Pierre
Guiglion
and
Martijn A.
Zwijnenburg
*
Department of Chemistry, University College London, 20 Gordon Street, WC1H 0AJ, UK. E-mail: m.zwijnenburg@ucl.ac.uk
First published on 12th June 2015
We use a combination of Time-Dependent Density Functional Theory (TD-DFT) and approximate Coupled Cluster Theory (RI-CC2) to compare trends in the optical gap and fluorescence energies of ortho-, meta- and para-oligomers of phenylene. We find that RI-CC2 and TD-DFT calculations using three different commonly employed XC-potentials (B3LYP, BHLYP and CAM-B3LYP) generally give consistent predictions. Most importantly, the fluorescence energy of m-phenylene is predicted to be independent of oligomer length, the fluorescence energy of p-phenylene to decrease with oligomer length and that of o-phenylene to increase. The origins of these differences in behaviour between the different isomers are analysed and found to stem from a subtle combination of steric and electronic factors.
The differences in the optical properties of the different phenylene isomers are not merely of academic interest. Polyphenylene finds application in light emitting diodes11 and as photocatalyst12–16 for the reduction of protons to molecular hydrogen and carbon dioxide to formic acid, both in the presence of a suitable electron donor. Most of these applications involve p-phenylene and it stands to reason that the other isomers would give rise to a different performance in such applications. Indeed a study that explicitly compared the ability of o-terphenyl, m-terphenyl and p-terphenyl oligomers to act as photocatalyst for the reduction of carbon dioxide found that p-terphenyl was significant more active than the other two isomers, and interestingly also more active than the p-phenylene polymer.14
Elucidating the origin of the starkly different optical properties of the isomers of such a conceptually simple polymer is clearly both an academically and practically relevant question. Not surprisingly, there is thus a large number of computational studies on the optical3,4,6,8 and related structural9,10 properties of oligomers of phenylene. Such studies generally focus on only one of the three isomers and attempt to correlate its structural and optical properties. Here we go a step further, and study oligomers of all three isomers of phenylene on an equal footing in order to uncover the overarching structural and electronic features that explain the deviation between the optical properties of the different isomers. In order to minimise the chance of computational artefacts complicating the comparison between the different isomers, we not only use time-dependent density functional theory (TD-DFT) to calculate the optical properties of the oligomers but also, where possible, approximate couple cluster theory. Finally, we carefully consider the treatment of intramolecular dispersive interactions, which will prove to be especially crucial in the case of o-phenylene.
For the conformational sampling, we employed the OPLS-2005 forcefield21 and the low-mode sampling algorithm,22 as implemented in Macromodel 9.9.23 We used a combination of 10000 Monte Carlo search steps and minimum and maximum low-mode move distances of 3 and 20 Å respectively. All the structures located within an energy window of 200 kJ mol−1 relative to the lowest energy conformer were saved.
The DFT and TD-DFT calculations employed three different hybrid Exchange–Correlation (XC) potentials; B3LYP,24–27 BHLYP26 and CAM-B3LYP.28 The B3LYP and BHLYP XC-potentials includes 20 and 50% Hartree-Fock-like exchange (HFLE) respectively, whereas the percentage of HFLE in CAM-B3LYP, a range separated XC-potential, changes from 19 to 65 with increasing interelectronic separation. As a result the asymptotic behaviour of the CAM-B3LYP XC-potential (the derivative of the XC-potential with respect to the interelectronic separation r) will be closer to the formal 1/r dependence of the exact XC-potential. Furthermore, in all TD-DFT calculations, the Tamm–Dancoff approximation to TD-DFT29 was used, which fixes among other things problems with triplet instabilities present in full TD-DFT.29,30 Finally, we performed in the case of B3LYP also calculations using Grimme's D3 empirical dispersion correction.31–33
In the B3LYP and BHLYP calculations, the double-ζ DZP34 basis set was used, while the CAM-B3LYP calculations typically employed the 6-31G** split-valence basis set.35 A limited number of calculations with other basis-sets such as the larger triple-ζ def2-TZVP36 were performed for selected systems in order to check the effect of the basis set size on the results.
