3
known limitations of such a method quoted above. In fact, it is known since a long time that
the exciton method is very useful and powerful method, which allows to analyse a circular
dichroism (CD) spectrum in a non empirical way arriving at a safe assignment of the absolute
configuration of organic and inorganic compounds. Usually in this model the exciton
coupling of only two electrically allowed transitions (oscillators) is taken into account: this
approach (from which derive the well known, largely used Harada and Nakanishi rules) has
the important advantage of an easy application but, sometimes, it may lead to wrong results.
In fact, in a molecule often many electric allowed transitions are present, so taking into
account only two oscillators is a approximation which could lead to wrong results. So, in this
thesis, a more general treatment, which allows to consider the simultaneous coupling of
several oscillators, i.e. the DeVoe model,
5
is extensively used and critically analysed. Taking
into account that the DeVoe model joins generality and reliability requiring an almost
negligible computational effort, it could represents one of the methods of choice for
stereochemical assignments, even by non specialists. On the other side, the ab initio
calculation of the optical rotation
6
is very attractive from the experimental point of view; in
fact, the measurement of the optical rotatory power is carried out by means of the simplest,
inexpensive and largely diffuse instrument: the polarimeter. However, the possibility of
carrying out the reliable theoretical prediction of the optical rotatory power remained
unexplored until a few years ago and, in the meantime, only simplified empirical models were
elaborated. Only very recently the ab initio (Hartree-Fock level of approximation) calculation
of the optical rotation at any wavelength is become a reality as shown by Polavarapu in the
1997.
6
As a consequence, the possibility of assigning the molecular absolute configuration
simply comparing the experimental optical rotation (say, at the sodium D line) with the
Hartree-Fock (HF) predicted value, resulted. Subsequent papers
6
clearly demonstrated the real
possibility of a computational assignment of the AC. On the other hand, other research
groups, in particular Stephens et al,
7
preferred the alternative approach based on the Density
Functional Theory (DFT). Moreover, today there are commercially available and relatively
inexpensive software packages, which allow the calculation of the OR value even by non-
specialists in theoretical chemistry. The main problem is that the Stephens’ conclusions
7
are
rather pessimistic regarding the HF/small basis set predictions: he claims that the use of DFT
methodologies in conjunction with particularly large basis sets is mandatory to obtain reliable
results. The implication of Stephens’ sentence is that the assignment of the absolute
configuration based on the ab initio calculation of optical rotation is, nowadays, unattractive
for the experimental organic chemist because the ab initio large basis set calculations cannot
be carried out using common personal computers (available in the majority of the organic
4
chemistry labs) on medium-large molecules. On the contrary, very powerful and expensive
computers have to be used. Now, the target molecules (natural or synthetic) have generally a
medium-large size; therefore, we have studied the conditions by which the ab initio
calculation of optical rotation using small basis set (which leads to simple and fast
calculations) can be done in a reliable way.
Our final target is to provide the research community with some reliable and simple tools to
solve the problem of the assignment of absolute configuration in solution and, at the same
time, to apply such methods in the case of molecules of applicative interest, such as bioactive
natural products, drugs, flavour and fragrances. For these reasons the present thesis is
organized in two different parts: in Part I we will discuss the basis of CD spectroscopy in the
VIS-UV region and the methods of interpretation of CD data, mainly by coupled oscillator
methods. Furthermore, a particular place will be left to the modern methods for the ab initio
calculation of optical rotation and ECD spectra. In Part II we will mainly discuss the
applications to assignment of the absolute configuration. We will treat the scope and
limitation of the ab initio calculation of the optical rotatory power using a small basis set
scheme. Afterwards we will assign in a non empirical way the absolute configuration to two
natural products ((-)-naringenin and (+)-diplopyrone) using both the analysis of ECD
spectrum and optical rotation data. A particular attention will be addressed to the coupled
oscillator analysis of the ECD spectrum of Troeger’s base. In the last chapter we will take
into account the AC assignment based on the ab initio prediction of the optical rotation
dispersion curve; with this new approach we will assign the absolute configuration of two
new bioactive interesting molecules (cis and trans isocytoxazone).
5
References
1) (a) Amato, I. Science 1992, 256, 964; (b)Stinson, S. C., Chem. Eng. News 2000, oct. 23,
55. (c) Baillie, T. A., Schultz, K. M. in The Impact of Stereochemistry on Drug Development
and Use; Aboul-Enein, H.; Wainer, I. W., Eds., Wiley: New York, 1997; Chapter 2, pp 21-43.
(d) Chirality in Agrochemicals; Kurihara, N.; Miyamoto, J., Eds., Wiley: Chichester, UK,
1998.
2) Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds, John Wiley & Sons,
Inc., New York, 1994, pp. 1142-1150.
3) (a) Ripa, L.; Hallberg, A.; Sandström, J., J. Am. Chem. Soc. 1997, 119, 5701. (b) Rosini,
C.; Scamuzzi, S.; Uccello-Barretta, G.; Salvadori, P., J. Org. Chem. 1994, 59, 7395.
4) Berova, N.; Nakanishi, K. in Circular Dichroism: Principles and Applications; Berova, N.;
Nakanishi, K.; Woody, R. W., Eds., Wiley-VCH: New York, 2000; pp 337-382.
5) (a) DeVoe, H. J. Chem. Phys. 1964, 41, 393. (b) ibidem 1965, 43, 3199. (c) for a recent
review see: Superchi, S.; Giorgio, E.; C. Rosini, Chirality 2004, 16, 422.
6) for a recent review see: Polavarapu, P. L. Chirality 2002, 14, 768.
7) Stephens, P.J.; Devlin, F.J.; Cheeseman, J.R.; Frisch, M.J., J. Phys. Chem. A, 2001, 105,
5356.
6
Part I
Theoretical
background
7
I.1 BASIC DEFINITIONS.
1, 2, 3
Optical rotation (OR) and circular dichroism (CD) are different aspects of the same physical
phenomenon: the interaction of plane polarized electromagnetic radiation with a collection of
chiral molecules. Right- and left-circularly polarized radiation beams having the same frequency,
intensity and phase (Figure 1a and 1b) can combine to afford plane polarized radiation (Figure
1c) (for simplicity only the electric vector is represented). In an optically active medium the left-
and right- circularly polarized components pass with different speeds, owing to their different
refractive indices, i.e. n
L
and n
R
.
Figure 1. Left- (a), right- (b) circularly polarised radiation and their resultant, a plane polarised
radiation beam, (c). On the right-hand side are reported the corresponding views by an observer
looking toward the source.
Leaving the chiral medium this difference in velocity has originated a difference in phase of the
two circularly polarized components and then a rotation of the plane of polarization. This
phenomenon is schematically described in Figure 2.
8
Figure 2. A beam of electromagnetic radiation produced by the source S, is made
monochromatic by the monochromator M and linearly polarized (along E
o
) by the polarizer
R
1
. Entering the optically active medium (point 0), the electric field vector is E
0
with in
phase (i.e. the arcs 0-E
0
R
and 0-E
0
L
are equal) circularly polarized components: at position a,
since n
R
> n
L
, the arc 0-E
a
R
will be greater than the are 0-E
a
L
(the two circularly polarized
components are not in phase anymore). The resultant electric field vector is rotated by an
angle ∆’ with respect to the original vector E
0
. Leaving the optically active medium, ∆’ will
be increased to ∆ (another layer of optically active molecules has been crossed). The
observer O placed after the polarizer P
2
will see a radiation having reduced intensity, (I ϖ
E
x
2
= (E
0
cos ∆
). To have maximum intensity, P
2
must be rotated of ∆ (optical rotatory
power of the medium).
In Figure 2 it is represented the electric vector (E
0
) of a plane polarized beam, coming from the
source S, the monochromator M, and the polarizer R
1
. Entering the sample the beam has right
(E
0
R
) and left (E
0
L
) circularly polarized components. We suppose that in the optically active
medium n
L
<n
R
(therefore v
R
>v
L
, since n=c/v). This means that at the point a, the right-handed
circularly polarized component will have covered an arc 0-E
a
R
greater than the arc 0-E
a
L
. The
two components do not have the same phase and the resultant electric vector E
a
will be rotated
by an angle ∆’ with respect to the incident vector P
0
. This effect will be amplified crossing also
the distance a–b: so leaving the optically active medium the final rotation will be ∆. This fact can
9
be revealed considering that the intensity of the radiation reaching an observer O placed after the
polarizer R
2
(called analyzer and placed parallel to R
1
) will be reduced because only the
component E
x
(=E
0
cos ∆) will reach O. To obtain the maximum intensity R
2
should be rotated by
an angle ∆. From this value the specific optical rotation [α ] can be calculated:
[ ∆]
T
Ο
= ∆ 100 / l c
where ∆ is the measured angle of optical rotation in degrees, l is the pathlength in dm, c is the
concentration in grams of solute in 100 cc of solution, T is the temperature and Ο is the
wavelength of the incident radiation in nm. Now, we are showing a simple physical picture
about the interaction of a single and fixed chiral molecule with the electro and magnetic field
of a polarized electromagnetic wave
1m
(see Figure 3.a). A simplest model of chiral molecule
can be a molecule with a clockwise spiral shape; in this way the electrons motion describe,
consequentially, a clockwise spiral profile and our model is like a current running into a coil.
