Carbocations generated under stable conditions by ionization of matrix-isolated radicals: The allyl and benzyl cations

Article abstract of DOI:10.1021/ja401890m

Carbocations are crucial intermediates in many chemical reactions; hence, considerable effort has gone into investigating their structures and properties, for example, in superacids, in salts, or in the gas phase. However, studies of the vibrational structure of carbocations are not abundant, because their infrared spectra are difficult to obtain in superacids or salts (where furthermore the cations may be perturbed by counterions), and the generation of gas-phase carbocations in discharges usually produces several species. We have applied the technique of ionizing neutral compounds by X-irradiation of cryogenic Ar matrices to radicals embedded in such matrices, thus producing closed-shell cations that can be investigated leisurely, and in the absence of counterions or other perturbing effects, by various forms of spectroscopy. This Article describes the first set of results that were obtained by this approach, the IR spectra of the allyl and the benzyl cation. We use the information obtained in this way, together with previously obtained data, to assess the changes in chemical bonding between the allyl and benzyl radicals and cations, respectively.

Full text of DOI:10.1021/ja401890m

Article
pubs.acs.org/JACS
Carbocations Generated under Stable Conditions by Ionization of
Matrix-Isolated Radicals: The Allyl and Benzyl Cations
Vladimir Misic, Krzysztof Piech,† and Thomas Bally*
̌
́
Department of Chemistry, University of Fribourg, Fribourg CH-1700, Switzerland
S
* Supporting Information
ABSTRACT: Carbocations are crucial intermediates in many chemical reactions;
hence, considerable effort has gone into investigating their structures and
properties, for example, in superacids, in salts, or in the gas phase. However,
studies of the vibrational structure of carbocations are not abundant, because their
infrared spectra are difficult to obtain in superacids or salts (where furthermore
the cations may be perturbed by counterions), and the generation of gas-phase
carbocations in discharges usually produces several species. We have applied the
technique of ionizing neutral compounds by X-irradiation of cryogenic Ar matrices to radicals embedded in such matrices, thus
producing closed-shell cations that can be investigated leisurely, and in the absence of counterions or other perturbing effects, by
various forms of spectroscopy. This Article describes the first set of results that were obtained by this approach, the IR spectra of
the allyl and the benzyl cation. We use the information obtained in this way, together with previously obtained data, to assess the
changes in chemical bonding between the allyl and benzyl radicals and cations, respectively.
generated under stable conditions, to probe them by different
forms of spectroscopy.
INTRODUCTION
■
Understanding the structure and the properties of reactive
intermediates can help to clarify the mechanisms of reactions
where these intermediates are involved. Carbonium ions1 are a
class of reactive intermediates, which are of considerable
importance in different organic reactions (electrophilic
additions and substitutions, SN1 and E1 reactions, etc.).2 A
variety of carbocations have therefore been studied by means of
NMR and UV spectroscopy in superacids,3 and occasionally
also their salts with nonnucleophilic anions by crystallography.4
However, much less is known about the vibrational structure of
carbocations because superacid solutions cannot easily be
probed by IR spectroscopy.
Carbocations can also be generated in the gas phase, either
by passing the precursors through an electric or microwave
discharge5 or by protonation.6 The vibrational structure of
cations may then be probed, for example, by multiphoton or
double resonance infrared photodissociation (IRPD) spectros-
copy, techniques that have yielded much valuable insight into
the vibrational structure of many charged species. Different
electronic states of carbocations can be observed by photo-
electron spectroscopy of the corresponding radicals.7,8 By
threshold ionization and/or detection of zero-kinetic-energy
electrons (ZEKE), even vibrational states of closed-shell cations
can be detected at high resolution.9 Finally, it should be
mentioned that high-lying Rydberg states of radicals show
properties that are very similar to those of the core cations,10
which may be exploited to learn about the vibrational structure
of carbocations.
In the 1980s, we had developed a technique for ionizing
neutral, closed-shell molecules embedded in cryogenic Ar
matrices by X-irradiation to form radical cations, which could
then be probed leisurely by “classical” UV/vis and IR
absorption spectroscopy.12,13
An extension of this technique to ionize radicals, in view of
forming closed-shell cations, is readily conceivable, but the
implementation of this idea requires a suitable source of
radicals. Often, radicals probed by matrix isolation spectroscopy
are generated by UV photolysis of suitable precursors, but the
disadvantage of this approach is that radicals are invariably
created in pairs that are trapped within the same matrix cavity
where they can (and often will) recombine, if not right after
their creation, then most probably after ionization in Ar, which
invariably results in some excess energy being imparted on the
resulting cations.