The CC2 calculations were carried-out using the frozen core approximation and the resolution-of-the-identity (RI-CC2) approximation to the electron repulsion integrals. The majority of RI-CC2 calculations, for reasons of computational tractability, further employed the small def2-SV(P)34 split-valence basis. However for single points on the smallest oligomers, calculations with the larger triple-ζ def2-TZVPP36 basis set were also performed.
Finally, all B3LYP, BHLYP and RI-CC2 calculations were performed with the Turbomole 6.5 code.37,38 The CAM-B3LYP calculations used NWChem 6.039 except in the case of the TD-DFT S1 relaxations, which were performed using GAMESS-US40 (version 1 October 2010 R1).
The class of p-phenylene conformer we focus on are the lowest-energy structures for each oligomer length. It consists of a linear backbone, and has alternating torsion angles of approximately +37° and −37° (see Fig. 1A). Another slightly higher energy class of p-phenylene conformer also has a linear backbone, but with +37° torsion angles between each phenylene unit, making it essentially helical. The latter structural difference, however, is of limited significance in the context of our study, since the optical properties of both conformers are generally very similar (see Section ESI-1 of the ESI†).
The class of o-phenylene conformer we focus on are again the lowest-energy structures for each oligomer length (when taking into account the dispersion correction). This class of conformer has a helical backbone, where phenylenes stack every three units (see Fig. 1B). For m-phenylene, finally, we consider three low-energy conformers: the flat lowest-energy conformer (see Fig. 1C), and two conformers with helical backbones (large helix and small helix, see Fig. 1D and E). All those three m-phenylene conformers yield almost identical optical properties (see Section ESI-1 of the ESI†), and are treated collectively below.
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Fig. 2 Optical gap values as a function of oligomer length for the different phenylene isomers calculated with TD-B3LYP (A), BHLYP (B), CAM-B3LYP (C) and RI-CC2 (D). |
For p-phenylene, a pronounced red shift in the optical gap with increasing oligomer length is observed, as previously reported in the literature1,3–5 (see also Section ESI-3 of the ESI†). o-Phenylenes show similar behaviour, again in line with literature.6,8,9 However in this case, use of Grimme's dispersion correction31–33 to DFT (DFT-D3) is needed to accurately describe Van der Waals interactions (arene–arene π-stacking) between the phenylene units, due to their spatial proximity. Calculations on o-phenylene without the use of DFT-D3 in contrast predict that the optical gap first decreases then increases and ultimately decreases again with increasing oligomer length. Finally, for m-phenylene, increasing the oligomer length does not result in any significant change in the calculated optical gap values beyond the trimer, again in agreement with literature10 where they are described as “conjugation breakers”.
Finally, the effective conjugation length of o-, m-, and p-phenylene was calculated in the case of TD-B3LYP using the methodology of Meier and co-workers.41 Among the three isomers, p-phenylene is predicted to have the longest effective conjugation length (∼20 repeat units, λ∞ ≈ 370 nm, E∞ ≈ 3.35 eV), followed by o-phenylene (∼10 units, λ∞ ≈ 293 nm, E∞ ≈ 4.23 eV), and ultimately m-phenylene (∼6 units, λ∞ ≈ 276 nm, E∞ ≈ 4.49 eV). The here predicted p- and o-phenylene conjugation lengths are larger than the values obtained from experimental spectra; 9 and ∼4 respectively, but the calculations and experiment agree on the relative conjugation lengths of the different isomers.7,41 The consistent difference in the absolute magnitude of conjugation lengths between the calculations and experiment is probably due to a combination of three factors. Firstly, our calculations ignore thermal effects that might reduce the effective conjugation length, secondly, experimentally the spectra of many longer oligomers do not show well-defined peaks, and thirdly, the general insolubility of the same oligomers in most solvents means that experimental spectroscopy is inherently limited to short oligomers.
