Electrical and mechanical anharmonicities from NIR-VCD spectra of compounds exhibiting axial and planar chirality: The cases of (S)-2,3-pentadiene and methyl-d3 (R)- and (S)-[2.2]paracyclophane-4-carboxylate

Article abstract of DOI:10.1002/chir.21013

The IR and Near infrared (NIR) vibrational circular dichroism (VCD) spectra of molecules endowed with noncentral chirality have been investigated. Data for fundamental, first, and second overtone regions of (S)-2,3-pentadiene, exhibiting axial chirality, and methyl-d₃ (R)- and (S)-[2.2]paracyclophane-4-carboxylate, exhibiting planar chirality have been measured and analyzed. The analysis of NIR and IR VCD spectra was based on the local-mode model and the use of density functional theory (DFT), providing mechanical and electrical anharmonic terms for all CH-bonds. The comparison of experimental and calculated spectra is satisfactory and allows one to monitor fine details in the asymmetric charge distribution in the molecules: these details consist in the harmonic frequencies, in the principal anharmonicity constants, in both the atomic polar and axial tensors and in their first and second derivatives with respect to the CH-stretching coordinates. Chirality, 2011. 2011 Wiley Liss, Inc. Copyright

Full text of DOI:10.1002/chir.21013

CHIRALITY 23:841–849 (2011)
Electrical and Mechanical Anharmonicities from NIR-VCD
Spectra of Compounds Exhibiting Axial and Planar Chirality:
The Cases of (S)-2,3-Pentadiene and Methyl-d (R)-
3
and (S)-[2.2]Paracyclophane-4-carboxylate
1,2
1,2
1
1,2
3
SERGIO ABBATE, * GIOVANNA LONGHI, FABRIZIO GANGEMI, ROBERTO GANGEMI, STEFANO SUPERCHI,
4
5
ANNA MARIA CAPORUSSO, AND RENZO RUZZICONI
Dipartimento di Scienze Biomediche e Biotecnologie, Universit a` di Brescia, Viale Europa 11, 25123 Brescia, Italy
CNISM, Consorzio Interuniversitario Scienze Fisiche della Materia, Via della Vasca Navale 84, 00146 Roma, Italy
1
2
3
Dipartimento di Chimica, Universit a` della Basilicata, Via dell’Ateneo Lucano, 85100 Potenza, Italy
Dipartimento di Chimica e Chimica Industriale, Universit a` di Pisa, Via Risorgimento 35, 56126 Pisa, Italy
4
5
Dipartimento di Chimica, Universit a` degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
Contribution to the Carlo Rosini Special Issue
ABSTRACT
The IR and Near infrared (NIR) vibrational circular dichroism (VCD) spectra of
molecules endowed with noncentral chirality have been investigated. Data for fundamental,
first, and second overtone regions of (S)-2,3-pentadiene, exhibiting axial chirality, and methyl-d3
(
R)- and (S)-[2.2]paracyclophane-4-carboxylate, exhibiting planar chirality have been measured
and analyzed. The analysis of NIR and IR VCD spectra was based on the local-mode model and
the use of density functional theory (DFT), providing mechanical and electrical anharmonic
terms for all CH-bonds. The comparison of experimental and calculated spectra is satisfactory
and allows one to monitor fine details in the asymmetric charge distribution in the molecules:
these details consist in the harmonic frequencies, in the principal anharmonicity constants, in
both the atomic polar and axial tensors and in their first and second derivatives with respect to
the CH-stretching coordinates. Chirality 23:841–849, 2011. VV C 2011 Wiley-Liss, Inc.
KEY WORDS: vibrational circular dichroism (VCD); density functional theory (DFT); atomic
polar tensors (APT); atomic axial tensors (AAT)
INTRODUCTION
not only of the C ꢀꢀ H bond in camphorquinone with respect
4
to that same bond in camphor but also to highlight the quite
Near infrared (NIR) vibrational circular dichroism (VCD)
spectroscopy has been known for many years, since Keiderl-
ing and Stephens in 1976 demonstrated the feasibility of
different behavior of C ꢀꢀ H with respect to the other C ꢀꢀ H
4
3
,8
bonds in camphorquinone itself. Herein, we wish to pursue
a similar investigation on the harmonic and anharmonic fea-
tures of C ꢀꢀ H bonds not only in natural product field but
also in ad hoc synthesized compounds endowed with non-
central chirality like (S)-2,3-pentadiene, sometimes referred
to as (S)-(1,3)-dimethylallene, (S)-1 displaying axial chirality
and enantiomeric methyl-d3 (R)- and (S)-[2.2]paracy-
clophane-4-carboxylate, (R)-2 and (S)-2 exhibiting planar
chirality (see Scheme 1).