If, however, radicals are generated by pyrolysis, they will be
trapped in different sites of a matrix when the effluent of the
pyrolysis tube is condensed on a cold window. Two different
pyrolytic techniques are available: flash vacuum pyrolysis,14
where the precursors are energized by collisions with the walls
of a pyrolysis tube (and can in principle recombine or undergo
other bimolecular reactions in the gas phase), and pulsed
pyrolysis of a precursor embedded in a large excess of an inert
host gas15 (Ar in our case), where activation occurs by
collisions with hot Ar atoms and where bimolecular reactions
are very unlikely to occur. We decided to use the latter
When carbocations occur as intermediates in nature, they are
often formed by oxidation of radicals.11 It occurred to us that
this approach might also be used to make closed-shell cations in
the condensed phase in a targeted fashion and, if they can be
Received: February 28, 2013
© XXXX American Chemical Society
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technique, because it has proven particularly suitable for the
generation of radicals.16
As our targets are presently carbocations, we used iodides R−
I to form radicals R• and iodine atoms I• because the latter
serve as excellent scavengers of the electrons which are
produced in the subsequent X-irradiation of the Ar matrix,
thus leaving the holes to travel through the matrix and be
trapped by the radicals R• to selectively form cations R+, as
shown in Scheme 1 for R = allyl, which we chose to serve as a
proof of principle. We then went on to investigate the benzyl
cation about which, despite it being a textbook case of a
resonance stabilized carbocation, surprisingly little is known.
Scheme 1. Generation of the Allyl Cation
As the spectra of the radicals and their corresponding cations
are now available from the same experiment, this allows one to
probe the changes in chemical bonding upon ionizing radicals,
changes that, in the case of the allyl and the benzyl radical, were
expected to be subtle at most, because ionization occurs from a
nonbonding orbital, shown in Figure 1.
Figure 2. Experimental difference spectra (blue) for the ionization of
the allyl radical, and calculated IR spectra for the H5 or D5 radicals
(green), and for the corresponding cations (red), respectively. The
bands in the experimental spectra are labeled “r” (radical), “c” (cation),
“p” (unpyrolyzed allyl iodide precursor), “rc” (allyl iodide radical
cation), and “w” (matrix-isolated water). Dashed lines denote
correlations between calculated and observed peaks (peaks labeled
c* are assigned to combination bands, cf., Table 1).
Figure 1. The singly occupied molecular orbitals (SOMOs) of the allyl
and the benzyl radical.
away and upward pointing peaks for species that are newly
formed in the course of the irradiation. In the present case, the
IR difference spectra shown in Figure 2 illustrate the conversion
of the allyl radical and of some the leftover allyl iodide into the
allyl cation and some allyl iodide radical cation, respectively.
The identity of the bands of the allyl iodide and its radical
cation was assessed in separate experiments without pyrolysis.
All bands that we attribute to the allyl radical and its
perdeuterated isotopomer, labeled by a green “r”, correspond
exactly to those that Nandi et al. had observed under similar
experimental conditions,19 so there can be no doubt about the
identity of this species. Most of the peaks that arise on
ionization of the H5 isotopomer turn out to be in good accord
with those observed recently by IRPD spectroscopy of the allyl
cation in Ar and N2 clusters,20 and/or as vibrational
progressions in high-resolution photoelectron spectra of the
allyl radical.9 Some additional bands in the protio- and five
bands in the deuterio species can be assigned to the allyl cation
on the basis of the excellent agreement with the frequencies
and intensities obtained from a scaled valence force field (Table
1, see Materials and Methods for details of the procedure).
To use the information contained in the vibrational spectra
of the radicals and the cations to assess the changes in chemical
bonding, a valence force field has to be established. We used for
this purpose a procedure introduced by Pulay et al. in the 1980s
whereby a force field calculated by a quantum chemical method
is transformed into valence coordinates and scaled such as to
obtain optimal agreement between calculated and observed
frequencies.17 The resulting valence force constants can then be
compared, for example, between different oxidation states of a
compound, as we had done it previously with butadiene and its
radical cation.18
RESULTS
■
The Allyl Cation. To obtain the required vibrational
spectra, we thus generated the allyl radical by pulsed pyrolysis
of allyl iodide in a 1000-fold excess of Ar (see Materials and
Methods), trapped the outflow of the pyrolyzer on a 10 K CsI
plate, and exposed the resulting Ar matrix to X-irradiation. IR
spectra were measured before and after X-irradiation, and their
difference shows downward pointing peaks for species that go
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Table 1. Calculated and Experimental Frequencies (in cm−1) of the Allyl Cation
normal modes
experimental frequencies
Douberly et al.20 (N2/Ar)
b
c
a
species
numbering
symmetry
calcd frequencies (intensities)
this work
Gasser et al.9 (PES)
+
C3H5
ν11
b1
b1
a1
b2
b2
b1
a1
b1
b2
b1
b1
b2
a1
b2
b2
1016.1 (44)
1116.3 (17)
[1234] (−)
1268.2 (44)
1416.1 (107)
[1450] (−)
1522.0 (11)
[1556] (−)
1580.6 (174)
756.1 (32)
925.4 (3)
1013
1113
−/1025
1136/1130
1226/1230
1278/1278
1418/1421
1009(2)
1111(2)
ν10
d
ν18+ν12
ν17
1218
1273
1412
1276(2)
ν16
d
ν11+ν7
ν4
1432
1516
d
ν10+ν7
ν15
1535
1577
758
1581/1585
+
C3D5
ν11
ν10
927
ν17
946.3 (10)
1040.0 (5)
1065.3 (20)
1500.4 (276)
952
ν5
1042
1071
1505
ν16
ν15
a
Harmonic frequencies from a scaled valence force field based on a B3LYP/6-31G* calculation; intensities are in km/mol, rounded to integers.
