χ ¼
π n L À n R
ð
Þ l
λ
:
ð15:17Þ
The results of S CB are as follows:
S CB ¼
sin 2θ cos χ sin
2 δ
2
sinχðcos 2 δ
2 sinχ þ sin
2 δ
2 cos2θÞ
:
ð15:18Þ
At first glance, the most important difference between S CD and S CB is the factor
Δε in the quantity of the former. Otherwise, all the other quantities contribute to both
S CD and S CB . We observe that S CD and S CB in the case δ approaching to zero
approach their corresponding values in the completely opposite direction, namely,
S CD increases nonlinearly when δ goes to zero due to the (tan (δ/2))
À1 factor, while
S CB approaches zero due to the (tan (δ/2))
2 factor. CD and CB should have the same
amplitude because they are connected by the Kramers–Kronig relationship; thus, the
ratio, S CD /S CB , in the small δ case is increased just by a factor of (tan (δ/2))
À3 ~ (δ/
2 + 1/6(δ/2)
3 )
À3
. In Fig. 15.3, we used δ as small as 0.02 rad; thus, S CD /S CB is on the
order of 10.
6 This zeroth-order estimate suggests us that the CB contribution to CD
measurement with elliptically polarized light provided by the retarder with small
retardance is vanishingly small. As a matter of course, we should note that this issue
should be explicitly treated by N-matrix formalism of Jones calculus [20].
15.4 Examples of Transient CD Spectrum: CD Spectrum
of [6]Carbohelicenes in Solution [17]
We employ the above described system to carry out TRCD experiments, by combining with ns-laser flash photolysis system, in a time interval of up to 1 μs
(Fig. 15.1). We selected a target molecule, optical active [6]carbohelicene ([6]CH),
which has photophysical properties and has been well studied and documented [21–
25]. Photoexcitation of [6]CH yields the excited triplet state (
3 [6]CH
à ) efficiently;
thus, early work suggested the CD spectrum of
3 [6]CH
à derivatives in frozen
2-methyltetrahydrofuran at 98 K with careful data analysis to eliminate the linear
dichroism (LD) component originating from the photo-selection in the frozen media
[26]. In this work, we aimed at observing the circular dichroism spectrum of
3 [6]CH
Ã
in solution, and at the μs timescale, we essentially observed an LD-free CD spectrum
because of the free rotation of
3 [6]CH
à and compare our results with the
previous ones.
Therefore, here we consider it worthwhile to show the transient CD spectra of
(P)- and (M)3 [6]CH
à in toluene at room temperature (RT) and the time-trace
analysis of transient absorption and circular dichroism measurement.
At this stage, we can evaluate the ΔS spectra of (P)- and (M)3 [6]CH
à at the initial
time (1–11 μs) observed as a function of the wavelength with the image-intensifier/
diode array. They showed a 620-nm peak signal with positive ΔS for (P)3 [6]CH
Ã
15 Transient Circular Dichroism Approach to Chirality Detection in Dark. . .
335
π n L À n R
ð
Þ l
λ
:
ð15:17Þ
The results of S CB are as follows:
S CB ¼
sin 2θ cos χ sin
2 δ
2
sinχðcos 2 δ
2 sinχ þ sin
2 δ
2 cos2θÞ
:
ð15:18Þ
At first glance, the most important difference between S CD and S CB is the factor
Δε in the quantity of the former. Otherwise, all the other quantities contribute to both
S CD and S CB . We observe that S CD and S CB in the case δ approaching to zero
approach their corresponding values in the completely opposite direction, namely,
S CD increases nonlinearly when δ goes to zero due to the (tan (δ/2))
À1 factor, while
S CB approaches zero due to the (tan (δ/2))
2 factor. CD and CB should have the same
amplitude because they are connected by the Kramers–Kronig relationship; thus, the
ratio, S CD /S CB , in the small δ case is increased just by a factor of (tan (δ/2))
À3 ~ (δ/
2 + 1/6(δ/2)
3 )
À3
. In Fig. 15.3, we used δ as small as 0.02 rad; thus, S CD /S CB is on the
order of 10.
6 This zeroth-order estimate suggests us that the CB contribution to CD
measurement with elliptically polarized light provided by the retarder with small
retardance is vanishingly small. As a matter of course, we should note that this issue
should be explicitly treated by N-matrix formalism of Jones calculus [20].
15.4 Examples of Transient CD Spectrum: CD Spectrum
of [6]Carbohelicenes in Solution [17]
We employ the above described system to carry out TRCD experiments, by combining with ns-laser flash photolysis system, in a time interval of up to 1 μs
(Fig. 15.1). We selected a target molecule, optical active [6]carbohelicene ([6]CH),
which has photophysical properties and has been well studied and documented [21–
25]. Photoexcitation of [6]CH yields the excited triplet state (
3 [6]CH
à ) efficiently;
thus, early work suggested the CD spectrum of
3 [6]CH
à derivatives in frozen
2-methyltetrahydrofuran at 98 K with careful data analysis to eliminate the linear
dichroism (LD) component originating from the photo-selection in the frozen media
[26]. In this work, we aimed at observing the circular dichroism spectrum of
3 [6]CH
Ã
in solution, and at the μs timescale, we essentially observed an LD-free CD spectrum
because of the free rotation of
3 [6]CH
à and compare our results with the
previous ones.
Therefore, here we consider it worthwhile to show the transient CD spectra of
(P)- and (M)3 [6]CH
à in toluene at room temperature (RT) and the time-trace
analysis of transient absorption and circular dichroism measurement.
At this stage, we can evaluate the ΔS spectra of (P)- and (M)3 [6]CH
à at the initial
time (1–11 μs) observed as a function of the wavelength with the image-intensifier/
diode array. They showed a 620-nm peak signal with positive ΔS for (P)3 [6]CH
Ã
15 Transient Circular Dichroism Approach to Chirality Detection in Dark. . .
335