn considering all electrons (a and b), only quasi-π orbitals (c and d), and contributions stemming from the subspace indicated by stars in Figures 4 and 5 (e and f). The top left arrow in each inset gives the magnitude of the maximum of the current density in benzene (jmax = 0.08 au). Red/blue arrows indicate a current density vector with a nonclassical component parallel/antiparallel to the magnetic field exceeding 10%. For an outgoing magnetic field, a diatropic/paratropic current density is clockwise/anticlockwise.

the molecular orbital approach does not indicate clearly that also the main transitions of 1 and 2 should be easily recognized in their altan homologues, although this could be expected using conjugated-circuit models.40a To further investigate the question, we analyzed the quasi-π contributions stemming from orbitals close to the Fermi level. In addition to the standard notation, orbitals have been labeled using the HANCs for the three loops (Figures 4 and 5). Indeed, if the loops were uncoupled, their HANCs would equal the quasi-angular momenta m, which are proper quantum numbers; in that case, the nature of the transitions could be determined by the cited rule for annulenes,19 and the current pattern of altan-1 and altan-2 could be expected to be the sum of the patterns of the parent fragments. Using HANC labeling also for the parent fragments, the main transitions already reported10,14 are Jn→n HOMO→LUMO for [4n]annulenes, (1−4)→(1−4) (2−4)→(1−5) J(2−3)→(1−4) HOMO→LUMO, and JHOMO−1→LUMO for 1 and JHOMO→LUMO and (2−4)→(2−4) JHOMO→LUMO+1 for 2. HANC labeling allows one to easily identify the two and three higher occupied degenerate orbital levels as the descendants of the parent fragments for altan-1 and altan-2,

Figure 5. Orbitals of altan-2 close to the Fermi level. See the caption of Figure 4 for drawing conventions.

respectively. Actually, in altan-1, the coupling with the annulene splits the (1−4) HOMO of 1 in two e1 levels. A similar splitting occurs for the relevant virtual orbitals of the parent fragments, which are recognized in two e1 levels for altan-1 and in two e1 levels and two e2 levels for altan-2. The current density map obtained with just these occupied orbitals compares well with the all quasi-π map for 1 (Figure 3e) but not for altan-2 (see the Supporting Information for details). In that case, inclusion of one more occupied level gives a reasonable matching (Figure 3f). This situation, also happening in [2n,5]coronenes,8,9 is due to the need of considering the Jn−1→n translational contribution for the 9022



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Figure 6. Semilogarithmic plot of circuit resonance energies versus circuit length. The diamonds ⧫ on the upper line refer to closed shell monocycles with 4n + 2 π electrons either neutral, mono, or dicharged. Entries around the two lower lines have been reproduced from the systems considered in ref 35. Filled or empty circles (● or ○) indicate stabilization or destabilization of conjugated circuits. Filled or empty circles (■ or □) indicate stabilization or destabilization of nonconjugated circuits. Intercepts and slopes for the three lines from top to bottom are −0.54 and −0.0339, −0.39 and −0.124, and −0.60 and −0.177.

topological ring current models, such as those of Gomes,39 Randić,40 Mandado,41 and Ciesielski.42 Armed with these rough tendencies of CRE decrease, we addressed the computation of CREs for altan-1 and altan-2 and compared them with the CREs of their parent molecules 1 and 2, to see whether their perimeters really have any peculiar relevance. Figures 7 and 8 report the results with the same convention of the semilogarithmic plot of Figure 6. Once again, the generalized Hückel rule generally holds. Moreover, in most cases, 4n + 1 circuits are stabilizing, while 4n + 3 circuits are destabilizing. The CREs of the perimetral circuits of 1 and 2 are not much far from the line of conjugated circuits. This is not surprising for the 18-membered perimeter of 2, but it shows that the contribution of the 15-membered perimeter of 1 (log(CRE) = −2.26) is an order of magnitude higher than the reference line for nonconjugated circuits. Moreover, it is the only stabilizing 15-membered circuit among those computed here (even including the same circuit in altan-1). This observation supports the view that the perimeter in 1 is an important source of aromaticity. It should be noted, however, that this relatively high CRE is considerably lower than the value expected for an isolated monocycle of the same length, which lies on the topmost reference line of Figure 6. The CREs of altan-1 and altan-2 are in reasonable agreement with the trends of the lines of the conjugated and nonconjugated circuits. The CREs of the perimetral circuits, however, depart considerably from the line of conjugated circuits, more so for altan-2. This finding is a further indication that the peculiar topology of altan-molecules is particularly well suited for the design of separable molecular moieties. The circuits which are common to 1 and altan-1 (2 and altan-2) have CREs which vary relatively little for smaller circuits with higher CREs (see plot S7 in the Supporting Information), which is consistent with the preserved pattern of current and geometries while passing from 1 and 2 to their altan homologues.

