Alma Mater Studiorum – Università di Bologna
Dipartimento di Farmacia e Biotecnologie
Dottorato in Chimica
Ciclo XXVI
SC: 03/D1
SSD: CHIM/08
Chiroptical properties of bioactive
molecules: sensitivity to
conformation and solvation
Tesi presentata da:
Daniele Tedesco
Coordinatore dottorato:
Prof. Aldo Roda
Relatore:
Prof. Carlo Bertucci
This Ph.D. thesis was awarded the G.P. Spada Medal for the
Best Ph.D. Project of the Year in Organic and Medicinal Chemistry
by the Alma Mater Studiorum – University of Bologna.
I
Index
Abstract
...
V
I
Introduction
...
1
1
Overview
...
3
1.1
Aim of the thesis
...
3
1.2
Outline of the thesis
...
4
1.3
Acknowledgements
...
5
2
Spectroscopy
...
7
2.1
Molecular absorption
...
7
2.2
Molecular optical activity
...
11
2.3
Optical rotation and circular dichroism
...
13
3
Stereochemical analysis
...
17
3.1
Empirical methods
...
19
3.2
Semi-empirical methods
...
20
3.2.1
Helicity rules
...
22
3.2.2
Sector rules
...
22
3.3
Non-empirical methods
...
24
3.3.1
Independent systems theory
...
24
3.3.2
Quantum mechanical calculations
...
25
II
Stereochemical characterisation
...
29
4
2-(fluoroaryl)propionic acids
...
31
4.1
Materials and methods
...
33
4.1.1
Experimental spectroscopy
...
33
4.1.2
Computational spectroscopy
...
33
4.2
Results and discussion
...
34
4.3
Conclusions
...
38
5
Difenoconazole
...
45
II
Index
5.1.1
Experimental spectroscopy
...
48
5.1.2
Computational spectroscopy
...
48
5.2
Results and discussion
...
49
5.2.1
Nuclear magnetic resonance spectroscopy
...
49
5.2.2
Electronic circular dichroism spectroscopy
...
52
5.2.3
Quantum mechanical calculations
...
52
5.3
Conclusions
...
55
6
Mycoleptone A
...
67
6.1
Results and discussion
...
68
6.1.1
Austdiol
...
69
6.1.2
Mycoleptone A
...
69
6.2
Materials and methods
...
74
III
Conformational flexibility
...
83
7
β-lactam derivatives
...
85
7.1
Materials and methods
...
88
7.1.1
Experimental spectroscopy
...
89
7.1.2
Computational spectroscopy
...
90
7.2
Results and Discussion
...
92
7.2.1
Structural features of β-lactam derivatives
...
92
7.2.2
Conformational analysis
...
93
7.2.3
Chiroptical properties
...
94
7.2.4
Effect of conformational flexibility
...
97
7.3
Conclusions
...
101
8
Fenoterol
...
117
8.1
Material and methods
...
119
8.1.1
Experimental spectroscopy
...
120
8.1.2
Computational spectroscopy
...
120
8.1.3
Conformational analysis
...
121
8.2
Results and discussion
...
122
8.2.1
Spectroscopic analysis
...
122
8.2.2
Conformational search
...
124
8.2.3
TD-DFT calculations
...
124
Index
III
8.3
Conclusions
...
126
IV
Solvation effects
...
149
9
Austdiol
...
151
9.1
Results and discussion
...
154
9.1.1
TD-DFT calculations without explicit solvation
...
154
9.1.2
Effect of the orientation of hydroxyl groups
...
155
9.1.3
TD-DFT calculations with explicit solvation
...
157
9.2
Conclusions
...
158
9.3
Materials and methods
...
160
9.3.1
Experimental spectroscopy
...
160
9.3.2
TD-DFT calculations
...
160
9.3.3
Standard DFT optimisation
...
161
9.3.4
DFT conformational scans
...