1
NIR-VCD experiments for the first overtone of camphor CH-
stretchings. Since then, a systematic investigation of terpene-
molecules was carried out in the NIR region, focusing the
attention mainly on the second and third overtones of the
2
CH-stretchings. Although the paucity of experimental data,
as well as their uncertain interpretation, prevented the use of
this valuable tool for several years; recently, the use of more
3
–6
sophisticated instruments,
conjointly with the develop-
Compound 2 was already investigated in our previous
ment of ab initio calculations of mechanical and electrical
anharmonic terms based on the density functional theory
DFT), gave a new impulse for more profitable investigation
1
1
work, where we showed that electrical anharmonicity is
essential to obtain the correct sign of NIR-VCD bands,
although anharmonic contributions from atomic axial tensors
(
in this field. This allowed us to reproduce NIR-VCD spectra,
thus gaining specific information unattainable by the more
(AAT) were disregarded there. New data in the NIR and bet-
7
–9
ter protocols for DFT calculations are now available. On the
widely used IR-VCD technique. In general, an approximate
but acceptable interpretation of NIR absorption spectra is
obtained by assuming the local-mode behavior for X ꢀꢀ H
stretchings, whose overtone and combination modes contrib-
Additional Supporting Information may be found in the online version of this
article.
Contract grant sponsor: Italian ‘‘Ministero dell’Istruzione, dell’Universit a` e
della Ricerca’’ (MIUR) (PRIN 2008LYSESR) (which was originally coordi-
nated by Professor Carlo Rosini).
1
0
ute in a preponderant way to the NIR spectra. By assuming
the local-mode model applicable to NIR-VCD, we were able
to acquire important information on the isolated X ꢀꢀ H
stretching vibrations, by combining NIR-VCD data and ab ini-
tio calculations performed with standard computer programs
*
Correspondence to: Sergio Abbate, Dipartimento di Scienze Biomediche
e Biotecnologie, Universit a` di Brescia, Viale Europa 11, 25123 Brescia, Italy.
E-mail: abbate@med.unibs.it
Received for publication 28 February 2011; Accepted 20 July 2011
DOI: 10.1002/chir.21013
Published online 7 September 2011 in Wiley Online Library
(wileyonlinelibrary.com).
7
,8
supplemented with our routines. For instance, we were
able to evidence the quite different spectroscopic behavior
VV C 2011 Wiley-Liss, Inc.

8
42
ABBATE ET AL.
21
using an InSb detector for measurements in the 3300–2700 cm fun-
damental CH-stretching region (1 mm quartz cell), while a HgCdTe
2
1
detector was used in scanning the 1600–900 cm
mid-IR region
(
500 lm BaF cell). Both VCD and IR spectra of the solvent were
2
subtracted. In all cases, the data are an average of 4000 scans, at
least.
3
Methyl-d (R)- [(R)-2] and (S)-[2.2]paracyclophane-4-carboxylate
[
(S)-2]. IR-VCD and IR absorption spectra were taken out of the previ-
Scheme 1.
11
ous work.
NIR and NIR-VCD Spectra
contrary, VCD data of the allene (S)-1 were never reported,
neither in the mid-IR nor in the NIR region; we remind
though that important VCD studies of other substituted
allenes in the mid-IR and in the C ꢀꢀ H-stretching region were
All NIR spectra, both in absorption (VA) and VCD, were taken with
dispersive instruments, which are linear in wavelengths. For a direct
comparison of the Dv 5 1 data with those of the current literature and to
make the discussion easier, the frequency values are reported in wave-
numbers.
1
2–15
first conducted by Narayanan and coworkers.
Both mol-
ecules present different types of C ꢀꢀ H bonds, whose spectro-
scopic behavior can be easily guessed by a skilled chemist.
Nevertheless, we wish to highlight finer details for them,
beyond the obvious differences in aliphatic and aromatic
C ꢀꢀ H bonds. In particular, we will take care in stressing the
peculiarity of the NIR-VCD spectra in connection with the
molecular chirality.
(
S)-2,3-Pentadiene [(S)-1]. NIR absorption spectra of neat samples
of (S)-1 were registered with a UV–vis-NIR CARY 05E instrument
using quartz cuvettes of 0.1–1.0 cm pathlengths. They are reported in
Figure 1 together with the spectra in the fundamental CH-stretching
region. The e values were obtained by referring to a density of 0.7 g
cm
23 17,18
.
Two bands of almost equal intensity are observed at high
overtones (Dv 5 3 and Dv 5 4), the narrower band at lower energy
and the broader one at higher energy. Their harmonic frequencies at
2
1
21
DESCRIPTION OF EXPERIMENTS AND CALCULATIONS
Sample Preparation
x
v
01 5 3063 cm
and x02 5 3118 cm
and their anharmonicities,
2
1
1 2
21
5 67 cm and v 5 68 cm , respectively, were derived from the
1
0
Birge-Sponer plot.
NIR-VCD spectra were obtained with
described earlier, with a special procedure for getting rid of base-
line artefacts. Neat samples were used for the Dv 5 3 region in a
-mm pathlength cell; CCl
ments in the Dv 5 2 region. To avoid evaporation of low boiling (S)-
during NIR absorption and VCD measurements, which take about
0 min, the liquid sample of (S)-1 was transferred at low temperature
from the bottle into the cuvettes, and the latter were tightly sealed.