outer annulene. For altan-1, that contribution was already included in the set of parent descendant orbitals.

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CIRCUIT RESONANCE ENERGIES To further assess the peculiar separability of the outer [4n]annulenes in altan-1 and altan-2, we resorted to a graphtheoretical decomposition of the Hückel−London resonance energy, allowing to quantify the contribution of any individual circuit: the circuit resonance energy (CRE).35 CREs are generally higher for conjugated circuits (those appearing with single/ double bond alternance in a Kekulé structure at least) than for nonconjugated ones and decrease increasing the size of the circuit.35 To better appreciate that trend, we have plotted the logarithm of CREs versus the size n of the circuits (Figure 6). We have considered the series of 4n + 2 π closed-shell monocycles in addition to the simple polycyclics considered in ref 35. The logarithmic CREs of monocycles (diamonds) decrease in a rather good linear fashion, while considerable more spread is observed for polycyclics. CREs of polycyclics are marked with circles or squares depending on their conjugated or nonconjugated character. In agreement with the many reports on the relevance of conjugated circuits,40a their CREs are generally higher than those of nearby nonconjugated circuits. Full and empty marks indicate positive and negative CRE values, respectively, and are thus in full agreement with the generalized Hückel rule stating that 4n + 2 (4n) circuits lead to stabilization (destabilization).36 Despite the spread of the CREs of polycyclics, one can still try to determine their best-fit linear decrease with ring size. This shows that the CREs of conjugated and nonconjugated circuits in polycyclics decrease more heavily than those of monocycles. This piece of information should be very useful considering the recent resurgence of interest37,38 in the setup and the assessment of 9023



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Figure 7. Semilogarithmic plot of circuit resonance energies versus circuit length of 1 (red) and altan-1 (black). For the meaning of the lines and the different marks, see the caption of Figure 6. The highlighted marks at n = 15 and n = 20 are those of the perimeters of the two molecules.

Figure 8. Semilogarithmic plot of circuit resonance energies versus circuit length of 2 (red) and altan-2 (black). For the meaning of the lines and the different marks, see the caption of Figure 6. The highlighted marks at n = 18 and n = 24 are those of the perimeters of the two molecules.

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MAGNETIC PROPERTIES The current density maps displayed in Figure 3 are evidence of strong paratropic currents on the perimeters of altan-1 and altan-2. This evidence can be complemented by a quantitative assessment of the intensity of the currents, integrating the current along planes bisecting chemical bonds.43−46 The resulting integrals are measures of electron fluxes, known as bond current susceptibilities or bond current strengths. We have

determined such bond current susceptibilities for 1, 2, and their altan homologues, and we have reported them in Table 2, after normalization to the value computed for benzene using the same method (12.55 nA T−1). In accord with previous works,6,7 the current susceptibilities in 1 and 2 indicate diatropic circulations on the perimeter and paratropic circulations on the hub. The strengths of these two currents are comparable in 1, while the paratropic current in 2 is less than half of the outer diatropic 9024



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we have performed a TDDFT calculation to estimate the lowest singlet and triplet excitation energies. Results are gathered in Table 2. As can be seen, at odds with their parent molecules 1 and 2, the altan-molecules in study have very low gaps to excited states, as low as 0.513 and 0.120 eV, respectively. These entries further qualify altan-1 and altan-2 as antiaromatic molecules.