161
9.3.5
DFT optimisation on a solvation cluster
...
162
9.3.6
Classical MD simulation
...
162
9.3.7
Ab initio MD simulation
...
163
9.3.8
Software
...
163
V
Conclusions
...
227
VI
Appendix
...
233
A
Data processing
...
235
A.1
Generation of theoretical spectra
...
235
A.2
Conformational analysis
...
242
A.3
Shell scripting
...
245
Publications
...
271
Bibliography
...
273
V
Abstract
Chiroptical spectroscopies play a fundamental role in pharmaceutical analysis
for the stereochemical characterisation of bioactive molecules, due to the close
relationship between chirality and optical activity and the increasing evidence of
stereoselectivity in the pharmacological and toxicological profiles of chiral drugs.
The correlation between chiroptical properties and absolute stereochemistry,
how-ever, requires the development of accurate and reliable theoretical models. The
present thesis will report the application of theoretical chiroptical spectroscopies
in the field of drug analysis, with particular emphasis on the huge influence of
conformational flexibility and solvation on chiroptical properties and on the main
computational strategies available to describe their effects by means of electronic
circular dichroism (ECD) spectroscopy and time-dependent density functional
theory (TD-DFT) calculations.
The combination of experimental chiroptical spectroscopies with
state-of-the-art computational methods proved to be very efficient at predicting the absolute
configuration of a wide range of bioactive molecules (fluorinated 2-arylpropionic
acids, β-lactam derivatives, difenoconazole, fenoterol, mycoleptones, austdiol).
The results obtained for the investigated systems showed that great care must
be taken in describing the molecular system in the most accurate fashion, since
chiroptical properties are very sensitive to small electronic and conformational
perturbations. In the future, the improvement of theoretical models and methods,
such as ab initio molecular dynamics, will benefit pharmaceutical analysis in
the investigation of non-trivial effects on the chiroptical properties of solvated
systems and in the characterisation of the stereochemistry of complex chiral
drugs.
1
Part I
2
Nature is a language
Can’t you read?
3
Chapter 1
Overview
1.1
Aim of the thesis
The intrinsic limitations of standard analytical techniques, which fail to
discrimi-nate the enantiomers of chiral molecules, prompted the development of specific
enantioselective methods, all based on the interaction between chiral analytes and
an anisotropic medium. In separation sciences, the employment of chiral
selec-tors of known stereochemistry has become a standard and widespread method,
which is also routinely employed in drug analysis.
In spectroscopy, the direct relationship between the chirality of chemical
sys-tems and their differential interaction with polarised radiation is the physical
reason for which spectroscopic techniques based on chiroptical properties, such
as optical rotatory dispersion (ORD) and circular dichroism (CD), have
estab-lished themselves among the main tools for the investigation on the
stereochem-istry of chiral drugs: stereochemical characterisation is indeed fundamental in
pharmaceutical research, due to the increasing evidence of stereoselectivity in
the pharmacological and toxicological properties of drugs.
[
1
–
4
]
The field of
appli-cation of chiroptical spectroscopies is wide and ranges from the determination
of the absolute configuration (AC) of organic molecules to the assessment of the
conformational and supramolecular organisation of large biomolecules.
The correlation between chiroptical properties and the dissymmetric
disposi-tion of atoms at the molecular level, however, is not a trivial task and requires the
development of accurate and reliable theoretical models. For this purpose, the
impressive improvement in the accuracy of quantum mechanical (QM) methods
4
Introduction
and the availability of increasingly powerful computational resources have laid
the path to a renewed interest in the stereochemical characterisation of chemical
systems by theoretical determination of their chiroptical properties.
[
5
]
The present thesis deals with the application of theoretical chiroptical
spec-troscopies in the field of drug analysis, with particular emphasis on the huge
influence of conformational flexibility and solvation on chiroptical properties
and on the main computational strategies available to describe their effects. Six
examples of stereochemical characterisation of chiral bioactive molecules will be
reported, which were achieved by means of a combined approach involving
ex-perimental analytical techniques, in particular electronic circular dichroism (ECD)
spectroscopy, and computational techniques, mainly based on time-dependent
density functional theory (TD-DFT).