1
13
H and C NMR spectra were recorded at room temperature on Var-
ian Gemini 200 and Bruker 400 instruments in CDCl solution using
SiMe as internal standard. Optical rotations were measured with a Per-
a home-made apparatus
3
3
4
19
kinElmer 142 automatic polarimeter using standard cuvettes (l 5 1 dm).
gas-liquid chromatography (GLC) analyses were performed on a Perki-
nElmer Mod. 5800 instrument equipped with a flame ionization detector
and a fused silica capillary column (BP1 bonded, 0.22 mm 3 12 m).
1
4
solution was used for VCD measure-
1
1
(
a]
S)-2,3-Pentadiene [(S)-1]. A sample of (R)-(1)-1-butyn-3-ol (3),
25
[
D
1 42.8 (c 5 3.2, dioxane) was obtained by resolution of the corre-
Methyl-d
3
(R)- [(R)-2] and (S)-[2.2]paracyclophane-4-carboxylate
(S)-2]. Both the NIR absorption data and the NIR-VCD data for (S)-2
and (R)-2 were taken on our home-made apparatus for measuring NIR
VCD spectra. To make easier the comparison between the two
molecules, the former spectra from the Supporting Information
of Ref. 11 are reported in Figure 2. We observe that, as for compound
S)-1, two features stand out for Dv 5 3 and Dv 5 4; their intensity and
shape is more similar than those observed for compound (S)-1, and this
makes the local mode hypothesis more tenable, providing x01 5 3045
16
sponding racemic hydrogen phthalate with (R)-1-phenylethylamine ; its
optical purity (ee 5 82%) was determined by GLC and H NMR of the
[
1
corresponding (S)-2-methoxy-2-(trifluoromethyl)phenyl acetate [(S)-
MPTA Mosher’s ester].
A slight excess of methanesulfonyl chloride (22.1 g, 0.19 mol) was
added to a well-stirred solution of 3 (9.9 g, 0.14 mol) and triethylamine
(
(
21.4 g, 0.21 mol) in dry dichloromethane (485 mL) at –508C, the cold
bath was removed, and the temperature was allowed to rise to 258C. Af-
ter further 30 min stirring, water (100 mL) was added, and the mixture
was extracted with dichloromethane (3 3 50 mL). The combined
21
21
21
21
1 2
cm and v 5 60.6 cm and x02 5 3173 cm and v 5 65.4 cm for
aliphatic and aromatic CH bonds, respectively, according to the Birge-
Sponer law. The procedure and conditions for registering NIR-VCD data
are described in Ref. 11, except for Dv 5 2, for which we use a new
extended InGaAs detector.
extracts were washed with water (2 3 50 mL), dried over Na
the solvent was evaporated at reduced pressure (20 Torr) affording (R)-
-butyn-3-ol methanesulfonate (4). The crude methanesulfonyl ester 4
20.0 g, 0.13 mol, 96%) was then added in 5 min, at –708C under dry
2 4
SO , and
1
(
nitrogen atmosphere, to a tetrahydrofurane (THF) solution of methylbro-
mocuprate [(MeCuBr)MgBr.LiBr, 0.270 mol], in turn prepared by add-
DFT Calculations
All calculations were run with the Gaussian03 or the Gaussian09
ing CH
mol) in THF at –508C while stirring. After 30 min, a saturated aqueous
NH Cl solution (50 mL) was added, and the organic materials were
extracted with THF (3 3 50 mL). The collected organic phases were
washed with additional aqueous NH Cl (2 3 50 mL) and dried with
Na SO . Pure (S)-1 (4.6 g, 50% yield) was recovered by reiterated distil-
lations with a Fischer SPALTROHOR column: b.p. 458C, d
3 2
MgBr (1 equiv.) to a freshly prepared solution of LiCuBr (0.270
2
0
set of programs. The employed functionals/basis sets were: B3LYP
and 6-31111G** for (S)-1 and B3LYP and TZVP for (R)-2. Quite
similar results were obtained with other functionals/basis sets. The
calculated IR-VCD, Dv 5 1 spectra of (S)-1, never reported before,
allowed us to reproduce spectra to compare with experimental ones.
The harmonic frequencies and dipole and rotational strengths were
obtained with Gaussian (spectra were reconstructed assigning a Lor-
4
4
2
4
25
4
0.6900,
CH¼), 1.63 (dd,
CH¼), C NMR (50 MHz) d 206, 84.7, 14.1.
25
1
[
a]
D
1 68.5, H NMR (200 MHz) d 5.00 (m, 2 H, CH
3
2
1
13
entzian bandshape of assumed bandwidth (Dm 5 16 cm
for the
J 5 4.5 and 5.6 Hz, 6 H, CH
3
2
1
CH-stretching region and Dm 5 8 cm for the mid-IR) to each vibra-
tional transition). For (R)-2 such data had been already presented in
Ref. 11.
Methyl-d
3
(R)- [(R)-2] and (S)-[2.2]paracyclophane-4-carboxylate
11
[
(S)-2]. These compounds were prepared as previously described.
