DFT calculations and structural comparisons

Optimised structures of the dyes with all-trans conformations of the propyl chains were obtained from DFT calculations and are shown in Figure 3.9. These optimised structures were used to obtain calculated IR, Raman and NMR spectra, and a comparison with the respective experimental spectra, presented in Appendix 1.4-1.6, shows a good match generally between experiment and calculation, providing support for the quality of these optimised structures.

Figure 3.9 Optimised structures of the dyes in all-trans conformations at the B3LYP/6-31g(d) level of theory.

All of the optimised dye structures exhibit an essentially planar anthraquinone core.

Using the numbering system shown in Figure 3.10, the calculated bond lengths between the non-hydrogen atoms in the anthraquinone core of the five dyes are listed in Table 3.6, along with those from experimental crystal structures of related compounds, which also show essentially planar cores. The calculated structures were not symmetry-constrained but, as can be seen from Figure 3.9, they may all be considered to exhibit approximately C2h symmetry when all the substituent phenyl conformations are

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considered. Thus, one half of the anthraquinone core was considered in the analysis of bond lengths.

The bond lengths within the anthraquinone cores are generally consistent between the dyes, both from the calculated structures and the crystal structures. In general, the longest C−C bonds are the C⁹−C¹³ and C¹⁰−C¹⁴ bonds in the central ring, and the shortest bonds are those around the outer ring. The presence of C¹³−C¹⁴ bonds that are shorted than the other C−C bonds in the central ring is indicative of the quinoidal nature of the central rings in all these anthraquinone compounds.¹⁷² Closer inspection of the bond lengths within the central ring of the anthraquinones shows that the C¹³−C¹⁴ bond lengths increase on going from less electron-donating substituents (e.g. 26B3 and 15SB3) to more electron-donating substituents (e.g. 15NB3 and 15NB3OH), whereas the C⁹−C¹³ and C¹⁴−C¹⁰ bonds show a slight tendency for the opposite behaviour. The C¹³−C¹ bond lengths are also shown to increase with increasing electron-donating character of the substituent at the 1- position.

Figure 3.10 Generalised structures and atom numbers used for labelling bond lengths and angles for the 1,5-disubstituted dyes (left) and the 2,6-disubstituted dyes (right).

Table 3.6 Selceted bond lengths (Å) of the anthraquinone cores for the optimised dye structures shown in Figure 3.9 and from the crystal structures of anthraquinone (AQ), ¹⁷¹ anthraquinone-1,5-dithiol (15SH), ¹⁷³ N,N'-diphenyl-l,5-diaminoanthraquinone (15NB0) ²¹⁸ and 2,6-diphenyl-anthraquinone (26B0), ¹³⁷ using the numbering scheme shown in Figure 3.10.

Dye CO 9-13 10-14 13-14 13-1 1-2 2-3 3-4 4-14

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Table 3.7 lists the bond lengths between the anthraquinone core and the directly attached substituent groups, from which it can be seen that the calculated C-S, C-N and C-C bond lengths of the dye-substituent groups generally match well with the respective bond lengths obtained from crystal structures of comparable compounds. The C-O and O-H bonds are calculated to be 1.34 Å and 1.00 Å, respectively, for both 15NB3OH and 26B3OH, showing that there is little difference between the bond lengths of either the carbonyl or the hydroxyl groups in these structures.

Table 3.7 Bond lengths (Å) between the anthraquinone cores and the directly substituted groups of the optimised dye structures shown in Figure 3.9 and for the crystal structures of related compounds,137, 173, 218

using the numbering scheme shown in Figure 3.10.

C¹-S¹ C¹-N¹ C²-C

The slight variations in the calculated structures of the anthraquinone cores between the dyes show changes in bonding that link to electronic, vibrational and related effects but these changes are relatively subtle, such that the variation in the overall molecular shapes evident in Figure 3.9 largely arises from the orientation and structural variation within the substituent groups. For the 1,5-disubstituted structures, there is a significant difference between the C-S-C and the C-N-C bond angles, which are calculated as 102°

for 15SB3, and 129° for both 15NB3 and 15NB3OH, such that the phenyl rings and alkyl chains are oriented further from the anthraquinone core in 15NB3 and 15NB3OH than in 15SB3.

The angles between the planes of the substituent phenyl rings and the plane of the anthraquinone core vary between all five structures, as shown in Figure 3.9 and also by the end-views of the structures shown in Figure 3.11. The molecular planes of the anthraquinone core and phenyl substituent rings were defined as the planes containing the axes of minimum and secondary moments of inertia of the respective sets of constituent carbon atoms to obtain the angles given in Figure 3.11. In the case of

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15SB3, the phenyl rings lie at 90° to the plane of the anthraquinone core (as shown also in Figure 3.9), whereas in 15NB3, 15NB3OH, 26B3 and 26B3OH the phenyl rings lie at 45°, 45°, 35° and 41° to the plane of the anthraquinone core, respectively. These calculated values are not entirely consistent with those of ca. 60° and 30° measured from crystal structures of 15NB0 and 26B0, respectively,^{137, 218} but this difference may be attributable to comparing the experimental geometries obtained from crystal structures with calculated gas-phase structures.