1.2
Outline of the thesis
The thesis is divided in six parts:
1.
a brief introduction covering the theoretical concepts at the basis of
spec-troscopy and reviewing the main methods used in stereochemical analysis to
correlate chiroptical properties and absolute stereochemistry.
[
6
]
2.
a part covering the projects mainly concerned with the stereochemical
char-acterisation of chiral bioactive molecules of unknown stereochemistry
(fluori-nated 2-arylpropionic acids,
[
7
]
difenoconazole
[
8
]
and mycoleptones
[
9
]
);
3.
a part covering the projects mainly concerned with the strong effect of
confor-mational flexibility on the chiroptical properties of chiral molecules (β-lactam
derivatives
[
10
]
and fenoterol
[
11
]
);
4.
a part covering the project mainly concerned with the investigation of solvation
effects on the definition of chiroptical properties (austdiol);
5.
a conclusion, where all the projects are summarised and critically discussed;
6.
an appendix, where the tools used in the processing of computational data
are explained.
The methods and results of each project are discussed in separate chapters, which
are based on the corresponding peer-reviewed publication (except austdiol).
Overview
5
1.3
Acknowledgements
Most of the experimental work discussed in this thesis was carried out using the
facilities in the Pharmaceutical Analysis Section at the Department of Pharmacy
and Biotechnology of the University of Bologna, while most of the computational
work was performed on the computing cluster of Prof. Riccardo Zanasi’s
re-search group at the University of Salerno. Particular acknowledgements are also
reported in each chapter.
I owe eternal gratitude to the supervisors of the projects I carried out during
the last 5 years, first as an undergraduate student then as a Ph.D. student: Prof.
Carlo Bertucci, Prof. Riccardo Zanasi, Prof. Dr. Barbara Kirchner and Dr. Alex
F. Drake. Each of them gave me the opportunity to test my skills in research in
full autonomy, supported me to follow my aspirations and taught me more that
I could ever imagine to learn.
I will always be grateful to my family for the patience they had during these
challenging years, for the pride they showed for me in good times and the love
they gave me in bad times: I love you for all you did for me.
Thanks to all my colleagues in Bologna and Leipzig, in particular to Marco
Pistolozzi, Manuela Bartolini, Angela De Simone, Cecilia Fortugno, Cláudia Seidl
and Eva Perlt: you are not colleagues, you are friends.
Thanks to all the friends who have always been on my side: Aurélie Bruno,
Matteo Staderini, Silvia Immediato, Andrea Felicetti, Giosuè Brulla, and
every-body else I didn’t mention. You helped me a lot through tough times, and I’ll
never forget that.
This thesis is dedicated to my best friend Rocco Truncellito: it doesn’t matter
where you are now, you’re always here with me.
7
Chapter 2
Spectroscopy
2.1
Molecular absorption
In chemical systems, the total energy of a molecule is the result of several
contri-butions, such as interactions between electrons and nuclei, electronic and nuclear
spin orientations, vibrations, rotations and translations. According to quantum
theory, these contributions generate a set of quantised (discrete) energy states
available for each molecule.
Transitions from a state of lower energy to a state of higher energy require
the exact amount of energy corresponding to the difference between two energy
levels to be supplied to the atom or molecule by an external source, i.e.
electro-magnetic radiation. The frequency (ν) of an electroelectro-magnetic radiation capable
of promoting the transition between two different energy states is defined by
Planck’s equation:
∆E
=
hν ,
(2.1)
where ν is in s
−1
, ∆E is the energy difference between the two levels and h
= 6.62606957
·
10
−27
erg s
a
is the Planck constant.