b
Fundamentals are numbered consecutively from higher to lower frequencies within each irreducible representation, the order of which is a1, a2, b1,
c
d
and b2. Assuming that the C2-axis is the z axis and the x-axis is perpendicular to the molecular plane. Combination bands; calculated frequencies are
the sum of those for the constituent fundamentals.
In the spectra of both isotopomers, there are also some
decreasing bands that cannot be attributed to allyl radical or
allyl iodide (e.g., the peaks at 1575 and at 1420 cm−1 in C3D5)
and increasing bands that cannot be assigned to the allyl cation
or the radical cation of allyl iodide (e.g., the peak at 850 cm−1 in
C3H5). They may stem from secondary decomposition
products or impurities that arise on pyrolysis.
Of the nine IR-active fundamentals that group theory and
DFT calculations predict to occur in the range that we observe
in our experiments (500−2000 cm−1), we can assign six each
for the H5 and for the D5 allyl cation (the three others having
very low predicted intensities; all of the fundamentals are listed
in the Supporting Information). In contrast to Douberly et al.,20
we prefer to assign the band at 1273 cm−1 to the fundamental,
ν17, predicted at 1268 cm−1, and that at 1218 cm−1 to a
combination band, predicted (in the harmonic approximation)
at 1234 cm−1. The fundamental ν4 at 1516 cm−1 had not been
detected by Douberly et al., and we observed two new bands
(at 1432 and 1535 cm−1), which we assign to combination
bands according to our calculations (see Table 1).
The Benzyl Cation. Despite its exemplary nature,
surprisingly little is known experimentally about the parent
benzyl cation. Even its UV spectrum has been a matter of
debate until recently: while some studies advocated a single
absorption at ca. 360 nm,21,22 others reported a strong band
peaking at ca. 310 and a weak one at 460 nm.23,24 Only in 2011
has it become possible to assign the 460 nm band
unambiguously to the benzyl cation isolated in a Ne matrix,25
so this question is now settled (we have observed the same
band in our experiments described below).
Many fundamentals and combination bands of the benzyl
cation and two deuterated isotopomers were observed in the
1990s by the group of Weisshaar using first ZEKE photo-
electron26 and later threshold photoionization spectroscopy.27
However, these studies missed out on most of the fundamentals
that were predictied by calculations to occur above 1200 cm−1.
Thus, we decided to subject the benzyl cation to the same
scrutiny as the allyl cation, in the hope of complementing the
above information.
The benzyl radical was produced by pyrolysis of benzyl
iodide, and so was its D7 isotopomer. The frequencies for the
H7 radical agree very well with those reported in 1993 by Baskir
et al.,28 except that we observed four additional fundamentals
(13 in total) and a combination band.
In the D7 isotopomer of the benzyl radical, which has not
been described before, we were able to assign 14 out of 21
fundamentals that are predicted to occur in our observation
range. Details of the vibrational structure of the benzyl radical
will stand at the focus of a forthcoming separate paper.
On X-irradiation of the resulting Ar matrices, the difference
spectra shown in Figure 3 were obtained. As in the above case
of the allyl system, a group of bands emerges that can be
assigned quite unambiguously to the benzyl cation, while a few
others are attributable to the benzyl iodide radical cation (the
bands of the benzyl iodide that remains after pyrolysis also
decrease on X-irradiation).
A problem in the benzyl case is that the strongest band of the
cation coincides with the (unavoidable) sharp peaks of matrix-
isolated water molecules, which are partly complexed to the
substrate molecules and which therefore change slightly in
frequency on ionization of that substrate. We have tried to
pinpoint this strong peak of the benzyl cation by careful
inspection of the similarities and the subtle differences in
spectra from a series of experiments. This has led us to the
conclusion that the peak at 1629 cm−1 in the protio species and
that at 1586 cm−1 in the deuterated isotopomer should be
attributed to the benzyl cation.
In Table 2, the frequencies of the fundamentals of the benzyl
cation reported in 1996 by Weisshaar27 and those observed in
the present study are juxtaposed to the ones calculated by the
scaled quantum chemical force field method (see Discussion).