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Fig. 3 TD-B3LYP average ground (right) and excited state (left) interphenylene torsion angles as a function of oligomer length for the different phenylene isomers. |
The case of using standard DFT when describing o-phenylene, where the optical gap is predicted to decrease, increase and decrease again, is a more complicated. The fact that o-phenylene forms helical structures with close contact between non-directly adjacent phenylene units means a more accurate description of non-covalent dispersion interactions is required than available in standard DFT. As a result, while DFT and dispersion corrected DFT-D predict essentially identical structures and optical gap values for p- and m-phenylene, their predictions differ considerably for o-phenylene. As can be seen in Fig. 3, use of standard DFT results in the prediction that the average interphenylene torsion angle of o-phenylene increases with oligomer length rather than stays constant. As a result the trend in the optical gap for o-phenylene and plain DFT is a convolution of two trends; the decrease in optical gap with increasing oligomer length and the increase in the optical gap with increasing torsion angle. It should be noted here that the effect of the dispersion correction is purely structural and single point TD-DFT vertical excitation energy calculations with DFT and DFT-D give identical results.
Which brings us to the non-conjugated nature of m-phenylene oligomers. From the average interphenylene torsion angle values for m-phenylene in Fig. 3 it is clear that that this lack of conjugation is not due to the torsion angle being close to 90°. As a matter of fact the average torsion angle values for o-phenylene oligomers are only very slightly larger than those of p-phenylene oligomers. Having ruled out that the lack of direct geometrical overlap is the origin of the lack of conjugation, we can consider alternative explanations. The most promising of such an alternative explanations, is the proposal by Hong and co-workers10 that the lack of overlap between the π-systems of adjacent phenylene units arises from the fact that the frontier orbitals contributing to this excitation only have small coefficients on the meta C atoms. Indeed, using DFT we find that for the dimer the atoms meta- with respect to the interphenylene bond have a much lower contribution to the frontier orbitals than the atoms that lie para- or ortho-. Similarly, in the valence bond perspective of van Veen and co-workers,42m-phenylene is cross-conjugated,43,44 meaning that one can not conceive a direct pathway involving alternating double and single bonds between more than two phenylene units (see Scheme 2), while the other two phenylene isomers are omniconjugated, and have such pathways. Both explanations thus suggest that the origin of the lack of conjugation in m-phenylene oligomers in a topological rather than a geometric feature. As a result, while the optical gap of p- and o-phenylene can be controlled by changing the interphenylene torsion angle by tuning of the steric bulk of substituents, this strategy does not work for m-phenylene.
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Scheme 2 Direct pathways of alternating double and single bonds in p- and o-terphenyl (A & C) and absence of such a pathway in m-terphenyl (B). |
The break in conjugation when introducing m-phenylene units, finally, can conveniently be observed by modelling an oligomer consisting of two p-phenylene regions (3 or 4 units, depending on the perspective) separated by a m-phenylene segment in the centre of the molecule (see Fig. 4). For this oligomers the TD-B3LYP predicted optical gap (4.06 eV) is very similar to the optical gap of an isolated p-phenylene tetramer (4.11 eV) and much larger than the value for the p-octamer (3.58 eV). This effect can also be observed from the electron density difference between the ground and the excited state (negative density difference in blue, positive difference in red), which shows that the lowest energy singlet excitation only involves to the para-chain ends (see Fig. 4).
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Fig. 5 Fluorescence energy values as a function of oligomer length for the different phenylene isomers calculated with TD-B3LYP (A), BHLYP (B), CAM-B3LYP (C) and RI-CC2 (D). |
A structural comparison of TD-B3LYP geometries shows that in the case of p-phenylene oligomers the main differences between the ground and relaxed excited state minimum energy structures responsible for the fluorescence are (i) a decrease in the interphenylene torsion angles relative to those in the ground state (see Fig. 3, 6, and Fig. S5 in Section ESI-5 of the ESI†) and (ii) a para-quinone like distortion of the bond lengths (see Fig. 7). Both distortions are in all cases symmetrically delocalised over the whole chain with the largest distortion in the centre.