[
12
]
As a result, radiation is
absorbed by the molecule; the intensity of absorption at a given frequency is
related to the absorption cross section of a molecule (W) by the following relation:
ln
I
0
I
t
=
W Nl ,
(2.2)
a
The erg is the physical unit for energy in the cgs system. 1 erg = 1 g cm
2s
−
2. Throughout
the chapter, the cgs system of physical units will be used, due to its widespread use in the
theoretical treatment of absorption in literature.
8
Introduction
where I
t
and I
0
are respectively the intensities of the transmitted and incident
radiation, l is the pathlength of the sample in cm and N is the number density
of the molecule in the sample in cm
−3
; W is then expressed in cm
2
.
This equation is very similar to the usual formulation of Lambert-Beer law:
A
=
log
I
0
I
t
=
εCl
,
(2.3)
where A is the absorbance of the sample, C the molar concentration in mol
L
−1
and ε is the molar absorption coefficient in the usual units of M
−1
cm
−1
.
Equations
2.2
and
2.3
can be combined to give:
W
=
ln 10C
N
ε
=
10
3
ln 10
N
A
ε
,
(2.4)
where N
A
= 6.02214129
·
10
23
mol
−1
is Avogadro’s number
[
12
]
and C has been
converted to N (C
=
10
3
N/N
A
); the conversion factor 10
3
accounts for the change
in units.
The intensity and frequency of ultraviolet absorption bands, however, are
usu-ally reported and discussed in terms of molar absorption coefficients (ε
max
) and
wavelengths (λ
max
), since these values are easily obtained by experimental
anal-ysis; these quantities are not useful when a theoretical approach is necessary. A
rigorous evaluation of the intensity of absorption requires the isolation of each
absorption band and the measurement of the area under the absorption curve;
in the frequency domain, then, equation
2.4
becomes:
W
=
10
3
ln 10
N
A
Z
ε
(
ν
)
dν ;
(2.5)
in cgs units, the integrated intensity of absorption is expressed in cm mol
−1
; if ε is
expressed in M
−1
cm
−1
, the integrated intensity may be expressed in M
−1
cm
−2
= 10
3
cm mol
−1
. However, intensity values are often reported in km mol
−1
= 10
2
M
−1
cm
−2
= 10
5
cm mol
−1
.
The isolation of bands is often difficult to obtain from experimental spectra, so
ε
max
is usually preferred as a convenient method of reporting spectroscopic data.
The absolute intensity of absorption, however, may be calculated theoretically for
each transition.
[
13
,
14
]
As light is absorbed or emitted by the molecule, an electric transition dipole
moment (µ
j
) is generated by the charge displacement due to the transition
Spectroscopy
9
molecule (µ) is defined by the distance r between the centres of gravity of the
positive (nuclei) and negative (electrons) charges multiplied by the magnitude
of the charges (e). The quantum mechanical expression of the electric dipole
moment vector (µ) is given by:
µ
= h
Ξ
0
|
ˆµ
|
Ξ
0
i
,
(2.6)
where the operator ˆµ extends over all nuclei and electrons, e = 4.80320425
·
10
−10
statC
b
is the elementary charge,
[
12
]
and Ξ
0
is the total (electronic, vibrational
and rotational) wave function of the molecule in the ground state.
Similarly, the electric transition dipole moment vector µ
j
is given by:
µ
j
= h
Ξ
0
|
ˆµ
|
Ξ
j
i
.
(2.7)
Assuming that the vibrational and rotational contributions to the total wave
functions can be factored out according to the Born-Oppenheimer
approxima-tion,
[
15
]
equation
2.7
reduces to the electronic wave functions (Ψ):
µ
j
= h
Ψ
0
|
ˆµ
|
Ψ
j
i
;
(2.8)
the dipole strength of the transition, D
j
, is then defined as:
c
D
j
= k
µ
j
k
2
.
