5 α-Amino Acids In Water: A Review of VCD and ROA Spectra
97
a chiral sample. It was defined by Atkins and Barron in 1969 [99] as a dimensionless circular intensity difference (CID), Δ, now called incident circular polarisation
RoA (ICP RoA),
∆ =
−
+
(
)/ (
)
I
I
I
I
R
L
R
L
(5.3)
where I
R
and I
L
are the scattered intensities in right- and left-circularly polarised incident light. Barron and Buckingham gave the theoretical background for this effect
[100]. the first experimental RoA spectra were published in 1973 [101] and were
confirmed by hug et al. in 1975 [102].
the intensity of RoA spectra is weak, ca. 10
−4
of the parent vibrational Raman
scattering. Experimental spectra can be registered using different scattering angle:
forward (0°), or right-angle (90°), or backward (180°). the conventional Raman
scattering intensities are identical in the forward and backward modes of operation.
For three scattering geometries there are three basic circular polarisation schemes:
incident circular polarisation (ICP), scattered circular polarisation (SCP), and dual
circular polarisation (dCP), the last one being a combination of ICP and SCP RoA.
In the ICP scheme, the incident laser is modulated between R- and L-circular polarisation states and the intensity is measured at a fixed linear or unpolarised radiation,
while in the SCP scheme, fixed linear or unpolarised incident laser radiation is used
and the difference in the R- and L-circularly polarised scattered light is measured.
Within the far-from-resonance approximation, the information obtained with ICP
and SCP schemes are the same [103]. the expressions for specific experimental
schemes for RoA can be found in the literature [104]. the best experimental choice
for most RoA registrations, particularly for studies of biomolecules in aqueous
solution, is the backward mode. Absolute scattering cross-sections are available for
molecules in the gas-phase; however, when RoA spectra are measured for liquids,
the intensity of RoA is modified [53].
Within the Born-oppenheimer approximation, (where only the linear contribution in the taylor series of polarisabilities about the equilibrium geometry contributes significantly), double harmonic approximation and the far-from-resonance
theory, as well as within the Placzek polarisability theory of the Raman spectra
the RoA intensity differences for the SCP backscattered mode can be written in
terms of the normal coordinate derivatives of three polarisability tensors: the electric dipole-electric dipole polarisability tensor, the electric dipole-magnetic dipole
polarisability tensor, and the electric dipole-electric quadrupole polarisability tensor, as follows [105]:
I
I
hc k T
R
L
in
i
i
B
i
i
+ ∝
−
(
)
−
−
(
)
+
ν
ν
ν
α
β
4
2
2
1
45
7
exp
Raman intensit
/
i ies
(5.4)
I
I
hc k T
R
L
in
i
i
B
G
A
i
i
− ∝
−
(
)
−
−
(
)
+
ν
ν
ν
β
β
4
2
2
1
12
4
exp
ROA intensit
/
y y differences
(5.5)
97
a chiral sample. It was defined by Atkins and Barron in 1969 [99] as a dimensionless circular intensity difference (CID), Δ, now called incident circular polarisation
RoA (ICP RoA),
∆ =
−
+
(
)/ (
)
I
I
I
I
R
L
R
L
(5.3)
where I
R
and I
L
are the scattered intensities in right- and left-circularly polarised incident light. Barron and Buckingham gave the theoretical background for this effect
[100]. the first experimental RoA spectra were published in 1973 [101] and were
confirmed by hug et al. in 1975 [102].
the intensity of RoA spectra is weak, ca. 10
−4
of the parent vibrational Raman
scattering. Experimental spectra can be registered using different scattering angle:
forward (0°), or right-angle (90°), or backward (180°). the conventional Raman
scattering intensities are identical in the forward and backward modes of operation.
For three scattering geometries there are three basic circular polarisation schemes:
incident circular polarisation (ICP), scattered circular polarisation (SCP), and dual
circular polarisation (dCP), the last one being a combination of ICP and SCP RoA.
In the ICP scheme, the incident laser is modulated between R- and L-circular polarisation states and the intensity is measured at a fixed linear or unpolarised radiation,
while in the SCP scheme, fixed linear or unpolarised incident laser radiation is used
and the difference in the R- and L-circularly polarised scattered light is measured.
Within the far-from-resonance approximation, the information obtained with ICP
and SCP schemes are the same [103]. the expressions for specific experimental
schemes for RoA can be found in the literature [104]. the best experimental choice
for most RoA registrations, particularly for studies of biomolecules in aqueous
solution, is the backward mode. Absolute scattering cross-sections are available for
molecules in the gas-phase; however, when RoA spectra are measured for liquids,
the intensity of RoA is modified [53].
Within the Born-oppenheimer approximation, (where only the linear contribution in the taylor series of polarisabilities about the equilibrium geometry contributes significantly), double harmonic approximation and the far-from-resonance
theory, as well as within the Placzek polarisability theory of the Raman spectra
the RoA intensity differences for the SCP backscattered mode can be written in
terms of the normal coordinate derivatives of three polarisability tensors: the electric dipole-electric dipole polarisability tensor, the electric dipole-magnetic dipole
polarisability tensor, and the electric dipole-electric quadrupole polarisability tensor, as follows [105]:
I
I
hc k T
R
L
in
i
i
B
i
i
+ ∝
−
(
)
−
−
(
)
+
ν
ν
ν
α
β
4
2
2
1
45
7
exp
Raman intensit
/
i ies
(5.4)
I
I
hc k T
R
L
in
i
i
B
G
A
i
i
− ∝
−
(
)
−
−
(
)
+
ν
ν
ν
β
β
4
2
2
1
12
4
exp
ROA intensit
/
y y differences
(5.5)