The method for calculating NIR and NIR-VCD spectra was illus-
IR and VCD Spectra in the Fundamental Region
7–9
trated earlier
and, in practical terms, consists in home-made com-
(
S)-2,3-Pentadiene [(S)-1]. The spectra of the allene 1 (0.1 M in
puter programs that make use of outputs from Gaussian. The proce-
dure is divided in two parts: one concerns the calculation of me-
CCl solution) were registered on a Jasco FVS4000 FTIR instrument
4
Chirality DOI 10.1002/chir

NIR-VCD OF CHIRAL ALLENES AND PARACYCLOPHANES
843
3
2
21
Fig. 1. Experimental CH-stretching fundamental (Dv 5 1) and overtone (Dv 5 2, 3, 4) absorption spectra of (S)-2,3-pentadiene ((S)-1) (e in 10 cm mol ).
chanical harmonic frequencies x
0
and anharmonicities v (local-mode
as well as their dipole strengths and rotational strengths using Morse
transition integrals and calculated APT and AAT characteristics. Finally,
as in the IR case, we assume Lorentzian bandshapes, to facilitate com-
parison of experimental and calculated data, with empirical values for Dx
for each CH-stretching region.
mechanical terms); the other concerns the calculation of atomic po-
lar tensors (APT), atomic axial tensors (AAT) and their first and
second derivatives with respect to C ꢀꢀ H stretchings (local mode
7
,8
electrical anharmonicities). The calculation of mechanical terms is
based on a numerical approach proposed by Henry and Kjaer-
2
1
gaard, while that of the electrical anharmonicities goes by an idea
2
2
23
of Bak et al., that, in turn, bases itself on the theory of Stephens
2
4
and of Buckingham et al. This approach allows one to calculate,
without approximations except the local-mode assumption, the fre-
quencies for the overtone transitions of all CH-stretchings by the
Birge-Sponer law:
RESULTS AND DISCUSSION
(S)-2,3-Pentadiene
A sample of allene (S)-1 was obtained as described above
according to the general procedure developed by Elsevier
and Vermeer for the synthesis of optically active allenes
2
xv ¼ ðx0 ꢀ vÞv ꢀ vv
ð1Þ
25
(Scheme 2).
3
Fig. 2. Experimental CH-stretching fundamental (Dv 5 1) and overtone (Dv 5 2, 3, 4) absorption spectra of methyl-d (S)-[2.2]paracyclophane-4-carboxylate
3 2 21
(
(S)-2). The poor signal-to-noise ratio at Dv 5 4 is due to the little quantity of sample used in taking the spectrum. (e in 10 cm mol ).
Chirality DOI 10.1002/chir

8
44
ABBATE ET AL.
Scheme 2.
Thus, enantiomerically enriched (R)-1-butyn-3-ol (3),
obtained with 82% ee by resolution of its hydrogen phthalate
conformation and exhibits fairly well defined features. Mod-
est broadening is possibly brought in by methyl hindered tor-
sion. The results in this region allow confirmation of the
absolute configuration (S) of the dimethylallene 1. By con-
trast, the results of the C ꢀꢀ H stretching fundamental region
(Figure 3-right) show off the effects of disregarding the
anharmonicity (including Fermi resonance, as in Ref. 11).
However, the succession of the calculated VCD features is
reminiscent of the observed VCD spectrum. Analogies with
previous VCD works in both mid-IR and C ꢀꢀ H stretching
region for other substituted allenes can be found by compar-
ing the present results with those of Refs. 12–15.
1
6
with (R)-1-phenylethylamine, was quantitatively converted
into the methanesulfonate 4 by reaction, at –508C in
dichloromethane, with methanesulfonyl chloride and triethyl-
amine. The crude compound 4 reacts nicely with the com-
plex organocopper reagent (MeCuBr)MgBr.LiBr, prepared
in THF from MeMgBr and LiCuBr , affording the dimethylal-
2
lene (S)-1 with good yield through a stereoselective 1,3-anti-
substitution. As it was checked that substrates and products
retain their stereochemical integrity under reaction condi-
2
5
tions, compound (S)-1 should be recovered with a high op-
2
5
tical yield. In fact, we can attribute to (S)-1, having [a]D
8.5 (Scheme 2), an enantiomeric excess of about 79% taking
into account the molar rotation /D which can be calculated
1
The DFT calculated values of x and v for inequivalent
0
6
C ꢀꢀ H bonds and, for sake of comparison, the corresponding
‘‘experimental’’ values derived from the Birge-Sponer plots
are reported in Table 1. While the v values are quite similar,
1
8,26
for this compound by the semiempirical Runge’s rule.
