Quantification of Structural Properties

As illustrated in the introduction 1.2, steric strain on the fluorophore and structural distortion resulting from it have been introduced as factors of fluorescence quenching by Mizobe et al.^{[49, 51]} Because their anthracene derivatives were close to perfectly planar, they quantified steric strain by IR spectroscopy. In contrast, the anthracene derivatives described here show tangible deformations induced by steric strain, which can be quantified by geometrical operations.

The crystal structure of SPAnPS@tol is depicted in Figure 3-19. It shows the SPAnPS molecule and two co-crystallized lattice solvent molecules in interaction with the aromatic π-system. This figure will be used to visualize the structural properties of anthracene derivatives which shall be quantified.

Figure 3-19: Crystal structure of SPAnPS@tol.

It exhibits one of two types of structural deformation of the fluorophore observed for anthracene derivatives. The anthracene moiety can undergo “folding”, whereupon both peripheral C6-perimeters are bent symmetrically away from the mean plane towards one another. This type of deformation was quantified by generating planes through the carbon atoms in 1,2,3,4-position and 5,6,7,8-position (Figure 3-20, bottom) and determining their intersecting angle. The atoms in these positions were chosen because they represent the outermost array of the anthracene moiety, at which the impact of folding is maximal and the largest angle relative to the former mean plane is spanned.

Figure 3-20: Planes generated for determination of the “folding angle” α of the anthracene moiety.

The second form of deformation is “twisting” of the anthracene moiety. In this case the peripheral C6-perimeters are twisted relative to the central ring (Figure 3-21). This can happen in symmetrical manner, when both outer rings are twisted in the same direction relative to the central ring, or in asymmetrical manner, when they are twisted in opposite directions.

Figure 3-21: Determination of the “twist angle” φ of the anthracene moiety: φ = + .

For quantification of this phenomenon a plane through the 8a,9a,4a,10a carbon atoms of the central ring of the anthracene moiety was generated. Then lines were plotted through the carbon atoms in 2,3-position and 6,7-position and the angles β1

and β2 which these enclosed with the plane of the central ring were determined (Figure 3-21, bottom). In un-substituted anthracene these lines are parallel to the plane of the central ring, only the twisting of the molecule leads to an intersection of line and plane. To acquire the total twist angle of the anthracene moiety, the angles of both lines were summed up to the total twist angle φ = + . The carbon atoms used for the line plots were again chosen because they represent the most peripheral bond in the anthracene molecule, at which the effect of twist deformation is strongest.

Both forms of deformation regularly occur in combination.

By this method a folding angle of 0° is found for SPAnPS@tol. This can be attributed to the symmetry of the compound. Because the asymmetric unit contains only one half of the SPAnPS molecule, the other half is generated by symmetry operations. This leads to the complete absence of folding. A twisting of the anthracene moiety however is observed. A symmetrical twisting of the outer rings – again induced by the symmetry of the compound – is found, producing two identical twist angles of 10.0°, adding up to a total twist angle of 20.0°.

The second important factor which can be derived from solid state structures and subsequently quantified is information on intermolecular interactions. While deformation is a property of an isolated molecule, intermolecular interactions result from the packing of molecules in the solid state, which makes the utilization of packing-plots inevitable. As pointed out in the introduction, the most prominent interaction of aromatic compounds like anthracene derivatives is π-π overlap, often also referred to as π stacking. This interaction has often been quantified by measurement of π-π distances and percentage of π-π overlap as indicators for the strength of the respective interaction.[47-48, 48e, 50, 53-54] Though the interpretation of such interactions regarding their influence on solid state fluorescence has been contradictory in several points (c.f. 1.2), this method was also applied to the illustrated by Nishio.^[66] Some arrangements are so stable that the conformation of the corresponding organic molecules even in solution is influenced by C–H^…π bonds.

Furthermore, recent calculations have verified the importance of this type of interaction despite the weak polarity of the C-H bond. The strength of the C–H^…π bond is not only determined by its length, also the angle of the C-H-bond to the π-system is crucial - an orthogonal orientation is regarded as the most stable arrangement generating the strongest interaction.^[67] Additionally, the polarity of the C-H-bond is an important factor in classifying the strength of a C–H^…π interaction. The strength of the interaction increases with rising polarity of the C-H-bond. Therefore aliphatic sp³ C-H-bonds produce weaker C–H^…π bonds than aromatic sp² C-H-bonds.^[66]

To quantify the observed C–H^…π interactions, the distance from the hydrogen atom to the plane of the participating aromatic ring was determined, as well as the angle of the C-H bond to this plane (Scheme 3-4).

Scheme 3-4: Quantification of C–H^…π interactions: d = Hydrogen-π distance, α = angle of C-H bond to the ring plane.

The importance of C–H^…π bonding in the structure of SPAnPS@tol was recognized by Fei et al. and the contribution of this interaction to the formation of the T-shaped excimer complex was stated.[44b, 44c]

Figure 3-19 shows the sp² C–H^…π bond from the toluene molecule to the π-system of the anthracene moiety. It encloses an angle of 76.8° with the π-system, which is fairly close to the optimum orthogonal orientation.

Though clearly weaker, there is a second C–H^…π interaction found between a methyl C-H of the toluene molecule and the anthracene π-system. This was not documented by Fei et al., presumably due to the slightly longer distance, the smaller angle of only 35.0° and the weaker polarity of the sp³ C-H bond. In the following all C–H^…π interactions will be classified this way when a noteworthy contribution of this type of interaction is present.