(2.9)
Similarly, the quantum mechanical expression of the magnetic transition dipole
moment vector (m
j
) can be defined as:
m
j
= h
Ψ
0
|
m
ˆ
|
Ψ
j
i
,
(2.10)
where the operator ˆ
m
= −
e
2m
e
c
∑
r
×
ˆp extends over all electrons, m
e
=
9.10938291
·
10
−28
g is the electron mass,
[
12
]
c = 2.99792458
·
10
10
cm s
−1
is the
velocity of light,
[
12
]
ˆp
= −
i ¯h∇ is the momentum operator, ¯h
=
h/2π is the
reduced Planck constant, and ∇
=
∂
∂x
i
+
∂
∂y
j
+
∂
∂z
k
is the Laplace operator,
which describes the motion of a microscopic particle.
d
b
The electrostatic unit of charge (esu) or statcoulomb (statC) is the physical unit for electrical
charge in the cgs system. 1 esu = 1 g
1/2cm
3/2s
−
1.
cThe physical unit of µ
j
in the cgs system is the debye (D); 1 D = 1 statC cm = 1 g
1/2cm
5/2s
−
1.
di
, j and k are the unit versors of the Cartesian coordinate system along the x-, y- and z-directions,
10
Introduction
Einstein introduced two types of coefficients: A to describe the probability of
spontaneous emission, and B to describe the probability of induced absorption
and emission.
[
16
–
18
]
The Einstein coefficient for induced absorption from the
ground state (B
0j
) is related to the dipole strength and to the absorption cross
section by the following relations:
B
0j
=
8π
3
3h
2
c
D
j
G
j
;
(2.11)
W
=
B
0j
hν ,
(2.12)
where G
j
is the degeneracy factor of state j (i.e. the number of degenerate wave
functions to which absorption can lead; usually, G
j
=
1). In this formulation, B
0j
is expressed in cm
2
erg
−1
s
−1
= s g
−1
.
In quantum mechanics, the intensity of a transition is espressed by means of a
dimensionless quantity, called oscillator strength, f
j
, which is directly related to
the absorption cross section W by:
f
j
=
m
e
c
πe
2
W ;
(2.13)
the combination of equations
2.11
,
2.12
and
2.13
gives the relation of f
j
with the
dipole strength D
j
:
f
j
=
m
e
ch
π
e
2
B
0j
ν
=
8π
2
m
e
3he
2
D
j
G
j
ν
.
(2.14)
At this point, the frequency can be substituted with the wavenumber (σ
=
ν/c,
expressed in cm
−1
); consequently, equation
2.14
becomes:
f
j
=
8π
2
m
e
c
3he
2
D
j
G
j
σ
.
(2.15)
Finally, the combination of equations
2.4
and
2.13
yields the expression relating
the oscillator strength ( f
j
) to the molar absorption coefficient (ε):
f
j
=
10
3
ln 10
m
e
c
π
N
A
e
2
Z
ε
(
ν
)
dν
=
1.44066
·
10
−19
Z
ε
(
ν
)
dν ,
(2.16)
Spectroscopy
11
which, in the wavenumber domain, becomes:
f
j
=
10
3
ln 10
m
e
c
2
πN
A
e
2
Z
ε
(
σ
)
dσ
=
4.31899
·
10
−9
Z
ε
(
σ
)
dσ .
(2.17)
2.2
Molecular optical activity
Optical activity is the physical phenomenon arising from the differential
interac-tion of chiral molecules with the left and right circular polarisainterac-tions of radiainterac-tion.
A detailed treatment on the historical and theoretical backgrounds of optical
activity is beyond the aims of this chapter, and only a brief overview will be
pro-vided: the interested reader is referred to a selected list of excellent contributions
on this subject.