The comparison between calculated and experimental IR
and mid-IR absorption and VCD spectra is given in Figure 3:
x values change remarkably from bond to bond, the highest
0
x values being assigned to the olefinic C ꢀꢀ H and to the
0
3
-right referring to the C ꢀꢀ H stretching fundamental region
methyl C ꢀꢀ H bonds lying in the C ¼¼ C ꢀꢀ C plane. This could
2
1
(
3200–2800 cm ) and 3-left to fundamentals of bending and
mean that a residual double bond character is exhibited
21
C ꢀꢀ C stretchings (1600–920 cm ). Keeping in mind that the
DFT calculations are run in this case at the harmonic level,
the results may be considered satisfactory, particularly in
the mid-IR (Figure 3-left). The molecule exists in just one
through that plane C –Csp2–Csp3, while the other two methyl
sp
C ꢀꢀ H bonds exhibit a more aliphatic character. We conclude
that hyperconjugation keeps all x values of C ꢀꢀ H bonds
0
close to each other and the drastic differentiation between
Fig. 3. Comparison of calculated (black) and experimental (grey) absorption and VCD spectra of (S)-2,3-pentadiene ((S)-1) for the mid-IR deformation/bend-
ing region (first column) and for the fundamental CH-stretching region (second column). Calculations are run in the harmonic approximation (i.e. are not shifted
20
to account for anharmonicity), with Gaussian and a 6-31111g(d,p) basis/B3LYP functional.
Chirality DOI 10.1002/chir

NIR-VCD OF CHIRAL ALLENES AND PARACYCLOPHANES
845
2
1
TABLE 1. (S)-2,3-Pentadiene ((S)-1): calculated harmonic frequencies (x
0
) and anharmonicities (v) (cm ) by the method illus-
trated in Ref. 9 for inequivalent CH bonds (see Scheme 1)
2
2
3
3
@2mx=@z@pz
3
2
@
lz=@z
@ l =@z
@ l =@z
@mx=@pz
@ mx=@z @pz
z
z
Experimental
(APT)
(APT’)
(APT’’)
(AAT)
(AAT’)
(AAT’’)
Bond
x
0
v
x
0
v
z-Components
C
C
C
C
1
Hop
1
Hop’
1
Hip
2
H
3049
3044
3103
3099
60.0
59.8
59.8
60.7
3063
3118
67
20.1636
20.1712
20.1114
20.1073
20.6386
20.6674
20.3872
20.6547
20.3724
20.3946
0.0385
0.2381
0.2045
0.2150
0.0999
0.5837
0.4570
0.6183
0.3504
0.0623
20.0249
20.1100
0.4750
68
20.7624
Corresponding experimental values derived on the basis of IR and NIR absorption spectra (see text). The zz components of APT (e) and xz of AAT (ea
their derivatives calculated at equilibrium (see Supporting Information Figure SI-1). Calculation method: B3LYP/6-31111g(d,p) (e is the electronic charge, a
the Bohr’s radius, ꢀh is the reduced Planck’s constant, c is the speed of light).
0
/ ꢀh c) and
is
0
olefinic and aliphatic CHs is not substantial. We now wish to
known that at Dv 5 1, the local-mode approach is in general
compare these values for x and v with the experimental val-
worse than the normal-mode one, and only the frequency
range is much better estimated, as anharmonicity is taken in
some consideration. From these results, it may be inferred
that the VCD spectrum in the C ꢀꢀ H stretching region con-
tains the contributions of two couplets that are resolved in
the experiments but not in the calculations of Figure 4. The
two VCD couplets are in correspondence with the two calcu-
lated absorption bands. The first couplet at higher frequen-
cies, coming from in-plane C ꢀꢀ H bond stretchings, provides
for a broad absorption and a VCD (2,1) doublet (starting
from high-frequency values). The second couplet coming
from the out-of-plane C ꢀꢀ H bond stretchings, shows a broad
and structured absorption and a quite weak (1,2)VCD cou-
plet. Even calculations in the normal-mode scheme do not
reproduce faithfully the observed features (Figure 3), and
this fact strongly suggests the possible existence of Fermi
resonances, especially in the absorption case. The Dv 5 2
region is a transitional region from normal-mode to local-
0
ues of x and v: by the latter, we mean the values obtained
0
by using in the Birge-Sponer eq. 1 the experimental values
1
0,27
for x for v 5 1, 2, 3, 4, and so on.
A least squares statisti-
v
cal fit is used to derive the values for the two parameters x0
and v from experimental frequencies. In this case, we used
the values x , which we read in Figure 1. We find that the
v
experimental values for x and v are larger than the calcu-
0
lated ones. This outcome could be attributed to some plausi-
ble deviation from the local-mode behavior; in particular, we
think that the broader, high-wavenumber features might
include combination modes that do not suit the present
model, as they appear at frequencies higher than pure over-
tones; anyway, a basis set and/or a solvent effect may also
play some role.
