Importance of C*-H based modes and large amplitude motion effects in vibrational circular dichroism spectra: The case of the chiral adduct of dimethyl fumarate and anthracene

Article abstract of DOI:10.1021/jp502544v

The role played by the C-H based modes (C* being the chiral carbon atom) and the large amplitude motions in the vibrational absorption (VA) and vibrational circular dichroism (VCD) spectra is investigated. The example of an adduct of dimethyl fumarate and anthracene, i.e., dimethyl-(+)-(11R,12R)-9,10- dihydro-9,10-ethanoanthracene-11,12-dicarboxylate, and two deuterated isotopomers thereof specially synthesized for this goal, are considered. By comparing the experimental and DFT calculated spectra of the undeuterated and deuterated species, we demonstrate that the C-H bending, rocking, and stretching modes in the VA and VCD spectra are clearly identified in well defined spectroscopic features. Further, significant information about the conformer distribution is gathered by analyzing the VA and VCD data of both the fingerprint and the C-H stretching regions, with particular attention paid to the band shape data. Effects related to the large amplitude motions of the two methoxy moieties have been simulated by performing linear transit (LT) calculations, which consists of varying systematically the relative positions of the two methoxy moieties and calculating VCD spectra for the partially optimized structures obtained in this way. The LT method allows one to improve the quality of calculated spectra, as compared to experimental results, especially in regard to relative intensities and bandwidths.

Full text of DOI:10.1021/jp502544v

Article
pubs.acs.org/JPCA
Importance of C*−H Based Modes and Large Amplitude Motion
Effects in Vibrational Circular Dichroism Spectra: The Case of the
Chiral Adduct of Dimethyl Fumarate and Anthracene
Marco Passarello,†,⊥ Sergio Abbate,*,†,‡ Giovanna Longhi,†,‡ Susan Lepri,§ Renzo Ruzziconi,*,§
and Valentin Paul Nicu*,∥
†Dipartimento di Medicina Molecolare e Traslazionale, Universita
‡CNISM Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, Via della Vasca Navale, 84, 00146 Roma, Italy
̀
di Brescia, Viale Europa 11, 25123 Brescia, Italy
§Dipartimento di Chimica, Biologia e Biotecnologie, Universita
̀
di Perugia, via Elce di Sotto 8, 06100 Perugia, Italy
∥Theoretical Chemistry, Vrjie Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
S
* Supporting Information
ABSTRACT: The role played by the C*−H based modes (C* being the chiral carbon atom) and
the large amplitude motions in the vibrational absorption (VA) and vibrational circular dichroism
(VCD) spectra is investigated. The example of an adduct of dimethyl fumarate and anthracene, i.e.,
dimethyl-(+)-(11R,12R)-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylate, and two deu-
terated isotopomers thereof specially synthesized for this goal, are considered. By comparing the
experimental and DFT calculated spectra of the undeuterated and deuterated species, we
demonstrate that the C*−H bending, rocking, and stretching modes in the VA and VCD spectra
are clearly identified in well defined spectroscopic features. Further, significant information about
the conformer distribution is gathered by analyzing the VA and VCD data of both the fingerprint
and the C−H stretching regions, with particular attention paid to the band shape data. Effects
related to the large amplitude motions of the two methoxy moieties have been simulated by
performing linear transit (LT) calculations, which consists of varying systematically the relative
positions of the two methoxy moieties and calculating VCD spectra for the partially optimized
structures obtained in this way. The LT method allows one to improve the quality of calculated spectra, as compared to
experimental results, especially in regard to relative intensities and bandwidths.
from them. (As shown in Scheme 1, the considered example
molecules will be referred hereafter as (R,R)-1, (R,R)-1-d6 and
(R,R)-1-d16, (S,S)-1, (S,S)-1-d6, and (S,S)-1-d16, respectively.)
The extensive use of deuteration (which localizes or, better
said, restricts the delocalization of the modes) together with the
C2 symmetry of the chemical structure for the chosen molecular
systems should allow us to better understand the nature of the
numerous monosignate and bisignate features in the vibrational
1. INTRODUCTION
Molecular chiral systems in most cases are devoid of symmetry,
though it is known that, to be chiral, an object should “only”
miss any of the following symmetry elements: mirror plane,
inversion center, Sn axes.1,2 This has made Cn-symmetry
endowed molecules, like, e.g., allene-based molecules, biphen-
yls, binaphthyls, and helicene-based systems, particularly
attractive in studying chiroptical properties like optical rotation
(OR) or electronic circular dichroism (ECD).3 In vibrational
circular dichroism (VCD) spectra3−16 many features are
present and symmetry could help classify different kinds of
bands as associated with different kinds of phenomena. Not
only is this particularly true for the mid-IR region, where we
recall the example of (S)-(1,3)-dimethyl allene17 and (1,2)-
trans-dideuterio-oxirane,18 but also the CH-stretching region
(even in the NIR region) was investigated in the past for these
and analogous systems.17−20
Scheme 1. Chemical Structures of the Compounds (R,R)-1,
(R,R)-1-d6, and (R,R)-1-d16 and Their Enantiomers (S,S)-1,
(S,S)-1-d6, and (S,S)-1-d16.
