4.3 Results and discussion
4.3.2 Excited-state structures and chiroptical properties
In helicenes, fluorescence usually occurs from the S1 state.240 Therefore, to study the emission properties and CPL activities, optimizations of the four structures in their S1
mx= 0.00 my= -0.12 mz= -1.95 µx= -0.00 µy= 10.40 µz= 148.87
|µ|= 149.23
|m|= 1.96
mx= 0.00 my= 0.05 mz= -0.65
|µ|= 212.74
|m|= 0.65
µx= -0.00 µy= 211.88 µz= 19.16 µx= -94.22 µy= -0.03 µz= 241.89
mx= 1.14 my= 0.00 mz= -2.03
|µ|= 259.60
|m|= 2.33
µx= -0.03 µy= 19.24 µz= -144.44
|µ| = 145.72
mx= 0.00 my= 0.07 mz= 2.01
|m| = 2.01
(a) (b)
(c) (d)
Figure 4.6: EDTM (first row) and MDTM (second row) densities of9Ha(a),9HaP (b), 9HaQ (c), and 11Ha (d) for the S1→S0 transitions. The four columns in each section correspond to total and three components, respectively. Magnitudes of these vectors are in CGS units. The magnitudes in CGS units are obtained from the values in atomic units (a.u.) as follows: |µ|/esu·cm=(254.1746×10−20 esu·cm)× |µ|/a.u. and
|m|/erg·G−1 =(-1)× (0.927401 × 10−20/erg·G−1) × |m|/a.u.. Results are obtained using the Multiwfn3.8 software.263 Isovalue = 0.002 a.u. is used.
the values ofφ1 betweenS0 and S1 for9Ha,9HaPand9HaQ shows that the absolute values in S1 are smaller by 2-5°. Similarly, φ2 changes only by 6-9°. As shown in Table 4.1, in all the four cases one terminal unit is tilted outwards by 20-27°more than the other terminal unit, similar to the ground state results. 11Ha shows the largest difference of 27° between|φ3|and |φ4|. Comparing the Rpitch values, it is observed that the values in theS1 state are smaller than the values inS0. It implies that excited state geometries are more compact, consistent with the results of previous studies.266,267
Various properties such as emission energies, corresponding |µ| and |m| values, angles between the vectors and gCPL values are tabulated in Table 4.3. There are two possible ways to achieve a large value ofgCPL: 1. by decreasing the value of|µ| which can be achieved by forming a fully CT state and 2. by increasing the value of |m|. In case of 9Ha, |m| and cos θ values do not change significantly from the corresponding values in absorption. However, there is an increase in the value of |µ| in the case of emission and this results in a decrease in dissymmetry factor for S1→S0 compared to S0→S1. Both|µ| and |m|comprise mainly of Z-axis components (as shown in Figure 4.6) and both are directed along the helical axes. Density plots for the Z-components
Z 9Ha µ/50
θ=180˚ θ=170˚
9HaP Z
X µ/50
µ/100 Y
Z
Y
Z
Y
µ/50
9HaQ 11Ha
θ=91˚ θ=172˚
m
m
m m
Figure 4.7: Directions of EDTM and MDTM vectors of 9Ha, 9HaP, 9HaQ, and 11Hafor the transitionsS1→S0. While the vectors in9Ha, 9HaP, and9HaQlie in
theY Z plane, these are in theXZ plane for11Ha.
of both the vectors show relatively larger slate blue (positive) region compared to cyan (negative) region. On the other hand, forX-components as examples, the cyan and slate blue isosurfaces cancel each other out. Maximum contribution to the |µz| comes from the phenanthroline units at the terminals. For9HaP,|µ|,|m|and cos θdo not change much from the corresponding values for9Ha, and the two vectors make an angle of 170° with each other, as shown in Figure 4.7. The largest value of |m|/|µ| (or decrease in the value of|µ|and a small increase in the value of|m|) in 9HaPresults in the largest value of gCPL, i.e., -0.055 among all the systems (as shown in Table 4.3). Similar to 9Ha, both the DTM vectors comprise mainly of their respective Z-axis components.
In 9HaQ, gCPL is the smallest among all. This is due to the smallest value of |m|
for the S1→S0 transition, and almost an orthogonal orientation of the two vectors (as shown in Figure 4.7). While the value of |m| is only 0.65×10−20 erg·G−1 in 9HaQ, values are either close to or greater than 2×10−20 erg·G−1 for the other three cases.
Like in9Haand9HaP,µandmin9HaQcomprise mainly ofY- andZ- components, respectively (as shown in Figure 4.6). However, the presence of Qx unit changes the scenario affecting the electronic and magnetic properties. Here, the µy densities are distributed over a larger area resulting in comparatively larger values for µy and |µ|
relative to that of 9Ha and 9HaP. In 9HaQ, electrons and holes are located in the Qx and5-6-5 units, respectively (as shown in Figure B7). Therefore,marises from the delocalized motion of electron over the small Qx unit only producing small |m| and R values. This result is in contrast to the results for carbohelicenes where improved CPL
is calculated as ΦFL= f
(Kf+Knr), where Knr stands for non-radiative rate constants.
For high spontaneous emission systems, Kf is much larger than Knr. Faster emission infers larger quantum yield. Qx-fused polyaza[5]-helicene and 7HQ show smaller ΦFL values compared to the respective parent systems.112 However, 9HaQ shows larger Kf compared to that of parent 9Ha as well as 9HaP. This is due to larger value of fosc for the corresponding transition. In 11Ha, delocalization of electron over a larger area (as shown in Figure B7) leads to the largest values of |µ| and |m|. However, gCPL value is smaller compared to those of 9Ha and 9HaP. It is to be noted that experimentalgCPLvalues were shown to increase with increase in the number of nitrogen atoms,11 i.e., from 7H to 9Ha. Similar to 9Ha and 9HaP, DTM densities in 11Ha are distributed along the whole molecule (as shown in Figure 4.6), and the two DTM vectors are directed almost anti-parallel to each other (as shown in Figure 4.7). In this case, however, contributions ofX-components are much larger than in9Ha. While the terminal rings contribute primarily to the X- and Z-axes components of EDTM (the densities in the 5-6-5 unit cancel each other), 5-6-5 and its adjacent rings participate for MDTM components. 11Ha, with the largest fosc value of 0.05, shows the largest Kf for the transition S1→S0. A large value of Kf hints at a small intersystem crossing decay in 11Ha.
From Figure B7, it is clear that the S1→S0 transitions in the four cases are CT transitions. Analysis using TheoDORE has also been carried out to check the values of ωCT. The results are tabulated along with |µ|in Table B3. While the value of ωCT is 0.72 in9Ha, it increases to 0.76 in the case of9HaPand decreases to 0.41 in9HaQ. On the other hand,ωCT value for11Hais very close to that of9Ha. It is worth noting that while CT occurs between5-6-5 units and the terminals in 9Ha,9HaP and11Ha, the central5-6-5 and Qx units take part in9HaQ(as shown in Figure B7), as mentioned in the previous paragraph. Generally, a state resulting from a smaller overlap of initial and final orbitals, i.e., a state with stronger CT character results in decrease in |µ| value.
This is due to the fact that EDTM operates on the spatial part only. Accordingly, while the |µ| value decreases from 9Ha to 9HaP accompanied by an increase in ωCT, the value increases to 212.74×10−20esu·cm for9HaQ. On the other hand,11Hahaving an ωCT value similar to9Ha shows a much larger|µ|, not showing the ωCT vs |µ|trend.