For the protio compound, this allows us to assign 24 of the 29
IR-active fundamentals that are predicted to occur below 2000
cm−1, 11 of which had not been observed previously. For the
D7 isotopomer, 15 fundamentals could be assigned with
confidence (of which five are new ones). It is satisfactory to
note that the three fundamentals that were observed both in
our and in the previous gas-phase study27 are within a few
C
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Table 2. Calculated and Experimental Frequencies (in cm−1)
of the Benzyl Cation
experimental
frequencies
normal modes
a
calcd frequencies
this
work
b
c
species numbering symmetry
(intensities)
ref 27
+
C7H7
ν24
ν17
ν36
ν23
ν13
ν35
ν16
ν22
ν21
ν12
ν34
ν10
ν19
ν18
ν33
ν32
ν9
b1
a2
b2
b1
a1
b2
a1
b1
b1
a1
b2
a1
b1
b1
b2
b2
a1
b2
a1
b2
b2
b2
a1
a1
b1
a2
b2
b1
a1
b2
a1
b2
b2
a1
a1
a1
b2
b2
a1
162 (6)
337 (0)
163
316
353
400
525
598
627
354 (2)
410 (1)
524 (4)
598 (2)
626 (0)
631 (46)
783 (24)
803 (3)
630
787
804
820
973
965 (1)
999 (2)
993
1025
1067
1112
1178
1187
1330
1355
1399
1448
1008
1030 (3)
1068 (25)
1112 (4)
1179 (9)
1189 (19)
1329 (6)
1360 (105)
1393 (23)
1448 (89)
1544 (1)
1565 (2)
1630 (250)
145 (5)
1115
1183
ν31
ν8
ν30
ν29
ν28
ν6
1547
1561
1624
ν5
+
C7D7
ν24
ν17
ν36
ν23
ν13
ν35
ν12
ν34
ν32
ν9
145
278
302
349
500
575
737
779
862
951
286 (0)
Figure 3. Experimental difference spectra (blue) for the ionization of
the benzyl radical, and calculated IR spectra for the H7 or D7 radicals
(green), and for the corresponding cations (red), respectively. The
bands in the experimental spectra are labeled “r” (radical), “c” (cation),
“p” (unpyrolyzed benzyl iodide precursor), “rc” (benzyl iodide radical
cation), and “w” (matrix-isolated water). Dashed lines denote
correlations between calculated and observed peaks (the peak labeled
r* is assigned to combination band, cf., Table 2 in the Supporting
Information).
302 (1)
360 (2)
498 (4)
574 (2)
728 (2)
771 (1)
859 (8)
942 (4)
ν8
1064 (30)
1252 (20)
1315 (7)
1404 (102)
1586 (288)
1057
1258
1313
1397
1590
cm−1, and that the two sets of experiment give almost perfectly
complementary information.
ν7
ν30
ν29
ν5
DISCUSSION
■
a
Let us recall that one of the goals of this study was to see
whether the chemical bonding changes upon ionization of the
allyl and benzyl radicals, notwithstanding the fact that
ionization occurs in both cases from a nonbonding π-molecular
orbital (cf., Figure 1). As we shall see, there is more to it than
this simple view reveals.
Harmonic frequencies from a scaled valence force field based on a
B3LYP/6-31G* calculation; intensities are in km/mol, rounded to
b
integers. Fundamentals are numbered consecutively from higher to
lower frequencies within each irreducible representation, the order of
c
which is a1, a2, b1, and b2. Assuming that the C2-axis is the z-axis and
the x-axis is perpendicular to the molecular plane.
One way to address the question would be to see how
vibrational frequencies shift on ionization. Yet if ionizaton does
affect the vibrational structure, then the normal modes that are
associated with the vibrational frequencies change also; that is,
they cannot be directly compared between the radicals and
their corresponding cations. As a consequence, shifts in
frequencies cannot be directly translated into chemically useful
information. What can be compared between similar structures
are the force constants for bond stretches, angular deformations,
and out-of-plane distortions.29
calculated by quantum chemical programs into force fields for
a set of valence coordinates.17 The purpose was to fit calculated
to experimental spectra by optimizing a set of factors by which
different types of valence force constants were scaled, as
opposed to the scaling of all calculated frequencies by a single
factor, as it was (and still is) customary in the field. By this
approach, a better agreement between experiment and
calculation can indeed be reached, and it has often helped to
achieve unambiguous assignments of vibrational transitions.
On the other hand, such scaling confers a measure of physical
reality to the computed valence force constants, and therefore
In the 1980s, Pulay et al. introduced a procedure to
transform the harmonic Cartesian force fields that are
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also to their comparison between different molecules. This is
especially true because methods have meanwhile become
available that reproduce experimental spectra quite well, even
without much scaling, which means that the force fields from
these methods are very likely to be physically reasonable to
begin with (as a matter of fact, Pulay’s method has largely fallen
into disuse because it is no longer needed to arrive at correct
assignments of most vibrational spectra).
We therefore decided to apply this method to the present
case; that is, we transformed the force fields for the allyl and
benzyl radicals and cations that were calculated by the B3LYP/
6-31G* method into a set of valence coordinates according to
the rules provided by Pulay et al.,17 which we separated into six
or seven groups (see Materials and Methods). Each group was
scaled separately so as to minimize the root-mean-square
deviation between all observed and calculated frequencies. The
discussion below will focus on those valence force constants
that are of most chemical interest and that undergo the largest
changes on ionization. The full force fields are given in the
Supporting Information.