To combine the virtues of symmetry and deuteration (as
recalled in refs 17−20 above), in this work we consider as our
case of study the dimethyl (+)-(11R,12R)-9,10-dihydro-9,10-
ethanoanthracene-11,12-dicarboxylate, its enantiomer dimethyl
(−)-(11S,12S)-9,10-dihydro-9,10-ethanoanthracene-11,12-di-
carboxylate and two specifically deuterated isotopomers derived
Received: March 13, 2014
Revised: May 19, 2014
Published: May 19, 2014
© 2014 American Chemical Society
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Scheme 2. Synthesis of Compounds (R,R)-1, (R,R)-1-d6, and (R,R)-1-d16 and Their Respective Enantiomers (S,S)-1, (S,S)-1-d6,
and (S,S)-1-d16
absorption (VA) and circular dichroism (VCD) spectra (as
found in refs 17−20). Indeed, as it will be shown, this
simplification of the spectra will allow us to gain significant
insight regarding:
used in different fields, such as medicinal chemistry,28,29
stereoselective synthesis,29,30 and material science.31
2. EXPERIMENTAL AND COMPUTATIONAL DETAILS
(1) the origin of the bands that dominate the VA and VCD
peaks in the fingerprint region,
2.1. Synthesis and Characterization of Adducts (R,R)-
1, (R,R)-1-d6, and (R,R)-1-d16 and Their Respective
Enantiomers (S,S)-1, (S,S)-1-d6, and (S,S)-1-d16. The six
stereoisomers have been synthesized ad hoc for this
spectroscopic study and were derived from the common
racemic dimethyl ( )-9,10-dihydro-9,10-ethanoanthracene-
11,12-dicarboxylate, which has been prepared in very good
yield (up to 90%) by AlCl3-catalyzed Diels−Alder cycloaddition
of dimethyl fumarate to both anthracene and its isotopomer
anthracene-d6 (Scheme 2).32−36
The alkaline hydrolysis of diester ( )-1 and the deuterated
analogue ( )-1-d10 provided the corresponding racemic acid
( )-2 and ( )-2-d10, which were resolved into the correspond-
ing enantiomeric acids (R,R)-2, (S,S)-2 and (R,R)-2-d10, (S,S)-
2-d10, by fractional crystallization of their diastereomeric
brucine salts. Each of the optically active acids was treated
with thionyl chloride to obtain the corresponding acyl chlorides
which was, finally, transformed into the esters (R,R)-1, (S,S)-1,
and (R,R)-1-d6, (S,S)-1-d6 by refluxing of the acyl chlorides in
methanol and methanol-d4. (R,R)-1-d16, and (S,S)-1-d16 were
obtained analogously by refluxing the acyl chlorides of (R,R)-2-
d10 and (S,S)-2-d10 in methanol-d4.
See section SI-1, part (a) in the Supporting Information
material for description of preparation and characterization of
synthesized molecules and deuterated products. The products
were fully characterized by elemental analysis, NMR, optical
rotations measured in solutions at 24 °C, at the sodium D-line
wavelength (589 nm) (OR), and electronic circular dichroism
(ECD). The ECD spectra of the three isotopomers are
reported in the Supporting Information in section SI-1, part
(b), whereas the OR values and melting points (mp) are given
in Table 1.
(2) the VCD bands in the CH-stretching region, which in
this case presents unusually broad monosignate bands
(we note these modes have been discussed for some time
in the literature as typical of alcohols, acids, and esters
and have been first rationalized in terms of the so-called
ring-current mechanism)21−25
(3) the bandshapes and bandwidths26,27 of the VA and VCD
spectra (these two important observables of VA and
VCD spectra have been little investigated in the past,
though it is clear that their understanding may help shed
some light onto overall molecular motions in solution,
e.g., translations, rotations, tumbling, etc. as well as
intramolecular relaxation phenomena, e.g., low-fre-
quency/large-amplitude motions).
In other words, the present study aims at investigating the
fundamental chiroptical properties of this molecule and
promises also to have the typical interesting applicative
characteristics of adduct-type molecules, viz. the shape of the
VA and VCD spectra of this type of compounds are influenced
to a great extent by the large amplitude methoxy pseudor-
otation. With these goals in mind, systematic density functional
theory (DFT) VA and VCD calculations have been performed
for many structures of the considered molecules. That is to say,
besides running calculations for the isolated molecule and
molecular complexes formed between one solute molecule and
two solvent molecules, the large amplitude methoxy pseudor-
otation has also been accounted for by performing linear transit
calculations.