[
19
–
30
]
From the point of view of classical electrodynamics, the electric
displace-ment field (D) and the magnetic field (B) for an electromagnetic wave travelling
through a medium are desbribed by the following equations:
D
=
eE
−
g
∂H
∂t
;
(2.18)
B
=
µH
+
g
∂E
∂t
,
(2.19)
where E and H are respectively the electric field and the magnetic field strength,
e
and µ are respectively the electric permittivity and magnetic permeability of
the medium. The g factor describes the dependence of the induced electric field
D
upon the time evolution of the magnetic field H and the dependence of the
induced magnetic field B upon the time evolution of the electric field H.
At the molecular level, a similar dependence can be recognised for the electric
(µ
j
) and magnetic (m
j
) transition dipole moments:
µ
j
=
αE
0
−
β
c
∂H
∂t
=
α
E
+
4π
3
P
−
β
c
∂H
∂t
;
(2.20)
m
j
=
χH
+
β
c
∂E
0
∂t
=
χH
+
β
c
∂E
∂t
+
4π
3
∂P
∂t
,
(2.21)
where E
0
=
E
+
4π
3
P
is the effective electric field, P is the polarisation field of the
medium, and the scalar parameters α and χ are respectively the polarisability
12
Introduction
and the magnetisability of the molecule. The P field and the analogous
magneti-sation field (M) are connected to the transition dipole moments by the following
relations:
P
=
Nµ
j
;
(2.22)
M
=
Nm
j
,
(2.23)
where N is the number density of the molecule in the sample in cm
−3
.
In equations
2.20
–
2.21
, the β/c factor plays the same role as the g factor in
equations
2.18
–
2.19
; both factors describe an anisotropic perturbation related to
the interaction with circularly polarised radiation. The relationship between the
two factors can be derived by the combination of equations
2.20
–
2.22
, yielding:
g
=
4πN
β
c
e
+
2
3
=
4π
β
c
γ
s
,
(2.24)
where γ
s
=
e
+
2
3
is the Lorentz factor. The β parameter is the averaged trace of
a rank-2 tensor, β, called Rosenfeld or optical rotation tensor:
β
=
1
3
Tr β ,
(2.25)
which, in turn, is related to the mixed electric dipole-magnetic dipole
polarisabil-ity of the molecule, G
0
:
β
= −
1
2πν
G
0
,
(2.26)
and to the rotational strengths (R
j
), the quantum mechanical quantities
describ-ing the response of molecules upon the interaction with left and right circularly
polarised radiation. In the frequency domain, the relationship between the β
parameter and the rotational strengths of the molecules is expressed by the
fol-lowing equation:
β
(
ν
) =
c
3πh
j6=0
∑
R
j
ν
2
j
−
ν
2
,
(2.27)
where the sum extends over all excited states.
Rosenfeld defined R
j
as the imaginary part of the scalar product of the electric
(µ
j
) and magnetic (m
j
) transition dipole moment vectors:
[
31
]
R
j
= =
µ
j
·
m
∗
j
Spectroscopy
13
a simpler formulation of R
j
is given by:
R
j
= k
µ
j
k · k
m
j
k ·
cos η ,
(2.29)
where the norm brackets denote the vector magnitudes and η is the angle
be-tween µ
j
and m
j
. For a transition, R
j
=
0 when either
k
µ
j
k =
0,
k
m
j
k =
0, or
when the vectors are perpendicular to each other (η
=
π
/2; cos η
=
0). One
of these conditions holds for every transition in non-chiral molecules, which
accordingly do not exhibit optical activity, and should also hold for inherently
non-chiral chromophores, such as phenyl and carbonyl groups. However, a chiral
environment, i.e. the asymmetric disposition of substituents around the
chro-mophore in a chiral molecule, induces perturbations in the charge displacement
of the transition, thus giving rise to a helical path: the rotational strength for the
transition is non-zero and the molecule exhibits optical activity. At the
macro-scopic level, optical activity gives rises to two phenomena: optical rotation and
circular dichroism.
