Linear acenes

We earlier recalled that one can build a huge number of molecules by simply assembling CeH rings, a scheme that was summarized in Table 1.4, and that a solid such as graphite can be obtained in this gedanken synthesis. Let us briefly discuss the case of linear acenes, which are linear polycyclic aromatic hydrocarbons (PAHs) composed of laterally fused CeHe rings. 

We also considered in Section 1.2 the possibility of preparing Mobius-band molecules from cycloacenes. In fact regular cycloacenes, that is molecules built from joining both ends of linear acenes without twisting, have never been obtained, despite several experimental attempts. They are interesting since they represent the basic cylindrical carbon units of zig-zag ( ,0) nanotubes. 

Finally, just a few words dedicated to the synthesis of polyphenylenes, extremely important polymers, and in particular substituted polyphenylenes such as PPV, which exhibit superb thermal and chemical resihence, semiconduchng properties upon doping and applicahons such as OLEDs. Contrary to their linear acenes counterparts, long polyphenylenes can be obtained e.g., by Bergman s method consisting in the thermal cycloaromatization of enediynes (Lockhart et al, 1981). 

Fig. 8. Correlation of the natural logarithms of molecular succeptibility, xm(B) and anisotropy, AK, for the linear acenes with the corresponding connectivity indices of the equivalent Gutman trees, yJT), Eq. 11, drawn to the left of the correlation lines...

Heilbronner mode symmetries have been tabulated for various series of n systems [13]. Some specific results are in unbranched polyenes, the unique Heilbronner mode is either totally symmetric (2/ )-polyene] or has the symmetry of a dipole moment along the chain [(2n + l)-polyene] in 2n -linear acenes the Heilbronner modes span nAg + nB u of D2h, and in [2n + l]-linear acenes have an extra BXu component the Heilbronner modes of the tetrahedron, cube and dodecahedron span E(Td), Eg + T2u(Oh), and //, + Hu(Ih), respectively, reducing the sets of modes to be considered from 2, 5 and 10 to just 1, 2, and 2 independent distortive modes which can be constructed easily by hand . 

Here the number of hexagons (h = 1,2,3,...) is indicated by subscripts. The relations (5) and (6) are illustrated in Fig. 9 and Fig. 10, respectively. From each system with h hexagons three systems with h + 2 hexagons are generated by adding two hexagons to the ends in three ways. One system, generated from the linear acene, must be added to the set. 

From algebraic equations (Section 5.2) cf. also (for h < 8) Balaban and Harary (1968) [13] Balaban (1969) [30]. Abbreviations a (linear) acenes c centrosymmetrical m mirror-symmetrical u unsymmetrical... 

A catacondensed benzenoid with dihedral symmetry, viz. D2h is either a branched system or an (unbranched) linear acene. A centrosymmetrical (C2h) catacondensed benzenoid is either branched or unbranched. The D2h systems under consideration have been enumerated by the efficient algorithm invoking SCS s (cf. Sect. 6.4) [80], Table 20, in combination with Table 17, shows the known numbers for the branched catacondensed Dlh and C2h benzenoids. The numbers of unbranched catacondensed benzenoids with C2h symmetry are found under the designation d in Tables 14 and 15 for h < 20 and 21 < h < 30, respectively. 

Fig 13 General hierarchies based on partitions of 6,7 and 8 respectively Top levels correspond to linear acenes, star trees and perfect graphs while bottom levels are those of the zigzag polyacenes and paths ... 

A more well known result is the case when a homologous set of linear acenes is defined where K(B.) = j+1 In Fig 14 we ow a number of homologous sereis of benzmoids Table 6 lists Clar [27] and sextet [39] polynomials for such equivalence classes ... 

The linear acenes, benzene to pentacene, are used as examples of the CURES-EC procedure. The results obtained utilizing MINDO/3 and AMI are compared. In addition to calculating the Ea by subtracting the energies of the optimized form, the LUMO of the neutral is compared with the experimental Ea. The electron affinity of hexacene has been estimated from the electronegativity and experimental ionization potential. As a further example of the use of CURES-EC, both the ionization potential and electron affinity of heptacene are estimated. The Ea of octacene and nova-cene are calculated for comparison to values obtained by using Koopman s theorem and a semi-empirical method based on a variable-parameter modification of the Pariser Parr Pople (PPP) approximation to the Hartree Fock equation [10]. 