Of course we are confident that this basic study will also be
appreciated outside fundamental science, because it is known
that anthracene adducts are precursors of compounds widely
2.2. Infrared Absorption (VA) and Vibrational and
Electronic Circular Dichroism (VCD and ECD) Spectra. IR
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2.3. Computational Details. All calculations have been
performed with the ADF program37−40 package using the BP86
functional41,42 and the ADF TZP43 basis set. Both vacuum and
COSMO44−46 calculations have been performed. In the
vacuum calculations all geometry optimizations and VA and
VCD calculations have been performed for the isolated free
molecules and molecular complexes. In the COSMO
calculations the considered free molecules and molecular
complexes were embedded in a dielectric continuum
corresponding to chloroform (dielectric constant of 4.8). For
brevity, we consider here only the results of the vacuum
calculations for the molecular complexes formed between
solute and solvent molecules, i.e., the calculations that have
reproduced the experimental spectra best. (See section 4 in the
Supporting Information (SI-4) for a comparison of all vacuum
and COSMO VA and VCD spectra.)
The linear transit (LT) calculations, devised to simulate the
pseudorotations of the methoxy groups, are performed in two
steps. First, a set of intermediate structures (hereafter referred
to as LT structures) is generated by varying a geometrical
parameter (e.g., bond length, bond angle, dihedral angle) from
an initial value to a final value in a given number of steps. The
geometrical parameter (hereafter referred to as the LT
parameter), its final value, and the number of LT steps are
defined by the user in the beginning of the LT calculation.
Then, a constrained geometry optimization is performed for
each LT structure generated in the first step; i.e., the value of
the LT parameter characterizing a given LT structure is kept
fixed during the geometry optimization of all other structural
parameters. (To obtain the reference structures, i.e., the
structure used as the starting point for all LT calculations, a
stringent convergence criterion for the geometry optimizations
was used, i.e., 1 × 10−4 hartree/Å for gradients. The
convergence criteria used for the constrained geometry
optimizations performed during the LT structure is 10−3
Hartree/Angstrom for gradients, i.e., ADF default.)
Table 1. Experimental Melting Points and Specific Rotations
at the Sodium D Line for Dimethyl (+)-(11R,12R)-9,10-
Dihydro-9,10-ethanoanthracene-11,12-dicarboxylate ((R,R)-
1) and Dimethyl (−)-(11S,12S)-9,10-Dihydro-9,10-
ethanoanthracene-11,12-dicarboxylate ((S,S)-1) and Two
Isotopomers Thereof
24
24
molecule
mp (°C) [α]D (c, 1.5, CHCl3) [α]D (c, 1.5, CH3OH)
(R,R)-1
89−91
90
+23.0
+21.1
−21.3
+7.0
(S,S)-1
−30.8
(R,R)-1-d6
(S,S)-1-d6
(R,R)-1-d16
(S,S)-1-d16
88−90
87−90
91−92
88−89
−7.8
+18.0
−20.0
absorption and VCD spectra were taken with a JASCO
FVS4000 apparatus, equipped with two detectors, an MCT one
employed in the mid-IR region from 900 to 1800 cm−1 and an
InSb one employed in the CH-stretching region. In the two
regions the same ZnSe photoelastic modulator (PEM) was
used. Two transparent solvents for both spectral ranges were
used, namely CDCl3 and CD3CN: no essential differences were
noticed, notwithstanding the different polarity of the solvents.
In the fingerprint region 2000 scans were taken and a 100 μm
path length cell was employed, whereas for the CH-stretching
region 5000 scans were taken and still a 100 μm cell was used.
In either case the VA and VCD spectra for the solvent taken in
the same conditions were subtracted. In the main text we
provide the VCD spectra for the (R,R)-1 enantiomers, obtained
as semidifferences of the original VCD spectra of the (R,R)-1
and (S,S)-1 enantiomers (good mirror image spectra had been
obtained).
ECD spectra (presented in section SI-1 of the Supporting
Information, part (b)) were measured in 0.05 M/CH3CN
solutions contained in 0.1 mm quartz cuvettes, with 1 scan at
100 nm/min scanning speed using a Jasco815SE apparatus.
Figure 1. Comparison of experimental VA (upper panel) and VCD (lower panel) spectra of dimethyl-(+)-(11R,12R)-9,10-dihydro-9,10-
ethanoanthracene-11,12-dicarboxylate and two deuterated isotopomers thereof, namely (R,R)-1, (R,R)-1-d6, and (R,R)-1-d16 (Scheme 1) in the three
spectroscopic regions: mid-IR (left), CO stretching (center), and CH stretching (right). For experimental details see section 2.2.
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The simulated VA and VCD spectra were obtained by
Lorentzian broadening of the dipole and rotational strength
using a half-width of 8 cm−1. The calculated harmonic
frequencies have been scaled with the following factors: 1.02
in the fingerprint region and 0.985 in the C−H stretching.
These values were found to provide the best agreement with
observed VA and VCD band positions.
of VA and VCD spectra conducted above has shown, the VCD
signals associated with normal modes involving the C*−H
bonds dominate, not only in the C−H stretching region (2800
to 3200 cm−1) but also in the fingerprint region between 1000
and 1400 cm−1 of the VCD spectra.