The Allyl Radical/Cation. As Table 3 shows, some of the
diagonal valence force constants change quite considerably
between the allyl radical and the allyl cation, which indicates
surprisingly strong differences in chemical bonding (we shall
not attempt to interpret the small changes for the in-plane
bending and the C−CH2 torsional modes, because these may
well be within the error limits of the B3LYP method or the
scaling model).
radical than it is in the cation (1.37 vs 0.56 aJ/Å2), which makes
the force constants for the symmetric and the antisymmetric
combinations of C−C stretches differ much more in the former
case.32
Thus, one finds that the force constant for the symmetric
stretching deformation changes insignificantly on ionization,
whereas that for the antisymmetric stretching increases by 38%
(from 4.836 to 6.685 aJ/Å2). The reason for this strong change
of the latter force constant is that the antisymmetric stretch
corresponds to a deformation of b2 symmetry, which optimally
couples the 2A2 ground state of the allyl radical to its low-lying
2B1 excited state. The resulting pseudo-Jahn−Teller effect leads
to a flattening of the potential surface for this deformation (i.e.,
a lowering of the force constant) in the ground state, and a
corresponding increase in the curvature in the excited state.33
The same effect does not come to bear as clearly in the other
symmetrized valence deformations of b2 symmetry (the
antisymmetric combinations of the CH2 scissoring and rocking
deformations), because these modes are much less effective in
coupling the 12A2 and the 12B1 states. This expresses itself in
tiny off-diagonal force constants for these two pairs of
deformations.
The Benzyl Radical/Cation. Twenty-seven of the 36
valence force constants for the benzyl system involve
deformations of the C6H5 ring and of the hydrogen atoms
that are attached to it. These force constants contain little
“chemically useful” information, and they change in fact
insignificantly on ionization. The values for the remaining
force constants, which all involve the exocyclic C−CH2 group,
are listed in Table 4. All of these force constants are very well-
defined by the available spectroscopic information, including
that provided in the 1990s by the Weisshaar group.27,34
Table 3. Diagonal Valence Force Constants of the Allyl
a
Radical and Cation
•
+
valence deformation
C3H5
C3H5
change in %
C−C stretch
CH2 scissor
CH2 rock
6.204
0.446
0.508
0.536
1.065
0.296
0.175
0.270
7.244
0.485
0.536
0.536
1.126
0.235
0.323
0.292
+16.8
+4.3
Table 4. Some Diagonal Valence Force Constants of the
Benzyl Radical and Cation, Which Involve the Exocyclic C−
a
+5.6
CH2 Moiety
b
C−H bend (ip)
C−C−C bend
C−H wag (oop)
CH2 pyramid
+0.6
•
+
valence deformation
C7H7
C7H7
change in %
+5.4
b
−20.4
+97.7
+7.4
>C−CH2 stretch
>C−CH2 rock (ip)
>C−CH2 wag (oop)
>C−CH2 torsion
−CH2 scissor (ip)
−CH2 rock (ip)
−CH2 wag (oop)
5.709
0.833
0.562
0.242
0.448
0.516
0.146
7.700
0.795
0.281
0.379
0.469
0.539
0.315
+35
−4.6
−50.1
+56.6
+4.7
b
C−CH2 torsion
b
a
Stretching force constants are in aJ/Å2 (=mdyn/Å), and those for
b
angular deformations are in aJ/rad2 (=mdyn·Å/rad2). ip = in-plane,
oop = out-of-plane.
−4.6
+115.5
a
Stretching force constants are in aJ/Å2 (=mdyn/Å), and those for
The most pronounced changes occur for the pyramidalizion
of the CH2 groups where the force constant nearly doubles on
ionization. This comes as no surprise, as methyl radicals are
much easier to pyramidalize than methyl cations: the frequency
of the umbrella mode increases from 606 cm−1 in the methyl
radical30 to 1404 cm−1 in the methyl cation.31
Conversely, the force constant for the central C−H wagging
mode decreases by 20% on ionization of the allyl radical, which
cannot be an artifact, because the corresponding force constant
is defined to >50% by the observed vibrations (see the
Supporting Information). We can currently offer no “chemical”
explanation for this intriguing feature.
Another unexpected change involves the (spectroscopically
also well founded) 16.8% increase of the C−C stretching force
constant on ionization of the allyl radical. To explain that, it
turns out to be judicious to consider the off-diagonal element of
the force constant matrix, which represents the interaction of
the two C−C stretches. This element is much larger in the allyl
b
angular deformations are in aJ/rad2 (=mdyn·Å/rad2). ip = in-plane,
oop = out-of-plane.