The dependence of APT and AAT (i,z) components (i 5
x,y,z) of all inequivalent hydrogen atoms on the C ꢀꢀ H
7
–9
stretching lengths, as calculated by our method, is shown
in Figure SI-1 of the Supporting Information file. The first
and second derivatives with respect to (z) C ꢀꢀ H stretching of
the APT z-component and the AAT x-component (which are
the largest ones) at equilibrium are reported in Table 1 (local
axes are chosen as follows: the z-axis is along the C ꢀꢀ H
bond under examination, the y-axis is in the H-C-C plane and
2
8
mode regime, and, thus, it is notoriously difficult to repro-
duce both in the normal-mode and in the local-mode
schemes. In facts, contrary to the calculations, which predict
just two absorption bands and a large negative VCD feature,
the absorption spectrum is rich in combination bands, the
NIR-VCD spectrum is positive and weak. On the contrary, at
Dv 5 3, where the local-mode behavior is generally fully op-
7
,9
x perpendicular to it ). The APT values at equilibrium are
8
10
similar to those we calculated previously for camphor, while
erative, we have a very good correspondence between
their first derivatives are slightly higher in absolute value,
except for the olefinic C ꢀꢀ H bond, which shows a quite small
APT first derivative. Large values of AAT in the x-direction at
equilibrium as well as those of their derivatives, entail large
circulations of charge (due to the CH-stretching) in the
C ¼¼ C ꢀꢀ C plane. While the NIR absorption spectra are deter-
mined by the z-component of APTs, the x-component of AAT
experiments and calculations. We are unable to reproduce
the broadness of the lower wavelength band, and this is still
due to the local-mode approximation. Nevertheless, inten-
sities are in the right range and, most importantly, we attain
the interpretation of the VCD data, and we can certainly state
that the most intense, negative feature is due to the olefinic
CHs. These bonds, very close to the origin of axial chirality,
(
together with the x-component of APT) largely determines
behave similarly to the C ꢀꢀ H in camphorquinone, which
4
the NIR-VCD spectra. From these and from the analogous
has been shown to be responsible for the high overtone
vibrational optical activity of this molecule and is close to two
C ¼¼ O double bonds (cfr. also the APT and AAT values).
7
,8
parameters for the corresponding bonded carbon atom, we
deduced the calculated VCD and absorption spectra ab initio
for Dv 5 1, 2, and 3 (Figure 4). In the latter figure, a compar-
ison with the corresponding experimental data is provided. It
should be remembered that, here, the Dv 5 1 is also calcu-
lated in the local-mode approximation, while the results at Dv
Methyl-d
3
(R)- [(R)-2] and (S)-[2.2]Paracyclophane-4-
carboxylate [(S)-2]
The comparisons of IR and mid-IR absorption and VCD
spectra were presented in Ref. 11 and were quite good as for
1. For (R)-2 two conformations were predicted by B3LYP/
5
1 for the normal mode case are reported in Figure 3. Let
us comment results from each spectroscopic region: it is
Chirality DOI 10.1002/chir

8
46
ABBATE ET AL.
Fig. 4. (S)-2,3-pentadiene: Comparison of calculated and experimental IR and NIR absorption (top) and VCD spectra. Left: Dv 5 1, CH-stretching fundamental
21
region (assumed bandwidth in the calculations (HWHM) Dx 5 8 cm ). Center: Dv 5 2, CH-stretching first overtone region (assumed bandwidth in the calcula-
21
21
tions, HWHM, Dx 5 20 cm ). Right: Dv 5 3, CH-stretching second overtone region (HWHM, Dx 5 40 cm ).
TZVP set with a 84:16 population ratio. The most populated
in large extent also the electric characteristics of the molecule,
conformer exhibits the C ¼¼ O bond facing the ethylenic
as we will comment immediately below.
bridge and the OCD in the opposite side; vice versa holds
In Figure SI-2 of the Supporting Information file, we have
plotted the calculated dependence of APT and AAT (i,z) com-
ponents (i 5 x, y, z) of the hydrogen atoms on the C ꢀꢀ H
stretching lengths (local bond axes chosen as for (S)-1). The
first and second derivatives of these curves at equilibrium
for APT-zz, together with the derivatives of largest AAT com-
ponents (y) with respect to z are reported in Table 2, in cor-
3
for the less populated conformer. The results for the mid-IR
and CH-stretching region are not reported here, and the
interested reader should consult Ref. 11. As anharmonic cal-
culations for the NIR region are pretty time-consuming, only
the most populated conformer was considered.
In Table 2, we report, together with other data, the calcu-
lated values of x and v for C ꢀꢀ H bonds and compare them
respondence with the calculated values of x and v. Let us
0
0
with the corresponding ‘‘experimental’’ values, derived, as
explained above, from eq. 1 and the spectra of Figure 2. The
consider the values and first derivatives of the z component
of hydrogens’ APT with respect to the CH-bond lengths l:
2
2
calculated values for v and x are different for aromatic and al-
they coincide with (ql/ql) and (q l/ql ) previously calcu-
lated by the more primitive approach of Ref. 11, and with the
same quantities derived by experimental NIR absorption data
0
1
1
iphatic CHs and similar to those obtained for ethyl benzene
2
9
and toluene by experimental NIR absorption spectroscopy.