Finally, the many similarities and few characteristic differ-
ences observed in the VCD spectra of the tree isotopomers
justify the decision to carry on the calculations just for the
(R,R)-1-d16 molecule, because the interpretation of the VCD
spectra of (R,R)-1-d16 will enable one to understand also the
VCD spectra of (R,R)-1-d6 and of (R,R)-1 as well. The
interpretation of VA spectra will come out as a consequence,
too.
3.2. Standard DFT Calculations. 3.2.1. Molecular
Structures. The concluding remarks of section 3.1 led us to
concentrate on calculations of geometries and spectra of (R,R)-
1-d16: of course we have also made sure that our predictions are
equally good for the undeuterated or less deuterated species.
(For ease of discussion we report in Scheme 3 the atom
numbering of (R,R)-1-d16, according to IUPAC convention.)
3. RESULTS AND DISCUSSION
3.1. Analysis of the Experimental VA and VCD
Spectra. In Figure 1 we compare the experimental VA and
VCD spectra of (R,R)-1 and of its (R,R)-1-d6 and (R,R)-1-d16
isotopomers, with the aim of identifying spectroscopic regions
which are either constant or variable with deuteration.
In the first frequency region between 1000 and 1100 cm−1
the VA spectra of (R,R)-1-d6 and (R,R)-1-d16 contain an intense
band at 1090 cm−1 that is assigned to C−D bending modes of
B symmetry (i.e., mostly umbrella motions localized on the two
methoxy groups), coupled to C−O stretching modes. In (R,R)-
1 this band is not present at 1090 cm−1, but another broad
band is found at ca. 1040 cm−1 and further changes are noticed
at higher frequencies (see below): this is due to CH3 groups
replacing CD3 ones. The corresponding VCD signals are very
weak.
Scheme 3. Structure of Dimethyl (+)-(11R,12R)-9,10-
Dihydro-9,10-ethanoanthracene-11,12-dicarboxylate, (R,R)-
1, and Atom Numbering According to IUPAC
In the next frequency region, i.e., between 1100 and 1400
cm−1, the three VCD spectra exhibit fairly similar patterns. This
suggests that the shape of the VCD spectra in this region is
determined almost entirely by normal modes involving the two
C*−H bonds (C* being either of the two stereogenic carbon
atoms); possible contributions from CO and CC stretchings
cannot be excluded, but their role is major in other
spectroscopic regions. The three VA spectra, on the other
hand, exhibit rather distinct features in this frequency interval,
which indicates the VA spectra are more sensitive to
movements of the C−H and C−D bonds than the VCD
spectra.
Moving further to the CO stretching region, i.e., to the
1650−1850 cm−1 frequency interval, one notices that the three
molecules have fairly similar VA and VCD spectra. As shown in
the middle panel of Figure 1, we have a broad IR band at ca.
1735 cm−1 and a (−, +) VCD couplet with the two
components located at 1735 and at 1750 cm−1, respectively.
Given the fact that the carbonyl stretching modes are almost
entirely localized on the CO bonds (i.e., they are very little, if
at all, contaminated by C−H bending modes), the similar
appearances of the VA and VCD spectra of the three molecules
are not surprising.
The conformers of (R,R)-1-d16 are determined by the relative
orientations of its two CO bonds. As indicated in Figure 2 by
the orange arrows, there are three possibilities. That is to say,
we have two conformers with C2 symmetry (i.e., C1 and C2),
and one conformer without symmetry (i.e., C3). However,
because the conformer C3 can be obtained in two ways (see
Finally, in the CH-stretching region, i.e., between 2800 and
3100 cm−1, the quite structured VA spectrum of the (R,R)-1
compound, containing all aromatic and aliphatic C−H
stretching features, is reduced in the (R,R)-1-d16 isotopomer
to a single broad band centered at 2920 cm−1, which is
determined solely by the stretching of the C*−H bonds. (Note
that the spectrum of the (R,R)-1-d6 isotopomer exhibits above
3000 cm−1 features associated only with the aromatic C−H
stretching modes). As can be seen in the right panel of Figure 1,
in correspondence with the broad VA band at 2920 cm−1, a
single broad positive band is observed in all three VCD spectra.
This band is associated with the C*−H stretching modes.
As stated in the Introduction, the VCD signals associated
with these C*−H stretching modes have long been
recognized21−25 as the prevailing signals in the VCD spectra
of alcohols, acids, and esters. However, as the empirical analysis
Figure 2. Optimized structures of the conformers C1, C2, and C3 of
dimethyl-(+)-(11R,12R)-9,10-dihydro-9,10-ethanoanthracene-11,12-
dicarboxylate. Upper panel: viewed from a direction perpendicular to
the C2 symmetry axis (in conformers C1 and/or C2). Lower panel:
viewed along the C2 symmetry axis (in conformers C1 and/or C2).
(The orange arrows indicate the direction of the CO bonds.)
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section 2 in the Supporting Information), it must be counted
twice, when computing the Boltzmann weights.
sets of calculations predict the conformer C2 and C3 to be
significantly populated at room temperature. That is, the
Boltzmann factors computed for the two conformers are 0.60
(C2) vs 0.36 (C3) when the free molecules are considered, and
0.63 (C2) vs 0.34 (C3) when the molecular complexes with
CDCl3 solvent molecules are considered. (We note that similar
results are obtained also with using the COSMO solvation
model.)