As in the above case of the allyl radical, the force constants
for in-plane C−H deformations change less than 5% on
ionization, while that for wagging (pyramidalization) of the
CH2 group more than doubles on going to the cation (the
effect is even larger than in the allyl radical, presumably because
of the higher spin density on that CH2 group in the benzyl
radical). Interestingly, the force constant for torsion around the
C−CH2 bond also increases by nearly 60%, in line with the
increase of the rotational barrier (from 11 kcal/mol in the
benzyl radical to 45 kcal/mol in the benzyl cation, according to
G4 calculations, cf., Supporting Information). The reason for
this increase may be that it takes more energy to formally
localize a charge than an unpaired electron on the exocyclic
CH2 group.
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leaves the holes to diffuse through the matrix until they are trapped by
the easily oxidizable radicals. At the same time, allyl or benzyl iodide
molecules that survived the pyrolysis is also ionized, but the identities
of the bands of these radical cations can be established in separate
experiments.
Another marked change is that for the C−CH2 out-of-plane
wagging motion, the force constant of which decreases by
almost 50%. As in the similar case of the wagging of the central
H-atom in the allyl system, the force constant of which also
decreases markedly on ionization, we can presently offer no
convincing “chemical” rationale for this feature, but we hope
that our study will incite somone to come up with an
explanation.
Computational Methods. Cartesian force constants were
calculated by the B3LYP/6-31G* method as implemented in the
Gaussian 09 program system.37 We tried several of the more “modern”
functionals (M06, B2PLYP, and others) and larger basis sets, but
B3LYP/6-31G* invariably gave the best accord with experiment after
scaling the frequencies by a single factor. Therefore, we decided to use
the B3LYP force field as a basis for the scaled valence force field.
The above force fields were transformed into a nonredundant set of
internal coordinates using the SCALE2 program of Pulay et al.17 For
the purpose of scaling, we grouped all force constants for (a) C−C
stretches, (b) C−C−C bends, (c) C−H bends, (d) C−H out-of-plane
wags, (e) CH2 pyramidalization, and (f) C−C torsion. For the benzyl
system, we additionally separated the CH2 scissoring and rocking
mode from the ring C−H bends, and we assigned a separate scaling
factor to C−CH2 out-of-plane wag. The C−H stretching force
constants were invariably left unscaled and were not used in the
analysis.
To scale the force fields of the radicals, we used mainly the
frequencies from the present matrix isolation experiments. In the case
of the allyl radical, those vibrational frequencies reported by Nandi et
al.,19 which we did not observe, were used in addition, if they were
predicted to within less than 15 cm−1 by the valence force field.
Thereby, we discovered some assignments of weak bands that are
probably erronous, because the difference between the predictions of
the scaled force field and the reported frequencies is beyond what can
be expected. In the case of the allyl cation, it was gratifying to note that
the optimized force field reproduced the low frequencies observed in
the gas phase by Gasser et al.9 within a few wavenumbers, with the
exception of the lowest one, which is probably a very anharmonic
distortion. Details of this will be reported in a forthcoming publication.
The definition of the valence coordinates, the full force fields in
these coordinates, and an analysis of all normal modes in terms of the
potential energy distribution over the valence coordinates are given in
the Supporting Information. Note that one has to exercise care and
circumspection when one applies a scheme with multiple scaling
factors, to avoid artifacts due to underdetermination. However, ample
previous experience with this method18,38 has taught us how to avoid
such pitfalls.
CONCLUSION
■
We have presented a new method to generate closed-shell
cations in Ar matrices by ionization of the corresponding
radicals, which are in turn generated by pulsed pyrolysis of
iodides. The electrons and the holes that are formed on
subsequent X-irradiation of the resulting Ar matrices are
scavenged by the iodine atoms and the (spatially separated)
organic radicals, respectively, which makes that the targeted
cations can be studied as isolated species that are unperturbed
by counterion or solvent effects. As solid Ar is transparent from
the UV to the far IR, this approach makes it possible to probe
both the precursor radicals and the corresponding cations in
the same experiment by electronic and vibrational spectros-
copies. The method is general in that it can be applied to all
radicals/cations for which precursors with a labile bond can be
made.
We have applied this method to study the allyl and the
benzyl radicals and cations, respectively. We used the
information obtained from our IR spectra of the protio- and
the perdeuterated isotopomers of each species, and from
previous gas-phase studies, to scale a force field in the same
valence coordinates for each precursor radical and its cation.
This allowed us to examine the changes in bonding on
oxidation of the radicals. As the electron that is removed on
oxidation comes from a nonbonding orbital, one expects these
changes to be minimal. However, we found that several of the
valence force constants change by surprisingly large amounts.
We offer “chemical” rationales for most of these changes,
although some of them remain unexplained.
MATERIALS AND METHODS
■
Syntheses. The iodide precursors were made from the
corresponding alcohols (which are commercially availabe, both in
the protio and in the perdeuterated forms) by reaction with HI, using a
slightly modified form or the procedure described by Klein et al.35 In
the case of the allyl alcohol, we simply added 1.7 equiv of HI (and no
phosphoric acid) and left the mixture at room temperature, which
resulted, after meticulous purification, in a ca. 10% yield of allyl iodide.
In the case of the benzyl alcohol, we found that we had to heat the
same mixture to 130 °C in a microwave oven to get the reaction to go.