They are also similar to the values derived by the Birge-
Sponer plot (Table 2). However, while the values for v are
2
9
in Ref. 29. As in the earlier literature, we find that the val-
ues (ql/ql) 5 APT (H) of both aromatic and aliphatic CHs
zz
very similar, a variety of x values are noticed, both in the aro-
are negative, and those of aromatic CHs are smaller in abso-
lute value, reaching a minimum of about 20.02 e for H(5),
while the aliphatic APT range from 20.1 e to about 20.15 e,
with the exception of H(1) and H(2), which are close to
20.08 e. Noteworthy, H(5), H(1), and H(2) are all close to
0
matic and in the aliphatic moiety. We find larger x (of the
0
21
order of ꢁ3170 cm ) for aromatic C ꢀꢀ H bonds in the ring
containing the substituent COOCD , especially for the C ꢀꢀ H
3
21
at position 5 (3205 cm ). In the aliphatic region, we also find
larger x0 for the CH CH group closer to the substituent.
the stereogenic substituent group COOCD . A similar trend
2
2
3
21
2
2
Among them, two bonds have x ꢂ 3100 cm , while for the
is observed for (q l/ql ) 5 (qAPT (H)/ql). Differently from
0
zz
21
other aliphatic CHs, x ꢃ 3080 cm . The COOCD group,
compound (S)-1, both the x and y components of AAT are
large and important.
0
3
that induces the chirality in the system, seems to determine
Chirality DOI 10.1002/chir

NIR-VCD OF CHIRAL ALLENES AND PARACYCLOPHANES
847
TABLE 2. Methyl-d
3
(R)-[2.2]paracyclophane-4-carboxylate ((R)-2): calculated harmonic frequencies (x
0
) and anharmonicities (v)
2
1
(
cm ) by the method illustrated in Ref. 9 for all CH bonds (see Scheme 1)
2
3
@2my
@z@pz
@3my
@
@
lz
z
@ lz
@ lz
@my
@pz
(APT)
2
(APT’)
3
(APT’’)
(AAT)
(AAT’)
2
(AAT’’)
@z
@z
@z @pz
Bond
x
0
v
z-Components
Aliph
1
1
3106
3065
3123
3072
3205
3171
3174
3070
3079
3065
3076
3166
3164
3174
3165
61
62
60
62
57
59
59
61
62
62
61
59
59
58
59
20.0935
20.1825
20.0768
20.1620
20.0250
20.0919
20.0909
20.1711
20.1341
20.1639
20.1509
20.0999
20.0985
20.0808
20.0966
20.3959
20.6561
20.4204
20.5437
20.3274
20.5136
20.4803
20.6311
20.4871
20.6082
20.5363
20.4975
20.4918
20.4237
20.4707
20.2540
20.1884
0.1363
20.1046
0.2455
20.0842
20.1233
20.1203
20.1886
0.3023
20.2870
0.2208
20.1704
0.1699
0.1407
0.1777
20.6153
0.2486
20.5250
0.6493
20.3500
20.4374
20.4280
20.5074
0.9340
20.8582
0.6500
20.6040
0.6237
0.6348
0.6671
20.1889
0
20.4566
20.3828
20.3390
20.4297
20.4304
20.4497
20.4887
20.3344
20.4765
20.3635
20.4852
20.4542
20.3679
20.4310
0.0050
20.3223
0.1020
20.0980
20.0756
20.1530
20.0716
0.3564
20.2985
0.1349
20.3030
0.2811
2
0
2
Arom
Aliph
5
7
8
9
0
9
1
1
0
0
0
Arom
12
1
1
1
3
5
6
0.4112
0.3523
Experimental
Aromatic
Aliphatic
3173
3045
65
61
Corresponding experimental values derived on the basis of IR and NIR absorption spectra (see text). The zz components of APT (e) and yz of AAT (ea
0
/ ꢀh c) and
their derivatives calculated at equilibrium (see Supporting Information Figure SI-2). Calculation method: B3LYP/TZVP (e is the electronic charge, a
0
is the Bohr’s
radius, ꢀh is the reduced Planck’s constant, c is the speed of light).
Figure 5 shows the absorption and VCD spectra calculated
on the basis of the quantities just commented for Dv 5 1, 2,
and 3. By comparing them with the corresponding experi-
mental data (the Dv 5 1 calculated results in Figure 5 are in
the local mode approximation, while the full normal mode
calculations by Gaussian plus discussion on the possible role
of Fermi Resonance is given in Ref. 10), we may conclude
that in this case, the results are slightly better than for (S)-1.