Further, because the two CO bonds of (R,R)-1-d16 form
intermolecular “hydrogen bonds” with deuterated chloroform
solvent molecules (as noticed, e.g., in ref 47), we have
performed calculations also for molecular complexes formed
between one solute molecule and two solvent molecules, i.e.,
one deuterated chloroform (CDCl3) molecule in the vicinity of
each C=O bond. Three molecular complexes (MC) have been
considered in total, i.e., one for each conformer. They are
labeled as C1-(CDCl3)2, C2-(CDCl3)2, and C3-(CDCl3)2. We
note that other relative geometries between CDCl3 and (R,R)-
1-d16 do not bear such low energy.
The optimized structures (BP86/TZP, vacuum) of the
molecular complexes formed with the dominant conformers,
i.e., C2-(CDCl3)2 and C3-(CDCl3)2, are shown in Figure 3.
3.2.2. Comparison of Experimental and Computed
Spectra. Figure 4 shows comparisons between the experimental
VA and VCD spectra of (R,R)-1-d16 and the spectra computed
for the C1-(CDCl3)2, C2-(CDCl3)2, and C3-(CDCl3)2 molec-
ular complexes for the fingerprint region (comparisons of
experimental and computed spectra of (R,R)-1 and (R,R)-1-d6
are shown in Section 5 of the Supporting Information) .
As can be seen in Figure 4, overall the spectra computed for
the C2-(CDCl3)2 complex reproduce the experimental spectra
very well, and, at the same time, significantly better than the
spectra computed for the other two conformers. On one hand,
this is in agreement with the Boltzmann factors computed in
Table 2 (which indicate that conformer C2 is the predominant
conformer). On the other hand, however, the spectra
comparisons in Figure 4 suggest that even though the C3-
(CDCl3)2 conformer has been predicted to possess a significant
population, very few signatures from the C3-(CDCl3)2
conformer exist in the mid-IR VA and VCD spectra.
The relative energies and the associated Boltzmann factors
computed for the isolated conformers and also for the three
molecular complexes are listed in Table 2. As can be seen, both
Table 2. Relative Energies (ΔE) and Boltzmann Weights
(BW) Computed for the Free Molecules (FM) and for the
Molecular Complexes (MC). Computational Details:
Vacuum, BP86, TZP
conformer.
ΔE (kcal/mol)
Free Molecule
BW
C2
0.000
0.60
0.18
0.18
0.04
CA3
CB3
C1
0.700
0.700
1.720
Molecular Complex
0.000
C2-(CDCl3)2
C3A-(CDCl3)2
C3B-(CDCl3)2
C1-(CDCl3)2
0.63
0.17
0.17
0.03
The analysis of the normal modes of conformer C2 has
shown that vibrational transitions associated with intense VA
and VCD signals in the frequency interval between 1100 and
1400 cm−1 do indeed contain large contributions from C*−H
bending modes. That is, 80% (or more) of the normal mode
0.790
0.790
1.640
Figure 3. Optimized structures (BP86/TZP, vacuum) of the molecular complexes formed between the conformers C3 (top panel) and C2 (lower
panel) of dimethyl-(+)-(11R,12R)-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylate-d16, ((R,R)-1-d16), and two CDCl3 molecules, i.e., C3-
(CDCl3)2 and C2-(CDCl3)2. (The atoms defining the dihedral angles varied during the linear transit (LT) calculations, i.e., O3C13C12C11 and
O2C14C11C12 have been tagged with numeric labels.)
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Figure 4. Fingerprint spectral region: comparison of the experimental VA (left) and VCD (right) spectra of dimethyl-(+)-(11R,12R)-9,10-dihydro-
9,10-ethanoanthracene-11,12-dicarboxylate-d16, (R,R)-1-d16, measured in CDCl3 to spectra calculated for the C1-(CDCl3)2, C2-(CDCl3)2, and C3-
(CDCl3)2 molecular complexes. Computational details: BP86/TZP, vacuum.
movements in these modes are localized on the C*−H bending
modes (with the remaining 20% consisting of C−C and/or C−
O stretching modes). This confirms the conclusions drawn in
section 3.1; i.e., not only the CH stretching region of the
spectra but also the fingerprint region between 1100 and 1400
cm−1 is determined by the modes localized on the C*−H
bonds.
In the carbonyl stretching region, i.e., between 1700 and
1800 cm−1, the VA spectra present a strong and broad band,
whereas the VCD spectra exhibit a couplet with (−, +) signs in
order of increasing wavenumbers. This feature is very well
reproduced by the spectrum computed for the C2-(CDCl3)2
complexwe have a very intense bisignate doublet (deter-
mined by CO stretching modes) with a negative band, at
1730 cm−1 (B symmetry) and a positive one at 1733 cm−1 (A
symmetry).
to be better for the VCD spectra than for the VA spectra (not
only for the C2-(CDCl3)2 spectra but also for the Boltzmann
averages shown later in Figure 8). As can be seen, the relative
intensities of the various bands in the fingerprint region are
predicted in the simulated VCD spectra better than in the VA
ones, where the carbonyl stretching bands should be
significantly more intense than the rest of the bands.