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Fig. 6 Variation of the TD-B3LYP calculated excited state interphenylene torsion angles along the oligomer for the different p-phenylene oligomers. |
For o-phenylene, a similar reduction in torsion angles relative to the ground state is observed (see Fig. 3, 8 and Fig. S6 and S7 in Section ESI-5 of the ESI†) but now combined with an ortho rather than a para-quinone like distortion of the bond lengths (as previously discussed by Hartley,8 see Fig. 9). Interestingly, the reduction of the torsion angle and the ortho-quinone like distortion of the bond lengths go together with two other types of distortions that are essentially unique to the excited state minimum of o-phenylene oligomers. Firstly, (i) there is a significant distortion of the planarity of the phenylene unit and, secondly, (ii) after excited state relaxations the interphenylene bonds typically do not lie (anymore) in the same plane as either of the phenylene units they connect. Both of these latter “planarity” distortions are to a certain extent already present in the ground state structure of o-phenylene oligomers but become magnified enormously after excited state relaxation. A tell tale sign, finally, of (ii) is that the magnitude of the torsion angle between two phenylene units is different depending on which pair of atoms beyond those directly involved in the phenylene–phenylene bond are chosen to represent the interphenylene torsion angle (by up to approximately 20°, see torsion angles 1–2–3–4 and 1′–2–3–4′ in Scheme 3) and the values in Fig. 3 and 8 are thus averages of the two unique angle choices.
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Fig. 8 Variation of the TD-B3LYP + D calculated excited state interphenylene torsion angles along the oligomer for the different o-phenylene oligomers. |
The number of phenylene units involved in the distortion and the degree to which it is predicted to be symmetric, differ with oligomer length and the use of dispersion correction. TD-B3LYP + D predict that the excited state minima remain symmetrical up to the heptamer, where most likely the excited state is delocalised over the whole oligomer length. The maximum distortion relative to the ground state structure is for all these oligomers in the centre of the chain and the most flattest torsion angles generally occur at either end of the oligomer. For the octamer, in contrast, TD-B3LYP + D predicts an asymmetric excited state minimum, where the excited state appears to localise on one side of the oligomer. Use of plain TD-B3LYP yields for oligomers up to and including the pentamer symmetric excited state minima with a delocalised excited state, and for the longer oligomers asymmetric structures, where the excited state has localised on one site of the chain (similar to that of the TD-B3LYP + D octamer excited state minimum). The increase of selected torsion angles far away from where the excited state localises in asymmetric excited state minima (i.e. torsion angles that are actually larger than in the ground state structure, as previously observed by Hartley8) is only observed in our calculations in the absence of dispersion correction. RI-CC2 calculations, finally, only numerically tractable for up to the pentamer, yield symmetric excited state minima, similar to those found with TD-B3LYP + D and plain TD-B3LYP.
For m-phenylene, finally, excited state relaxation results in an extremely well localised excited state (see Fig. 3, 10 and Fig. S8 in Section ESI-5 of the ESI†). In line with the lack of conjugation in this isomer, already discussed above, always only two adjacent torsion angles and the associated two interphenylene bond distances are significantly distorted. The distortion in terms of intraphenylene bond distance changes (see Fig. 11) is limited to the three phenylene units around these torsion angles and does not follow a simple pattern, perhaps because there is no such thing as a meta-quinone like distortion.
