ΔI ¼ I L À I R
are simultaneously determined, where I L and I R are the emission intensities of leftand right-handed circularly polarized light. Because the evaluation of absolute I and
ΔI values is generally difficult, degree of chirality is generally discussed in terms of
dissymmetry factor of luminescence, g lum , which is defined by the difference
emission divided by an averaged emission intensity, as follows:
g lum ¼
I L À I R
1
2 I L þ I R
ð
Þ
¼ 2
ΔI
I
The index g lum is occasionally called as luminescence anisotropy factor or more
simply g factor. Note that the emission anisotropy is also used to quantify a linearly
polarized luminescence; therefore, dissymmetry is a probably more favorable term.
By definition, minimum and maximum g lum factors are À2 and +2.
In most of recent studies to explore the CPL responses in molecular and supramolecular systems primarily concern the g lum value, as this parameter has been
always the most limiting factor, especially in small organic molecules where g lum
values are typically in an order of 10
À3 to 10
À5 range. However, in order to fully
compare the overall CPL efficiency, it should be more appropriate to consider other
photophysical parameters beside the polarization efficiency (i.e., dissymmetry factor), such as efficiencies of light absorption (oscillator strength, f ) and emission
intensity (quantum yield, Φ). The magnitude of f for an electronic transition is related
to the maximum molar absorption coefficient (ε) and full width at half maximum of
the absorption band (Δν):
f / ε Â Δν
Accordingly, a circular polarization luminosity (Λ CPL ) from the single chiral
molecule in the excited state is described as follows, defined as an intrinsic CPL
efficiency based on a single chiral molecule or matter:
Λ CPL ¼ f Â Φ Â
g lum
j
j
2
/ ε Â Φ Â g lum
j
j
By definition, the Λ CPL values should be in the range between 0 and 1. Assuming
comparable band-shape (Δν), Λ CPL becomes proportional also to ε. The latter term,
ε Â Φ, is commonly referred to as molecular brightness B. In principle, the materials
with larger Λ CPL (or g lum within the similar systems assuming the brightness is
comparable) values at the desired excitation and emission wavelengths are considered as favorable chiroptical materials.
From a theoretical point of view, the emission intensities (as well as absorption
intensities) f are proportional to the dipole strength D produced by the action of
electromagnetic radiation on an electric dipole of substances. The value D is defined
1 Frontiers of Circularly Polarized Luminescence Chemistry of Isolated Small. . .
5
are simultaneously determined, where I L and I R are the emission intensities of leftand right-handed circularly polarized light. Because the evaluation of absolute I and
ΔI values is generally difficult, degree of chirality is generally discussed in terms of
dissymmetry factor of luminescence, g lum , which is defined by the difference
emission divided by an averaged emission intensity, as follows:
g lum ¼
I L À I R
1
2 I L þ I R
ð
Þ
¼ 2
ΔI
I
The index g lum is occasionally called as luminescence anisotropy factor or more
simply g factor. Note that the emission anisotropy is also used to quantify a linearly
polarized luminescence; therefore, dissymmetry is a probably more favorable term.
By definition, minimum and maximum g lum factors are À2 and +2.
In most of recent studies to explore the CPL responses in molecular and supramolecular systems primarily concern the g lum value, as this parameter has been
always the most limiting factor, especially in small organic molecules where g lum
values are typically in an order of 10
À3 to 10
À5 range. However, in order to fully
compare the overall CPL efficiency, it should be more appropriate to consider other
photophysical parameters beside the polarization efficiency (i.e., dissymmetry factor), such as efficiencies of light absorption (oscillator strength, f ) and emission
intensity (quantum yield, Φ). The magnitude of f for an electronic transition is related
to the maximum molar absorption coefficient (ε) and full width at half maximum of
the absorption band (Δν):
f / ε Â Δν
Accordingly, a circular polarization luminosity (Λ CPL ) from the single chiral
molecule in the excited state is described as follows, defined as an intrinsic CPL
efficiency based on a single chiral molecule or matter:
Λ CPL ¼ f Â Φ Â
g lum
j
j
2
/ ε Â Φ Â g lum
j
j
By definition, the Λ CPL values should be in the range between 0 and 1. Assuming
comparable band-shape (Δν), Λ CPL becomes proportional also to ε. The latter term,
ε Â Φ, is commonly referred to as molecular brightness B. In principle, the materials
with larger Λ CPL (or g lum within the similar systems assuming the brightness is
comparable) values at the desired excitation and emission wavelengths are considered as favorable chiroptical materials.
From a theoretical point of view, the emission intensities (as well as absorption
intensities) f are proportional to the dipole strength D produced by the action of
electromagnetic radiation on an electric dipole of substances. The value D is defined
1 Frontiers of Circularly Polarized Luminescence Chemistry of Isolated Small. . .
5