In the CH-stretching region, both VA and VCD experimental
spectra are quite simple and consist of a single positive feature,
which in both cases is quite broad though not very intense. As
can be seen in Figure 5, all computed spectra provide a good
description of experimental ones; viz., in all cases the predicted
bands have the correct VCD sign and have good enough VA
and VCD intensities (the same can be said about the prediction
of VA and VCD spectra in the CH-stretching region for (R,R)-
1, Figure SI-5, Supporting Information). However, in spite of
their simplicity, the spectra in CH-stretching region, unlike the
rich fingerprint spectra, seem to provide evidence that, as
predicted in Table 2, conformer C3 is also populated in the
experimental sample. Indeed, in both VA and VCD spectra, the
single peak calculated for the C2-(CDCl3)2 spectra is positioned
in correspondence with the most intense experimental band. At
the same time, this peak is situated right between the two peaks
obtained in the C3-(CDCl3)2 spectra whose positions also agree
quite well with the positions of the shoulders observed in the
experimental spectra. Regarding the assignment of the bands in
the 2800−3000 cm−1 frequency interval, as discussed in section
3.1, all peaks in the computed spectra are associated to C*−H
stretching modes. We note that, although the importance of
We note that the performed normal-mode analysis confirms
that the observed signs can be explained by the vibrational
coupled dipoles mechanism, discussed in the early days of VCD
by Holzwarth,48 later studied by ab initio methods by Bour
̌
and
Keiderling,49 and recently thoroughly discussed, on the basis of
DFT calculations, by Taniguchi and Monde.50 In accordance
with the exciton chirality rule formulated by Taniguchi and
Monde,50 in the (R,R)-1 case one CO bond has to be rotated
anticlockwise to eclipse the other CO bond, providing the
(−) case, as observed in all experimental and calculated VCD
spectra in Figures 1 and 4.
It is also interesting to note that in the fingerprint region, the
agreement between experimental and computed spectra seems
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Figure 5. CH stretching regions: comparison of the experimental VA (left) and VCD (right) spectra of dimethyl-(+)-(11R,12R)-9,10-dihydro-9,10-
ethanoanthracene-11,12-dicarboxylate-d16, (R,R)-1-d16, measured in CDCl3 to spectra calculated for the C1-(CDCl3)2, C2-(CDCl3)2, and C3-
(CDCl3)2 molecular complexes. Computational details: BP86/TZP, vacuum.
Figure 6. Variation of the energy of dimethyl-(+)-(11R,12R)-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylate-d16, (R,R)-1-d16, during the
LT scans. Left panel: (1) Energy dependence of C2-(CDCl3)2 on the dihedral angles O3C13C12C11 and O2C14C11C12 (black curve). The two angles
were varied symmetrically in steps of 3° to preserve the C2 symmetry of C2-(CDCl3)2. (2) Energy dependence of C3-(CDCl3)2 on the dihedral
angles O3C13C12C11 (blue curve). The angle was varied in steps of 10° whereas the second dihedral angle, i.e., O2C14C11C12, angle was not varied as
C3-(CDCl3)2 does not have symmetry. Right panel: (1) Energy dependence of C3-(CDCl3)2 on the O2C14C11C12 dihedral angle (black curve). The
O2C14C11C12 LT scans have been performed for each O3C13C12C11 value (i.e., diamond on the blue curve) situated in the highlighted 1 kcal/mol
interval. O2C14C11C12 was varied in steps of 10°. (2) (Blue) C3-(CDCl3)2 energy curve in the left panel which shows the O3C13C12C11 values for
which O2C14C11C12 LT scans have been performed. (See Figure 3 and Scheme 3 for definition of dihedral angles involved in LT calculations.)
this VCD band in numerous cases encompassing alcohols,
sugars, acids, amino acids, and esters has been recognized by
Nafie et al.21−23 already in 1986, the mechanism responsible for
this rather intense VCD band is still a matter of discussion.24,25
We can therefore conclude that the standard DFT
calculations performed for the C1-(CDCl3)2, C2-(CDCl3)2,
and C3-(CDCl3)2 molecular complexes have yielded spectra
that overall reproduce the experimental ones quite well (as
shown in section 5 in the Supporting Information, this is the
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Figure 7. Fingerprint spectral region: comparison of experimental and Boltzmann weighted VA (left) and VCD (right) spectra of dimethyl-
(+)-(11R,12R)-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylate-d16, (R,R)-1-d16. The upper spectra (in blue), labeled MC, are Boltzmann
averages over the spectra computed for the “steady” molecular complexes formed with the three conformers (the Boltzmann factors are given in
Tables 2). The lower spectra (in red), labeled LT, are Boltzmann averages over all spectra computed for the (R,R)-1-d16 molecule, i.e., the spectrum
computed for C1-(CDCl3)2, and the spectra computed for the C2-(CDCl3)2 and C3-(CDCl3)2 LT structures.
case also for (R,R)-1 and (R,R)-1-d6). However, there are still a
few details in the experimental spectra that are not well
reproduced by these calculations, namely, (1) the relative
intensities bands (most notably in the in the fingerprint VA
spectra) and (2) the broad character of some experimental
bands. Both these issues will be discussed in the next section.