2.3
Optical rotation and circular dichroism
Optical rotation (OR) is a consequence of circular birefringence, which consists
in the different velocity of propagation, i.e. refractive index (n), for the two
cir-cular polarisations (n
LCP
6=
n
RCP
). Since a linearly polarised radiation may be
considered as the combination of coherent LCP and RCP components of equal
amplitude, circular birefringence induces a change in the phase difference of the
LCP and RCP components. As a result, the plane of polarisation of a linearly
polarised radiation, passing through an optically active medium, is rotated by
an angle α, which is dependent upon temperature (t) and wavelength of the
ra-diation (λ). The resulting OR is either measured at a single wavelength or as a
function of wavelength (optical rotatory dispersion, ORD).
The circular birefringence is related to the g parameter by the equation:
n
LCP
−
n
RCP
=
4πνg ,
(2.30)
while the corresponding optical rotation ϕ of a chiral molecule at frequency ν is
given by:
ϕ
(
ν
) =
πν
14
Introduction
consequently, the combination of equations
2.24
,
2.30
and
2.31
yields:
ϕ
(
ν
) =
16π
3
Nν
2
c
2
β
(
ν
) =
16π
3
N
A
C
0
ν
2
c
2
M
β
(
ν
)
,
(2.32)
where ϕ is in rad cm
−1
, C
0
is the concentration in g cm
−3
and M is the molecular
weight in g mol
−1
; from now on, the Lorentz factor (γ
s
∼
1) will be omitted.
The experimental OR values are reported as specific rotatory powers,
[
α
]
t
ν
,
expressed in deg cm
3
g
−1
dm
−1
:
[
α
]
t
ν
=
α
(
ν
)
C
0
l
,
(2.33)
where t is in Celsius scale, α is in deg and the pathlength l is in dm. Usually, the
specific rotatory power is measured at the D spectral line of sodium (589.3 nm;
[
α
]
D
t
).
Taking into account the conversion from ϕ (rad cm
−1
) to α (deg) :
α
(
ν
)
10l
=
180ϕ
(
ν
)
π
,
(2.34)
equations
2.32
,
2.27
and
2.33
can be combined to yield:
[
α
]
t
ν
=
1800
π
C
0
·
16π
3
N
A
Cν
2
c
2
M
·
c
3πh
j6=0
∑
R
j
ν
2
j
−
ν
2
=
9600
πN
A
ν
2
hcM
j6=0
∑
R
j
ν
2
j
−
ν
2
.
(2.35)
On the other hand, circular dichroism (CD) is the differential absorption of LCP
and RCP radiation, i.e. the molar absorption coefficients (ε) for the two
polarisa-tions are different (ε
LCP
6=
ε
RCP
). This differential absorption (∆ε
=
ε
LCP
−
ε
RCP
),
also called Cotton effect (CE), occurs for each electronic and vibrational
transi-tion of a chiral molecule. Electronic circular dichroism (ECD) and vibratransi-tional
circular dichroism (VCD) spectra arise from the same physical phenomenon and
are simply measured in different ranges of the electromagnetic spectrum. The
insurgence of CD is related to the charge displacement occurring during the
tran-sition from ground to excited state. In chiral molecules, the charge displacement
occurs along a helical path: one of the two circular polarisations interacts more
effectively, and is more absorbed, than the other.
Spectroscopy
15
The intensity of differential absorption for each transition is related to the
correspoinding rotational strength (R
j
) through the following equation:
R
j
=
10
3
ln 10
3hc
32π
3
N
A
Z
∆ε
(
σ
)
σ
dσ
(2.36)
=
2.29648
·
10
−39
Z
∆ε
(
σ
)
σ
dσ ;
(2.37)
all the quantities are expressed in cgs units except ∆ε, which is expressed in
M
−1
cm
−1
; R
j
is then expressed in erg cm
3
or other equivalent units, e.g. erg esu
cm G
−1
e
and esu
2
cm
2
. All these units reduce to g cm
5
s
−2
.
e