When the coil is kept as in figure 3.b (coil axes along the y axis) the electric field of the
radiation (which is along the x axis) induces an electric dipole µ
x
along the x axis.
Simultaneously, the variable magnetic field ∂H/ ∂t of the radiation (which is along the y
axis) generate, for the Lenz’s law, a clockwise current in the coil; in a clockwise coil this
means a charge movement in –y direction, i.e. it is induced an electric dipole µ
y
along the -y
axis. The effect produced by E and ∂H/ ∂t are simultaneous, so the general effect is to
produce a new electric field E’ rotated by a angle Ι respect to E.
When the coil is kept as in figure 3.c (coil axes along the x axis) the magnetic field of the
radiation (which is along the y axis) induces a magnetic dipole m
y
along the y axis.
Simultaneously, the variable electric field ∂E/∂t of the radiation (which is along the x axis)
generate a current in the clockwise coil along x direction; this is like a solenoid crossed by
current, so it is induced an electric dipole m
x
along the x axis. The effect produced by H and
∂E/ ∂t are simultaneous, so the general effect is to produce a new magnetic field H’ rotated
by a angle Ι respect to H. In other words, the plane of the incident polarized electromagnetic
wave has been rotated by an angle Ι around the axis z, the propagation direction of the
radiation (see fig 3.d)
10
y
x
z
E
H
Polarized electro-magnetic wave
y
x
z
Π
x
Π
x
is proportional to E
Π
y
Π
y
is proportional to
y
x
z
Π
x
Π
y
Ι
E'
y
x
z
m
x
m
y
m
y
is proportional to H
m
x
is proportional to
y
x
z
m
x
Ι
H'
m
y
y
x
z
E'
H'
Polarized electro-magnetic wave rotated by
Ι
Ι
Ι
a)
b)
c)
d)
Figure 3.
11
Similarly, when the two circularly polarized components are also differentially absorbed by the
optically active medium, (Figure 4a), the modules of the two electric vectors of the right- and
left-circularly polarized beams are reduced to a different extent, so two different molar extinction
coefficients originate, Η
L
and Η
R
. The difference ∋ Η = Η
L
– Η
R
constitutes the circular dichroism
(CD) (Figure 4b).
Figure 4. The two circularly polarised components (
L
E and
R
E ) are differentially absorbed by
the optically active medium (a). This leads to a different molar extinction coefficient for the two
circularly polarised radiation beams (in this case, Η
L
> Η
R
). The difference ∋ Η = Η
L
- Η
R
consti-
tutes the circular dichroism: a positive band (b) results in this case.
Both n
L
– n
R
, that determines [ ∆], and Η
L
– Η
R
are depending
1a-f
on Ο (Figure 5).
Figure 5. The refraction index n and the molar absorption coefficient Η are functions of the
wavelength.
In Figure 6 are reported the shape of [ ∆] and ∋ Η, corresponding to the same electronic transition,
for the two antipodes of a hypothetic chiral molecule, as well as the allied absorption curve
(Abs).
12
Figure 6. Absorption (Abs), optical rotatory dispersion (ORD) and circular dichroism (CD)
corresponding to the same electronic transition for the two antipodes of the same chiral mol-
ecule. The ORD and CD curves are called Cotton effects. On the left-hand side, a negative
Cotton effect (going from longer to shorter wavelengths the negative branch is encountered first)
is reported in ORD and CD (a negative CD band). On the right-hand side, positive Cotton effects
are represented.
A plot of [ ∆] versus Ο constitutes an ORD spectrum, whilst a plot of ∋ Η versus Ο provides a CD
spectrum. Each of the curves present in the CD and ORD spectrum is named Cotton effect. In
ORD we have a positive Cotton effect if, going from longer to shorter wavelengths, the positive
branch is encountered first, while in CD spectra the Cotton effect is named positive when
∋ Η Η
L
– Η
R
> 0, i.e. a positive CD band appears. Clearly, a real molecule possesses several
absorption bands, so the general aspect of the electronic absorption, ORD and CD curves is
commonly much more complex. In figure 7 are reported the UV, ORD and CD curves of (S)-6-
6’-dinitro-2,2’-dimethyl-biphenyl as an example.
13
Figure 7. Absorption, ORD and CD curves of (S)-6-6’-dinitro-2,2’-dimethyl-biphenyl.
As previously reported, the circular dichroism is due to the differential absorption of the two
circularly polarized components of an electromagnetic wave by the optically active medium. If
the absorbed radiation is in the VIS-UV spectral range then the origin of the absorption has to be
found in the electronic transitions and we are examining the electronic circular dichroism (ECD,
or more simply, CD). If the absorbed radiation is in the IR spectral range, then the origin of
phenomenon is due to vibrational transitions in its electronic ground state and we are examining
the vibrational circular dichroism (VCD).