3.2.3. Linear Transit Calculations. To simulate the effects
induced in the spectra by the large amplitude pseudorotations
performed by the two methoxy groups, the relative orientation
of the two carbonyl groups was systematically varied by
performing linear transit (LT) calculations (described in
section 2.3) for the C2-(CDCl3)2 and C3-(CDCl3)2 molecular
complexes. This approach had been tried somewhat empirically
previously,51−55 but here we proposed, as also proposed in ref
56, to Boltzmann average the VA and VCD spectra of all LT
structures, as for hindered rotations or torsions defining flat
energy curves, it is practically impossible to define an absolute
energy minimum. Two dihedral angles have been varied during
the LT calculations, i.e., O3C13C12C11 and O2C14C11C12 (the
atoms defining these two angles are shown in Figure 3; see also
the IUPAC numbering in Scheme 3). In the case of the C2-
(CDCl3)2 molecular complexes, which has C2 symmetry, the
two dihedral angles have been varied symmetrically (i.e., to
preserve the C2 symmetry) by 48° in steps of 3° starting from
their initial value of 6°. In the case of the C3-(CDCl3)2
complexes, which does not belong to the C2-symmetry group,
we have first run a LT calculation for the O3C13C12C11 angle
(see the blue energy curve in the left panel in Figure 6), then
for each LT structures whose energy was within 1 kcal/mol
with respect to the reference C3-(CDCl3)2 structure, we have
run additional LT calculations for the O2C14C11C12 angle (see
the right panel in Figure 6). In this case, the two angles have
been varied by 60° in steps of 10°, viz. to sample significantly
different spectra, a larger LT step was needed in the case of C3-
(CDCl3)2. The variation of the energy during these linear
transit scans is shown in Figure 6.
VA and VCD calculations have been performed for all LT
structures within the 1 kcal/mol energy intervals highlighted in
the left and right panels of Figure 6, i.e., for 17 C2-(CDCl3)2 LT
structures and for 48 C3-(CDCl3)2 LT structures.
Finally, we note that the high frequency modes in the
fingerprint and CH stretching regions (in which we are
interested) are associated with coordinates that have been fully
optimized during the LT scans; i.e., they do not involve the
coordinates defining the pseudorotations of the two methoxy
groups that have been only partially optimized during the LT
scans. Consequently, these modes are predicted accurately by
the frequency calculations performed here for the partially
optimized LT structures.56
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Figure 8. C−H stretching regions: comparison of experimental and Boltzmann weighted VA (left) and VCD (right) spectra of dimethyl-
(+)-(11R,12R)-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylate-d16, (R,R)-1-d16,. The upper spectra (in blue), labeled MC, are Boltzmann
averages over the spectra computed for the “steady” molecular complexes formed with the three conformers (the Boltzmann factors are given in
Tables 2). The lower spectra (in red), labeled LT, are Boltzmann averages over all spectra computed for the (R,R)-1-d16 molecule, i.e., the spectrum
computed for C1-(CDCl3)2, and the spectra computed for the C2-(CDCl3)2 and C3-(CDCl3)2 LT structures.
Figures 7 and 8 show comparisons between the experimental
VA and VCD spectra and simulated spectra. The simulated
spectra shown in the upper part of each plot in Figures 7 and 8
(labeled as MC) have been obtained as Boltzmann averages of
the spectra computed for the fully optimized structures of the
molecular complexes C1-(CDCl3)2, C2-(CDCl3)2, and C3-
(CDCl3)2. The simulated spectra in the lower part of Figures
7 and 8 (labeled as LT) have been obtained as Boltzmann
averages over all spectra computed for the (R,R)-1-d16
molecule, i.e., the spectrum computed for C1-(CDCl3)2, and
all spectra computed for the C2-(CDCl3)2 and C3-(CDCl3)2 LT
structures. More specifically, to preserve the Boltzmann
populations in Table 2, the C2-(CDCl3)2 and C3-(CDCl3)2
sets of LT spectra have been first averaged separately using the
energies obtained during the LT scans, viz. we have much more
LT structure for the conformer C3-(CDCl3)2 than for
conformer C2-(CDCl3)2. Then, the two Boltzmann weighted
spectra obtained for the C2-(CDCl3)2 and C3-(CDCl3)2 LT
structures, have been averaged together with the spectrum
computed for conformer C1-(CDCl3)2 using the Boltzmann
factors given in Table 2.
the relative magnitude of the various bands in the experimental
spectrum significantly better than the MC spectrum. The LT
spectrum improves upon the MC spectrum also when the VCD
spectra are reviewed, notice in particular the bandwidths of the
(−, +) doublet observed in experiment at ca. 1300 and 1370
cm−1, which are calculated broader, whereas all other couplets
are narrow and the same as in the MC case and as observed.