Figure 3.11 End-views of the optimised structures of the dyes showing the angle made between the plane of the anthraquinone core (drawn vertically in each case) and the plane of the phenyl substituents for each of the dyes.

Considering the overall molecular shapes, it can be seen qualitatively from Figure 3.9 that the 2,6-disubstituted structures are the most “rod-like” of the dyes studied, and this property may be quantified in terms of the calculated aspect ratios of the molecules. In order to calculate the aspect ratios, the long axes of the dyes were defined as the minimum moment of inertia (MOI) axes of the optimised structures. The van der Waals structures of the dyes are shown in Figure 3.12, along with bounding dimensions calculated parallel and perpendicular to the minimum moment of inertia axes to define the molecular lengths and widths, respectively, from which the aspect ratios were determined.

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Figure 3.12 van der Waals structures and bounding boxes indicating the molecular lengths and widths from which the aspect ratios of the dyes were calculated.

These calculated lengths, widths and aspect ratios are listed in Table 3.8, and a comparison of the aspect ratio values is shown graphically in Figure 3.13. It is evident from the structures in Figure 3.12 that, for the dyes studied in this work, the presence of the terminal alkyl chains has a significant influence on the molecular lengths and hence on the aspect ratios of the dyes. Optimisations of equivalent dye structures with the terminal propyl groups replaced with hydrogen atoms were carried out and the trend in aspect ratios was found to be the same as that listed in Table 3.8 (see Table A1.7 in Appendix 1.7), indicating that the variation in the aspect ratios between the dyes is due to the differences in the nature of the anthraquinone substituents rather than the specific conformations or lengths of the terminal propyl chains on the phenyl substituent groups.

Table 3.8 Molecular lengths, widths and aspect ratios of the dyes measured from the van der Waals surfaces of the optimised structures shown in Figure 3.12.

Dye Length / Å Width / Å Aspect ratio

15SB3 26.44 8.84 2.99

15NB3 26.93 10.13 2.66

15NB3OH 26.92 10.62 2.53

26B3 26.99 8.48 3.18

26B3OH 27.10 8.37 3.24

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Figure 3.13 Comparison of the aspect ratios calculated for the dyes.

The aspect ratio values show quantitatively that the 2,6-disubstituted species are the most like of the five dyes, and they also indicate that the amine dyes are less rod-like than the sulfide dye. This latter comparison is consistent with the experimental observations that, in general, the order parameters of sulfide-substituted anthraquinone dyes are higher than those of amino-substituted anthraquinone dyes.^{59, 65, 66}

For the 1,5-disubstituted structures, the difference in aspect ratios between the dyes may be rationalised in terms of the specific structural units: the C-S-C bond angle is calculated to be smaller than the C-N-C angle, and hence the phenyl rings and alkyl chains lie closer to the long axis of the anthraquinone core in 15SB3 than in both of the amine dyes, resulting in a more rod-like structure for 15SB3 than 15NB3 and 15NB3OH. In addition, the perpendicular orientation of the phenyl rings in 15SB3 with respect to the plane of the anthraquinone core reduces the molecular width, causing an additional slight increase in the aspect ratio. The effect of the hydroxyl groups in 15NB3OH is to decrease the aspect ratio slightly compared with 15NB3, because the oxygen atoms directly increase the molecular width, albeit only by a small amount. By contrast, the effect of the hydroxyl groups in 26B3OH is to slightly increase the aspect ratio compared with 26B3. This is an indirect effect, because the position of substitution means the hydroxyl groups do not directly influence the molecular dimensions, as can be seen in Figure 3.12, but the relatively high atomic mass of the oxygen causes a slight change in the axis of minimum moment of inertia along which the aspect ratio is measured, resulting in 26B3OH having both a longer length and a narrower width than 26B3.

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When analysed in the context of the colours of the dyes, the interplay between the molecular shape and colour may be seen. In the case of the 1,5-diphenylamino substituted dyes, the addition of hydroxyl groups to 15NB3 to form 15NB3OH results in absorption at a longer wavelength, but decreases aspect ratio and hence the rod-like nature of the molecular shape. In the case of the 2,6-diphenyl substituted dyes, the addition of hydroxyl groups to 26B3 to form 26B3OH also results in longer wavelength absorption but, by contrast, it results in a slight increase in the aspect ratio and hence the rod-like nature of the molecular shape.