The experimental and theoretical Ea for the linear acenes are shown in Table 7.2. The optimum CURES-EC values are equal to experiment within the uncertainty. They are compared with MINDO/3 LUMO, the AMI LUMO, the earlier Pariser Parr Pople Ea, and the calculated VEa. From the calculation for pentacene the MINDO/3 UHF value at 1.35 eV is the best value. The AMI results are all larger than those obtained by experiment. The best one, 1.44 eV, is the RHF(0033) or... 

Figure 7.1 Plot of the semi-empirical Ea versus the experimental Ea for the linear acenes 1 to 9. The squares are the CURES-EC values that are equal to the experimental values within the uncertainties [8], The x s stand for the Pariser Parr Pople calculated values [10]. The latter have systematic uncertainties that vary with magnitude.

The calculated MINDO/3 LUMOs for these molecules are lower than the experimental Ea by 0.70 eV and for AMI are higher than the experimental Ea by about 0.1 eV. These are shown in Figure 7.2. The systematic uncertainties remain constant. Figure 7.3 provides the optimum values of the VEa for the linear acenes. The VEa are between the A Ea and MINDO/3 LUMO values. The calculated VEa for hexa-cene to novacene support the AEa values of 1.65 eV to 2.0 eV. The systematic difference is the rearrangement energy. It is approximately 0.2 eV for anthracene and above. 

The charge densities for the anions can be displayed in HYPERCHEM as illustrated in Figure 7.5, where the charges on C and H are shown for the naphthalene anion. The Values of the linear acenes vary from —0.06 to 0.26q for benzene to —0.05 to 0.15q for naphthalene, to 0.04 to 0.18q for anthracene and tetracene. For pentacene the range is lowered to 0.03 to 0.14q. Thus, the solution energy differences should be smaller for the higher acenes and fullerenes. In predicting the reduction potential value for heptacene, this variation should be included. The reduction potential based on a value of 0.6 V versus Hg pool for hexacene is predicted to be —0.5 V versus the Hg pool. The value, if we assume a constant... 

The linear acenes illustrate the effect of extended conjugation. As the number of rings is extended in both the hydrocarbons and perfluorinated hycrocarbons, the Ea increases. However, for a nonlinear extension the Ea may or may not increase. For example, the Ea of phenanthrene is 0.30 0.02 eV, while that for anthracene is 0.68 0.02 eV. Likewise, the Ea of benzanthracene is less than that of tetracene. The curves for the linear acenes are an upper limit for the electron affinities of polycyclic aromatic hydrocarbons with the same number of six membered rings. The inclusion of five or seven membered rings will increase the electron affinity above those with solely six rings. The simplest example is the Ea of azulene, 0.8 eV, versus that of naphthalene, 0.16 eV. Interestingly, the calculated electron affinity of the perfluorinated azulene is 2.6 eV or about 0.2 eV per fluorine atom. 

Figure 7.20 Plot of the experimental electron affinities of the linear acenes and the calculated electron affinities of the perfluorinated linear acenes versus number of rings. The values are calculated using AMI. The values are given in Table 7.6.

Systematic studies of the absorption spectra of benzenoid aromatic hydrocarbons, mostly done by Clar in the 1930s and 1940s,279 showed that these compounds exhibit four types of UV VIS absorption bands, which are shifted in a regular way along a homologous series such as the linear acenes (benzene, naphthalene, anthracene,. ..) (Figure 4.16). 

In Fig. 15 the linear acene represents the most unstable system while the all-kinked acene being the most stable. These limits may be modelled respectively with a star tree (or a row of boxes) and a path (or a column of boxes). The para bands of UV spectra are indicated for some cases for which data are available (Clar (1972). It is interesting to observe that sequences of numbers which represent (yi, y2, yj, y4) lead to bifurcations (i.e. incomparable pairs) when the sequences, which correspond to Young diagrams, are also incomparable For example at the first bifurcation (Fig. s 10, 12) one finds the following pair of sequences of y s. 

The bisadduct 87, synthesized from anthracene bis-(l,4-epoxide) (88) and tetraphenylcyclone (89), is a synthetic equivalent of the [l,2-c 4,5-c ]benzodi-furan 90 (R=H). Adduct 87 reacts thermally with dienophiles including some exceedingly weak ones to give linear acene derivatives in moderate to very good yields (see Scheme 44 [142b]). 

Miao, Q. et ah, Self-assemhly and electronics of dipolar linear acenes, Adv. Mater. 17... 

M. L. Tang, T. Okamoto, and Z. Bao. High-Performance Organic Semiconductors Asymmetric Linear Acenes Containing Sulphur. Journal of the American Chemical Society, 128(50) 16002-16003, 2006. 

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