In particular, they allow understanding why the aromatic
region presents very low intensity in absorption and is nearly
absent in VCD spectra of the fundamental (Dv 5 1 region),
while it is as intense as, or even more intense than, the ali-
phatic region for Dv ꢂ 2. This has been known since long in
lated bands (1,2,2) is in correspondence with the observed
features for (R)-2. At Dv 5 3, where the local-mode behavior
1
0
is fully operative, the two main absorption bands, with
approximately equal intensities, are attributed to aromatic
and aliphatic CHs in a ratio equal to the number of aromatic
and aliphatic C ꢀꢀ H bonds (7:8). Additionally, minor features
are predicted between the two major bands, as observed:
this is originated by the unequal distribution of CH-stretch-
ing frequencies. Finally, the experimental Dv 5 3 NIR-VCD
spectrum consisting of two doublets of (oppositely) alternat-
ing signs is interpreted as due to the local modes. Starting
from high frequencies, the contributions of aromatic CHs for
the bonds close to the COOCD substituent (positive intense
3
2
9
absorption spectroscopy and it was clarified in 2007 for
VCD for (R)-2) come first, followed by those of the other aro-
matic CHs (negative intense VCD). The less intense doublet
at lower wavenumbers is due to aliphatic CHs, the largest
frequency component among the latter being due to aliphatic
CHs close to carboxylate group. The present calculations do
not account for the last component of the observed couplet.
1
1
VCD as being due to the nonlinear dependence of electric
and magnetic dipole moment on C ꢀꢀ H stretching coordi-
nates. Coming to the details of the various Dv regions, we
may say the following: at Dv 5 1 the local-mode approach is
worse than obtained directly by the Gaussian harmonic cal-
culations, except that the frequency range is better esti-
mated, since some mechanical anharmonicity is taken into
21
SUMMARY AND CONCLUSIONS
account (below 2900 cm
another anharmonic phenom-
enon, i.e., Fermi resonance, is present, but it is not consid-
In this work, we have reported on the CH-stretching funda-
mental and first two overtone vibrational absorption (VA)
and VCD spectra of (S)-2,3-pentadiene [alias (S)-(1,3)-dime-
thylallene] (1) and of methyl-d3 (R)- and (S)-[2.2]paracy-
clophane-4-carboxylate (2), spanning from the standard IR
into the NIR region. We have also reported mid-IR VA and
VCD spectra of allene 1, and we provide the harmonic and
anharmonic calculations of their spectra. The anharmonic
calculations highlight interesting features in the previously
neglected parts of the spectra, providing insight into the
behavior of APT and AAT of different CH bonds in the mole-
cule: quite different parameters are indeed calculated for
CHs next or away from the stereogenic part of the molecules
and this difference permits to rationalize the observed NIR-
1
1
ered here ). In the case of (R)-2, the Dv 5 2 region is sim-
pler than for (S)-1: the experimental absorption spectrum
consists of three features and the calculations provide two
major but quite structured bands, since a large variety of aro-
matic CH, as well as aliphatic CH overtones, the ones close
to the substituent and ‘‘bordering’’ the aromatic CHs have to
be considered. It is possible that combination modes add to
this scheme. The calculated VCD spectrum compares
reasonably with the experimental one, better than for
allene (S)-1. This proves that, in this case, the local-mode
approximation works better on a large variety of different
types of local CHs and produces the structuring of the VCD
spectra. Most important, the succession for convoluted calcu-
Chirality DOI 10.1002/chir

8
48
ABBATE ET AL.
Fig. 5. Methyl-d
3
[2.2]paracyclophane-4-carboxylate. Comparison of experimental IR and NIR absorption (top) and VCD spectra of both enantiomers (R, in
black, and S, in gray) with the corresponding calculated spectra for the (R)-enantiomer. Left: Dv 5 1, CH-stretching fundamental region (assumed bandwidth in
2
1
21
the calculations, (HWHM) Dx 5 16 cm ). Center: Dv 5 2, CH-stretching first overtone region (assumed bandwidth in the calculations, HWHM, Dx 5 20 cm ).
21
Right: Dv 5 3, CH-stretching second overtone region (HWHM, Dx 5 40 cm ).
VCD spectra. We think that the local-mode model works bet-
ter for 2 than for 1. In any case, at Dv 5 3, the calculations
based on this model work fine on quantitative grounds for
2. Abbate S, Longhi G, Ricard L, Bertucci C, Rosini C, Salvadori P, Mosco-
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terpenes. J Am Chem Soc 1989;111:836–840.
7
–9
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3
. Castiglioni E, Lebon F, Longhi G, Abbate S. Vibrational circular dichro-
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Enantiomer 2002;7:161–173.
Previous calculations of NIR VA and NIR VCD spectra con-
cerned molecules with a stereogenic carbon atom; in the
present case, where other types of chirality are considered,
namely the axial and planar ones, we were able to obtain
results of similar quality and could also define how parame-
4. Cao X, Shah RD, Dukor RK, Guo C, Freedman TB, Nafie LA. Extension
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21
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. Guo C, Shah RD, Dukor RK, Freedman TB, Cao X, Nafie LA. Fourier
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21
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. Ma S, Freedman TB, Dukor RK, Nafie LA. Near-infrared and mid-infra-
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ACKNOWLEDGMENTS
Professor Rosini proposed and inspired part of this work
but prematurely and unfortunately passed away last year.
The Researchers from Brescia thank CILEA (Consorzio
Interuniversitario Lombardo Elaborazione Automatica) for
access to their computational facilities.
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. Gangemi F, Gangemi R, Longhi G, Abbate S. Calculations of overtone
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