The C−H stretching region (see Figures 8), which is
essentially due to local C*−H stretching modes in all
conformers, is better evaluated by the LT approach, as far as
the bandwidth and intensity is concerned, for both VA and
VCD spectra. Although the MC spectra provide a very good
representation of the experimental spectra with the narrow
bands falling right on top of the peaks and shoulders observed
in the experimental spectra, LT calculations appear to distribute
the C*−H frequencies around the two main peaks for the C2
and C3 conformers over a wider region. Indeed, in this region a
crucial role is played by the frequency of the C−H stretching
modes in the two conformers. A long time ago57 the
dependence of C−H stretching frequency with respect to the
lone pairs of a nearby oxygen atom was studied and
subsequently proved by ab initio techniques.58 Those findings
as well as the present ones may have some relevance in the
dispute of the ring-current mechanism, introduced to ration-
alize VCD spectra of a C*−H bond in alcohols, acids, etc.21−25
The spectra comparisons in Figures 7 will be discussed first.
In the case of the VA spectra, the LT simulated spectrum
reproduces the experimental spectrum significantly better than
the MC simulated spectrum; viz., the LT spectrum reproduces
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Present Address
Indeed, all previous observations about CH-stretching VCD
spectra in alcohols, esters, amines, etc. have reported broad and
intense C*−H features. Our explanation of the band shape is
thought to corroborate the previous quoted evidence.
⊥Dipartimento di Chimica, Materiali e Ingegneria Chimica “G.
Natta” − Politecnico di Milano, Piazza Leonardo da Vinci 32,
20133 Milano, Italy.
Notes
4. CONCLUSIONS
The authors declare no competing financial interest.
In this work we have presented a fundamental VA and VCD
study using as example the dimethyl-(+)-(11R,12R)-9,10-
dihydro-9,10-ethanoanthracene-11,12-dicarboxylate molecule
and two deuterated isotopomers specially synthesized for this
study with a chemical structure endowed with C2 symmetry.
The spectra are particularly “clean” and the VCD spectrum in
the fingerprint region consists of doublets of alternating sign,
whereas in the C−H stretching region it contains a single broad
band. The simplicity of the spectra is traced back in the
symmetry of the molecule and the extensive use of deuteration.
The comparisons of the VCD spectra measured for the
undeuterated and the two deuterated species has demonstrated
clearly that the normal modes involving movements of the C*−
H bonds (C* being either of the two stereogenic carbon
atoms) determine the shape of the VCD spectra not only in the
C−H stretching region but also in the fingerprint region.
Though C*−H stretchings were thoroughly investigated in the
past,21−25 the C*−H rockings and bendings modes have been
considered only recently.52
The computed DFT spectra reproduce well the experiment
and allowed to confirm the crucial role played by the C*−H
rocking, bending and stretching modes. Moreover, comparisons
of the experimental and computed spectra have shown that
more information about the conformer distribution from
experimental data can be obtained by considering both the
fingerprint and the CH stretching regions. Best computations
are obtained by considering the effect of the solvent, through
the introduction of explicit solvent molecule.
ACKNOWLEDGMENTS
■
This work was supported by The Netherlands’ Foundation for
Scientific Research (VENI grant VPN). S.A., G.L., and R.R.
thank the Italian “Ministero dell’Istruzione, dell’Universita e
̀
della Ricerca” (MIUR) for financial support, under the auspices
of the program PRIN 2008LYSEBR. M.P. thanks the HPC
program (EU) for the HPC-Europa2 transnational program
fellowship that has allowed him to visit the lab of V.P.N. for two
months.
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ASSOCIATED CONTENT
* Supporting Information
■
S
SECTION SI-1 (a): Synthesis and characterization of adducts
(R,R)-1, (R,R)-1-d6, and (R,R)-1-d16 and their respective
enantiomers (S,S)-1, (S,S)-1-d6, and (S,S)-1-d16. SECTION
SI-1 (b): ECD and UV absorption spectra of (R,R)-1 and (S,S)-
1. SECTION SI-2: Conformers C3 and C3 . SECTION SI-3:
A
B
Anthracene dihedral angle. SECTION SI-4: Vacuum, COSMO,
and LT calculations for C2- and C3-(CDCl3)2 (TBE vs LT
parameters, VA and VCD spectra). SECTION SI-5: Compar-
ison of vacuum calculations for (R,R)-1 and (R,R)-1-d16 in the
C2-conformation (VA and VCD spectra). This information is
available free of charge via the Internet at http://pubs.acs.org
AUTHOR INFORMATION
Corresponding Authors
*S. Abbate: sergio.abbate@ unibs.it.
*R. Ruzziconi: renzo.ruzziconi@unipg.it.
*V.P. Nicu: v.p.nicu@vu.nl, vp.nicu@gmail.com.
■
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