The yields of the benzyl iodides after purification were 80% or more.
Pulsed Pyrolysis Matrix Isolation. The details of our pulsed
pyrolysis apparatus will be described in a forthcoming publication.
Briefly, a mixture of the iodide with Ar was passed at ca. 200 Torr
through a pulsed valve and pyrolized in a ca. 4 cm long SiC tube (ID =
1 mm) held at ca. 800 °C in the case of allyl iodide, and 950 °C in the
case of benzyl iodide. The yields of radicals were optimized with the
help of a time-of-flight mass spectrometer as described by Zhang et
al.16 The resulting molecular beam was trapped on a CsI plate held at
10 K in a closed-cycle cryostat. IR spectra were recorded by a Bomem
DA3 interferometer at 0.5 cm−1 resolution.
ASSOCIATED CONTENT
■
S
* Supporting Information
(a) Figures and tables showing the definition of the valence
coordinates, (b) an Excel spreadsheet containing the full results
of the scaled force field calculations (all calculated and observed
frequencies, and full force constant matrix and potential energy
distribution of all normal modes in terms of the valence
coordinates), and (c) geometries and energies of all of the
species discussed in this work (pdf file, containing also the full
quotation of ref 23). This material is available free of charge via
the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
thomas.bally@unifr.ch
Present Address
Ionization. Ionization was effected by exposing the Ar matrices
containing the radicals and iodine atoms to X-rays emanating from a
tungsten target tube operated at 40 kV/40 mA. This leads to the
formation of electron−hole pairs in the Ar matrix.36 Because of its high
electron affinity, the iodine atoms trap most of the electrons, which
†Perkin-Elmer Swizerland.
Notes
The authors declare no competing financial interest.
F
dx.doi.org/10.1021/ja401890m | J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
Article
(27) Eiden, G. C.; Lu, K. T.; Badenhoop, J.; Weinhold, F.; Weisshaar,
J. C. J. Chem. Phys. 1996, 104, 8886.
(28) Baskir, G. E.; Maltsev, K. A.; Korolev, A. V.; Khabashesku, N. V.;
ACKNOWLEDGMENTS
■
This work is part of project no. 200020-121747 of the Swiss
National Science Foundation. We are very indebted to Prof. G.
B. Ellison (University of Colorado, Boulder) and his
collaborators for helpful advice in the buildup of the pulsed
pyrolysis apparatus, and to Prof. Peter Pulay (University of
Arkansas) for putting the SCALE2 program at our disposition
and advising us in its use. We are very idebted to Ms. Anne
Schuwey for the synthesis of the precursor iodides.
Nefedov, M. O. Russ. Chem. Bull. 1993, 42, 1438.
(29) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations:
The Theory of Infrared and Raman Vibrational Spectra; McGraw Hill,
Inc.: New York, 1955.
(30) Stancu, G. D.; Ropcke, J.; Davies, P. B. J. Chem. Phys. 2005, 122,
̈
014306.
(31) Cunha de Miranda, B. K.; Alcaraz, C.; Elhanine, M.; Noller, B.;
Hemberger, P.; Fischer, I.; Garcia, G. A.; Soldi-Lose, H.; Gans, B.;
́ ́
Vieira Mendes, L. A.; Boye-Peronne, S.; Douin, S.; Zabka, J.;
Botschwina, P. J. Phys. Chem. A 2010, 114, 4818.
REFERENCES
■
(32) To obtain the force constants for the symmetric and the
antisymmetric C−C stretching deformations, one simply has to add or
subtract the off-diagonal element for the coupling of the two modes to
or from the diagonal elements, respectively.
(1) Carbonium Ions; Olah, G. A., Schleier, P. v. R., Eds.; John Wiley &
Sons: New York, 1968−1972; Vols. 1−5.
(2) Anslyn, E. A.; Dougherty, D. A. Modern Physical Organic
Chemistry; University Science Books: Sausalito, CA, 2006.
(3) Olah, A. G.; Prakash Surya, K. G. Superacid Chemistry, 2nd ed.;
John Wiley & Sons: New York, 2009.
(4) Kato, T.; Reed, A. C. Angew. Chem., Int. Ed. 2004, 43, 2907.
(5) Freivogel, P.; Fulara, D.; Lessen, D.; Forney, D.; Maier, J. P.
Chem. Phys. 1994, 189, 335.
(6) Chiavarino, B.; Crestoni, E. M.; Fornarini, S. J. Phys. Org. Chem.
2004, 17, 957.
(7) Dyke, J.; Neville, J.; Morris, A. J. Electron Spectrosc. Relat. Phenom.
1979, 15, 45.
(8) Hayashibara, K.; Kruppa, G. H.; Beauchamp, J. L. J. Am. Chem.