1n,o
The first VCD measurements
1o
were reported in the
1970s, however VCD was very difficult to measure because the intensities of VCD bands
relative to their parent unpolarized infrared (IR) absorption bands are generally an order of
magnitude smaller than that of electronic CD. However two major advancements made this
technique potentially very powerful for structural determinations. First of all, commercial Fourier
transform instrumentation for the measurement of VCD spectra has become available, greatly
enhancing the accessibility of the technique. Second, a theoretical ab initio method has been
developed and implemented, permitting the routine, reliable prediction of VCD spectra.
However, nowadays the VCD is not widely used as electronic CD, reasonably owing to the
expensive instrumentation. In our job we have used only electronic CD based methods, so we
will show only theory and applications related to electronic CD. It is interesting to note that ORD
and electronic CD give equivalent information; in fact they are two aspect of the same physical
14
phenomenon: the interaction of the polarized light with the chiral matter. In effect, it is possible
to get the ORD spectrum from the ECD spectrum (and viceversa) by Kronig-Kramers
transforms
1a,l, 3a
:
> ≅
22
0
''
2099.6 '
(')
d
Η Ο Ο
Ι Ο
Ο Ο
φ ∋
≥
and
> ≅
2
4
22
0
''
1.9303 10
'
(')
d
Ι Ο Ο
Η Ο
Ο Ο Ο
φ
υ
∋
≥
I.1
Where ∆ε (λ ) is the molar circular dichroism and [ Ι ] (λ ) the molar optical rotation at a specific
wavelength λ . It is noteworthy that this relation is extensive on the full spectral region (λ’ goes
from zero to infinite), thus in the practice is impossible to get optical rotation at any frequency
from ECD measured in solution because the absorption of any solvent prevent the possibility to
measure the ECD spectrum at short wavelengths (generally less than 180 nm). Therefore, these
two methods are strongly connected, but they have different characteristic:
- electronic CD spectroscopy derives from light absorbance at well defined wavelengths, i.e.
each Cotton effect is coming from a single electronic transition, so a reliable knowledge of the
wave function of the ground and just the excited state involved in the transition could be enough,
at least in principle, to make some prediction about the absolute configuration. For these reasons,
in order to predict the absolute configuration through the ECD spectroscopy exist a lot of
approaches which are very different in complexity. The more used methods in practical
applications start from completely qualitative rules as those formulated by Harada and
Nakanishi, passing from the coupled oscillator methods until the quantum mechanical methods,
both at the semiempirical and ab initio level.
1l
- by contrast, the ORD derives from light birifringence, therefore at each frequency the value of
the optical rotation is always measurable, but attempting at providing any interpretation of this
property as due to simple contributions may be very difficult. In fact in the 1893, Drude
showed
1e
that the experimental shape of an ORD spectrum can be represented by the following
equation:
λ
22
[]=
n
n
n
K
Ι
Ο Ο
ƒ
I.2
where λ is the wavelength of the incident radiation , K
n
is the molecular rotation constant for
the n-th electronic transition and λ
n
its wavelength. In the quantum mechanical formulation,
Rosenfeld
1p
(1928) defined the nature of the constant K
n
, i.e. he showed the way to obtain the
optical rotation ([ Ι ], in cgs units) :
15
2
2
00
λ
22
0
16 N
[] =
3
nn
n
n
R
hc
Ο Σ
Ι
Ο Ο
φ
ƒ
I.3
It is simple to note that the molecular rotation constant K
n
of the Drude’s equation is equal to
(16π
2
N/3hc)·R
0n
·λ
2
0n
,where R
0n
is the rotational strength for the electronic transition 0→n ,
λ
0n
is the corresponding wavelength in nm , λ is the wavelength of the incident radiation and
N the number of molecules per cm
-3
. It is clear that the optical rotation depends on all the
possible transitions and not just from some of them; in other words it needs to take into
account all the Cotton effects in the full VIS-UV spectral range. Therefore, generally, ECD is
often a simpler propriety to be predicted than ORD, but the latter is more informative because
it is measurable in all the spectral region, also far from any absorption. In particular, this
means that for a molecule in solution and without chromophores (i.e. without absorptions at
wavelengths longer than 200nm) it is possible to measure the ORD but you cannot measure
any ECD band.
Summarising, since ECD can be measured only in correspondence of an absorption band, the
interpretation of ECD data is generally easier than those coming from its dispersive counter-
part, ORD. Therefore we will start considering the CD spectroscopy, showing the more used
methods, and than we will take into account the ORD based methods.
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