Table 2. Selected Magnetic Properties and Lowest Excitation Energies symmetry-unique relative current strengthsa b

bond

1

a b c d e f g h i j k

−0.76 −0.01 0.79 0.80 0.79

ξc Δξc T1d S1d

−3347 −4263 2.653 3.410

altan-1 −0.39 −0.01 0.80 0.73 0.78 −0.06 −0.69 −0.69 −0.08 −0.64 −0.64 −3808 2816 0.513 0.841

2 −0.46 0.00 1.27 1.24 1.27

−4778 −8173 2.331 3.227

altan-2 −0.28 −0.00 1.06 1.03 1.07 −0.01 −0.40 −0.42 −0.03 −0.42 −0.42

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CONCLUSION Placing corannulene 1 and coronene 2 inside annulenes, in such a way that outgoing C−H bonds are substituted by C−C bonds to alternating carbon atoms of [4n]annulenes, leads to altancorannulene (altan-1) and altan-coronene (altan-2), whose magnetically induced current density patterns show three contra-rotating paratropic/diatropic/paratropic loops. The almost separable character of the outer [4n]annulene is not restricted to these two molecules. Indeed, it was previously reported for three [2n,5]coronenes (which could now be called altan-[n]annulenes) and for three more altan-molecules recently investigated.51 Among all these molecules, altan-1 and altan-2 appear to be the less hindered systems. Moreover, altan-1 is a fragment of known fullerene cages.23,25,27,29 The synthesis of these fullerene fragments as isolated species could benefit from the recent advances in alkyne chemistry,52 but it would be hampered by their very small excitation energies. Actually, the only attempt reported in the literature was faced with an unexpected cyclization, which could be well interpreted as a way to escape antiaromaticity.49 On the other hand, the reduced forms of these altan-molecules can be expected to be stable and to disclose an interesting chemistry, just as happened for corannulene ions,5 and many more polyarenes.53 Indeed, the many fullerene cages endowed with an altan-1 fragment are negatively charged.23,25,27,29

−5381 −1218 0.120 0.604

a

Bond current susceptibilities have been computed at the CTOCDDZ1/6-31G(d,p)//B3LYP/6-31G(d) level. A relative bond current strength of 1 corresponds to 12.55 nA T−1, i.e., the bond current susceptibility of benzene computed at the same level. Positive (negative) values indicate a current flowing in the directions a → b → c → d → e, f → g → h → i, or j → k. bBond labels as in Scheme 1. c Isotropic magnetizabilities ξ, magnetizability anisotropies computed at the CHF/6-31G(d,p)-GIAO level. Entries in 10−30 J T−2. d Excitation energies to the lowest singlet and triplet states computed at the TDDFT/B3LYP/6-31G(d,p) level. Entries in eV.

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ASSOCIATED CONTENT

S Supporting Information *

current. Consistently with the previous discussion on geometries and CREs, the patterns on the two inner loops of altan-1 and altan-2 are unchanged with respect to the parent systems; from a quantitative point of view, the innermost loop has a smaller current in altan systems, while the intensity on the middle loop is (semi)quantitatively preserved. The outermost circuits host strong paratropic currents, of intensity roughly half of the benzene reference value. Eventually, the presence of large paratropic circuits should cause a substantial effect on magnetic properties. Proton chemical shifts are poor probes of these ring currents, considering that in these bowl-shaped molecules protons are so bent to be close to the angle of transition from paratropic to diatropic contribution of ring currents.47,48 This limitation does not occur for magnetizabilities. Indeed, although HF calculations indicate that altan-1 and altan-2 are still diamagnetic as the parent systems 1 and 2, the increase of isotropic magnetizability ξ is far less than could be expected by the increase of the number of carbon atoms and the anisotropy Δξ = ξ∥ − ξ⊥ shifts toward more positive values, in agreement with a larger contribution of paratropic currents when the field is aligned along the symmetry axis. Notably, the anisotropy of altan-1 is positive, which is just the opposite of what is customarily found in aromatic molecules.

Optimized geometries, computed chemical shieldings, additional current density maps, plot of an orbital with transparency to better appreciate its HANCs, circuit resonance energies of 1 and 2 and a plot of their variation upon formation of their altanhomologues. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +39 89 969570. Fax: +39 89 969603. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the MIUR and the University of Salerno is gratefully acknowledged. REFERENCES

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STABILITY Beyond the successful design of an outer paratropic current, the question arises of whether altan-1 and altan-2 can be stable enough to be prepared experimentally. Actually, the only effort known to us to perform the synthesis has been unsuccessful.49 In order to address this point and following the approach of ref 50, 9025



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