(33) It has never been attempted to pinpoint the frequency of a b2
vibration that prominently involves the antisymmetric C−C stretch in
the richly structured weak first absorption band of the allyl radical (
Tonokura, K.; Koshi, M. J. Phys. Chem. A 2000, 104, 8456 ). However,
according to CASSCF(3,3)/TZV calculations, the frequency of that
vibration increases from 1165 cm−1 in the ground state (1177 cm−1
according to our scaled force field) to 1764 cm−1 in the first excited
state (cf., Tonokura and Koshi), which is a strong indication that the
potential surface for the antisymmetric C−C stretching is indeed much
steeper in the excited state than in the ground state.
(34) After careful scaling of the force field, two fundamentals that
were proposed by Eiden et al.27 showed significantly larger deviations
from the predicted values than any of the others, which may hint
toward a misassignment. We therefore removed these two modes (that
reported at 316 cm−1 in the protio compound, which is off by 20 cm−1,
and that reported at 349 cm−1 in the perdeuterated isotopomer) from
the scaling procedure. After that, the combined root-mean-square
deviation between all calculated and observed fundamentals of both
isotopomers dropped to 4.5 cm−1, a very satisfactory value.
(35) Klein, S. M.; Zhang, C.; Jiang, Y. L. Tetrahedron Lett. 2008, 49,
1638.
Soc. 1986, 108, 5441 and references cited therein.
(9) Gasser, M.; Schulenburg, A. M.; Dietiker, P. M.; Bach, A.; Merkt,
F.; Chen, P. J. Chem. Phys. 2009, 131, 014304. In this work, additional
low-frequency vibrations of the allyl cation were assigned. These
frequencies were also used in the scaling of our force field.
(10) Bacon, J. A.; Pratt, S. T. Chem. Phys. Lett. 1999, 311, 346.
(11) Halliwell, B.; Gutteridge, J. M. C. Free Radicals in Biology and
Medecine, 3rd ed.; Oxford University Press: Oxford, 1999.
(12) Bally, T. In Radical Ionic Systems; Lund, A., Shiotani, M., Eds.;
Kluwer: Dordrecht, 1991.
(36) Bally, T. Matrix Isolation. In Reactive Intermediate Chemistry;
Moss, R. A., Jones, M., Platz, M. S., Eds.; Wiley: New York, 2003;
Chapter 17.
(13) For a recent example, see: Muller, B.; Bally, T.; Pappas, R.;
Williams, F. J. Am. Chem. Soc. 2010, 132, 14649−14660.
(14) Hedaya, E. Acc. Chem. Res. 1969, 2, 367.
̈
(37) Frisch, M. J.; et al. Gaussian 09, revision C.01; Gaussian, Inc.:
Wallingford, CT, 2009. (The full reference is given in the Supporting
Information.)
(15) Kohn, D. W.; Chen, P. Rev. Sci. Instrum. 1992, 63, 4003 and
references cited therein.
(16) Zhang, X.; Friderichsen, A. V.; Nandi, S.; Ellison, G. B.; David,
D. E.; McKinnon, J. T.; Lindeman, T. G.; Dayton, D. C.; Nimlos, M.
R. Rev. Sci. Instrum. 2003, 74, 3077.
(38) Tang, W.; Bally, T. J. Phys. Chem. 1993, 97, 4365.
(17) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J.
Am. Chem. Soc. 1983, 105, 7037.
(18) Tang, W.; Zhang, X.; Bally, T. J. Phys. Chem. 1993, 97, 4373.
(19) Nandi, S.; Arnold, A. P.; Carpenter, K. B.; Nimlos, R. M.;
Dayton, C. D.; Ellison, B. J. Phys. Chem. A 2001, 105, 7514.
(20) Douberly, G. E.; Ricks, A. M.; Schleyer, P. v. R.; Duncan, M. A.
J. Chem. Phys. 2008, 128, 021102. There had been an earlier study of
the IR spectrum of the allyl cation in superacid matrices ( Buzek, P.;
Schleyer, v. R. P.; Vanick, H.; Mihalic, Z.; Gauss, J. Angew. Chem., Int.
Ed. Engl. 1994, 33, 448 ), but most of the assignments proposed there
cannot be reproduced by the experiments of Douberly et al. and by
ours.
(21) Dorfman, M. L.; Sujdak, J. R.; Bockrath, B. Acc. Chem. Res. 1976,
9, 352.
(22) Andrews, L.; Keelan, B. W. J. Am. Chem. Soc. 1981, 103, 99.
(23) Fujisaki, N.; Compte, P.; Gaumann, T. J. Chem. Soc., Chem.
̈
Commun. 1993, 848.
(24) McClelland, A. R.; Chan, C.; Cozens, F.; Modro, A.; S., S.
Angew. Chem., Int. Ed. Engl. 1991, 30, 1337.
(25) Nagy, A.; Fulara, J.; Garkusha, I.; Maier, P. J. Angew. Chem., Int.
Ed. 2011, 50, 3022.
(26) Eiden, G. C.; Weinhold, F.; Weisshaar, J. C. J. Chem. Phys. 1991,
95, 8665.
G
dx.doi.org/10.1021/ja401890m | J. Am. Chem. Soc. XXXX, XXX, XXX−XXX