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Fig. 10 Variation of the TD-B3LYP calculated excited state interphenylene torsion angles along the oligomer for the different m-phenylene oligomers. |
Focussing first on the question of the origin of the difference between o- and p-phenylene, it is clear that this cannot be simply related to the magnitude of the excited state interphenylene torsion angle. Comparing oligomers of similar size, the torsion angles in the excited state structure of o-phenylene are consistently significantly larger than that of p-phenylene (see Fig. 3, 6 and 8). As the excited state for these smaller oligomers is always delocalised one would thus, based on the link between torsion angle and π-systems overlap, naively have expected the fluorescence energy of o-phenylene to be larger than that of p-phenylene. Similarly, for short o- and p-phenylene oligomers the change in torsion angle between the ground and excited state is similar in magnitude but the Stokes shift (and its ESSE and GSDE components) is much larger in the case of o-phenylene than for p-phenylene oligomers of the same size. Also, the excited state interphenylene bond distances of o- and p-phenylene oligomers of the same size are very similar (see Fig. S9 in Section ESI-5 of the ESI†), suggesting no link between this structural degree of freedom and the fact the fluorescence energy of p-phenylene is larger than that of o-phenylene either. Finally, partial excited state optimisation of dimeric clusters cut from the o-phenylene trimer and tetramer excited state minima, where all atoms but the newly added one or two terminating hydrogen atoms are held fixed, have larger fluorescence energies than the fully optimised dimer. The planarity distortions thus also cannot explain the low o-phenylene fluorescence energies, at least not for dimer fragments. Having effectively ruled out most structural explanations, it thus stands to reason that the lower fluorescence energies of short o-phenylene oligomers relative to their p-phenylene counterparts must find its origin in the inherent electronic structure of o-phenylene in general, and the presence of an ortho-rather than a para-quinone like distortion in particular, as the optical gap appears well behaved. Support for this hypothesis comes from the observation that, independent of the XC-potential employed and oligomer length, the difference between the Kohn–Sham orbital energy gap for the pair(s) of orbitals responsible for the lowest energy TD-DFT excitation and its TD-DFT energy is always considerably larger for o-phenylene than for p-phenylene. For example, in the case of TD-B3LYP the energy difference between the Kohn–Sham gap and the lowest TD-B3LYP excitation energy is of the order of 0.1–0.2 eV for the p-phenylene oligomer excited state minima and 0.4–0.6 eV for their o-phenylene counterparts. In linear response TD-DFT the Kohn–Sham gap is the zeroth-order approximation to the lowest TD-DFT excitation energy, with all higher-order corrections due to a combination of the contributions of the Hartree and XC kernel (fXC, the functional derivative of the XC-potential with respect to the density48). The larger difference between the Kohn–Sham gap and lowest TD-DFT excitation energy for o-phenylene oligomers thus suggest that the Hartree and fXC correction is much larger for o-phenylene than for p-phenylene and that the two oligomers indeed fundamentally differ in their many-body electronic structure beyond simply the constituting Kohn–Sham orbitals.
Which brings us, finally, to with the question of the origin of the characteristic blue shift of the fluorescence energies of o-phenylene oligomers with increasing oligomer length. Focussing on the oligomers with symmetric excited state minima and delocalised excited states, it is clear that the torsion angles of the excited state minima steadily increase with oligomer length for o-phenylene (e.g. in terms of the average torsion angle for TD-B3LYP + D an increase from 23° for the trimer to 40° for the hexamer, see Fig. 3). For p-phenylene there is also an increase in the excited state torsion angle with oligomer length but the magnitude of the change is considerably smaller than for o-phenylene (e.g. in terms of the average torsion angle for TD-B3LYP an increase from 10° for the trimer to 17° for the hexamer, see Fig. 3). If we now assume that the change of fluorescence energy with oligomer length is a balance between two competing effects; the decrease in excitation energy with increasing oligomer length and the increase in excitation energy with increasing torsion angle, then it appears that for o-phenylene and p-phenylene different terms dominate. For p-phenylene oligomers, the increase in torsion angle with oligomer size is relatively small and the decrease in excitation energy with increasing oligomer length dominates, resulting in the conventional red shift in fluorescence energy with oligomer length. While for o-phenylene oligomers the increase in excitation energy with increasing torsion angle dominates, giving rise to the rather unique blue shift with oligomer length. The large change in torsion angle with increasing o-phenylene oligomer length, finally, is probably related to an increase in steric repulsion due to a growth of the number of intraoligomer close arene–arene π-stacking contacts with increasing oligomer length (i.e. 0, 1, 2 and 3 for n = 3, 4, 5 and 6 respectively). Such close arene–arene π-stacking contacts are completely absent in p-phenylene oligomers and all other “straight” conjugated polymers, while for helical structures their effect probably decreases with increasing size of the pitch (4 in the case of o-phenylene), explaining why a blue shift in fluorescence energy with increasing oligomer length is such a rare phenomena.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5cp01916h |
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