Photolysis of (3-methyl-2H-azirin-2-yl)-phenylmethanone: Direct detection of a triplet vinylnitrene intermediate

Article abstract of DOI:10.1021/jo200877k

The photoreactivity of (3-methyl-2H-azirin-2-yl)-phenylmethanone, 1, is wavelength-dependent (Singh et al. J. Am. Chem. Soc. 1972, 94, 1199-1206). Irradiation at short wavelengths yields 2P, whereas longer wavelengths produce 3P. Laser flash photolysis of

Full text of DOI:10.1021/jo200877k

ARTICLE
pubs.acs.org/joc
Photolysis of (3-Methyl-2H-azirin-2-yl)-phenylmethanone: Direct
Detection of a Triplet Vinylnitrene Intermediate
Sridhar Rajam,† Rajesh S. Murthy,† Abhijit V. Jadhav,† Qian Li,† Christopher Keller,† Claudio Carra,§
Tamara C. S. Pace,‡ Cornelia Bohne,‡ Bruce S. Ault,† and Anna D. Gudmundsdottir*,†
†Department of Chemistry, University of Cincinnati, Ohio 45221-0172, United States
‡Department of Chemistry, University of Victoria, Victoria, BC, Canada
§Division of Space Life Science, Universities Space Research Association, Houston, Texas 77058, United States
S Supporting Information
b
ABSTRACT: The photoreactivity of (3-methyl-2H-azirin-2-yl)-
phenylmethanone, 1, is wavelength-dependent (Singh et al.
J. Am. Chem. Soc. 1972, 94, 1199À1206). Irradiation at short
wavelengths yields 2P, whereas longer wavelengths produce 3P.
Laser flash photolysis of 1 in acetonitrile using a 355 nm laser
forms its triplet ketone (T1K, broad absorption with λmax
390À410 nm, τ ∼ 90 ns), which cleaves and yields triplet
∼
vinylnitrene 3 (broad absorption with λmax ∼ 380À400 nm, τ = 2 μs). Calculations (B3LYP/6-31+G(d)) reveal that T1K of 1 is
located 67 kcal/mol above its ground state (S0) and has a long CÀN bond (1.58 Å), and the calculated transition state to form 3 is
only 1 kcal/mol higher in energy than T1K of 1. The calculations show that 3 has significant 1,3-carbon iminyl biradical character,
which explains why 3 reacts efficiently with oxygen and decays by intersystem crossing to the singlet surface. Photolysis of 1 in argon
matrixes at 14 K produced ketene imine 7, which presumably is formed from 3 intersystem crossing to 7. In comparison, photolysis
of 1 in methanol with a 266 nm laser produces mainly ylide 2 (λmax ∼ 380 nm, τ ∼ 6 μs, acetonitrile), which decays to form 2P. Ylide
2 is formed via singlet reactivity of 1, and calculations show that the first singlet excited state of the azirine chromophore (S1A) is
located 113 kcal/mol above its S0 and that the singlet excited state of the ketone (S1K) is 85 kcal/mol. Furthermore, the transition
state for cleaving the CÀC bond in 1 to form 2 is located 49 kcal/mol above the S0 of 1. Thus, we theorize that internal conversion of
S1A to a vibrationally hot S0 of 1 forms 2, whereas intersystem crossing from S1K to T1K results in 3.
’ INTRODUCTION
the literature where such intermediates have been detected and
characterized directly. Irradiation or thermal activation of simple
vinyl azides yields azirine products, presumably via singlet vinyl-
nitrene intermediates or in a concerted rearrangement from the
excited state of the vinyl azide, rather than forming triplet vinyl-
nitrenes.
There is evidence, however, that vinylnitrene intermediates
are formed by photolyzing 2H-azirine derivatives.15À21 For
example, Singh and co-workers found that photolyzing 1 with
light below 313 nm gives oxazole 2P, whereas irradiation at
334 nm yields isoxazole 3P (Scheme 1).15 Singh et al. proposed
that 2P comes from cleaving the CÀC bond in the azirine ring to
form a singlet biradical 2, whereas longer-wavelength irradiation
was assumed to break the CÀN bond in the azirine ring, yielding
triplet vinylnitrene 3.
Triplet nitrenes with electron-donating substituents, i.e., sta-
bilized nitrenes such as alkyl and phenylnitrenes, are long-lived
intermediates with lifetimes of milliseconds in solutions.1À3
These triplet nitrenes are highly stabilized because they do not
react with the solvent but rather decay by dimerization to form
azo compounds.1,2,4À6 For example, triplet phenylnitrenes have
been stabilized in hemicarcerands and rendered stable in
crystals.7,8 In contrast, electron-deficient or less stable triplet
nitrenes such as esternitrenes are more reactive and thus shorter-
lived.9,10 Calculations show that vinylnitrenes are stabilized just
like phenyl- and alkylnitrenes.11 The open shell singlet in
vinylnitrene is 15 kcal/mol less stable than the triplet form and
is thus comparable to the tripletÀsinglet gap of 18.5 kcal/mol for
phenylnitrene.12,13 Comparatively, the tripletÀsinglet gap in
alkylnitrenes has been measured to be 38 kcal/mol.14 Thus,
the vinyl group reduces the singletÀtriplet separation by ap-
proximately 20 kcal/mol as a result of the delocalization of the
one unpaired electron and the corresponding reduction of
electronÀelectron repulsions in the singlet state, which is similar
to what has been observed for phenylnitrenes.
Recent findings by Murata et al. further support that triplet
vinylnitrenes are formed by photolyzing 2H-azirine because irr-
adiating 4 at 366 nm at ambient temperature in the presence of
oxygen and acrylonitrile yields 1-naphthaldehyde and 5(Scheme2).21
These photoproducts can be attributed to trapping triplet
Although the calculation cited above supports the view that
triplet vinylnitrene intermediates exist, there are no examples in
Received: April 29, 2011
Published: July 06, 2011
r
2011 American Chemical Society
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Scheme 1. Photoreactivity of 1 in Solution
Scheme 2. Photolysis of 4
Figure 1. Phosphorescence spectrum of 1 in ethanol at 77 K.
and reacts more like a carbon centered radical rather than a
nitrene intermediate.
Scheme 3. Photolysis of 4 in Matrixes
’ RESULTS
Product Studies. Photolysis of 1 via a Pyrex filter yielded only
3P (Scheme 4), whereas irradiation via a quartz filter gave 2P
(Scheme 1). This result is in agreement with product studies
reported earlier by Singh et al.15 Furthermore, irradiation of 1 via
a Pyrex filter in an oxygen-saturated solution and the presence of
acrylonitrile also yield 3P as the only product, which demon-
strates that one cannot trap any intermediates in solution with
oxygen or acrylonitrile to yield any stable products.
Scheme 4. Photolysis of 1 in Solution
Phosphorescence. The phosphorescence spectrum of 1 was
obtained in ethanol glass at 77 K with excitation at 300 nm
(Figure 1). The (0,0) band for the phosphorescence is estimated
to be around 393 nm; thus the energy of the first excited tri-
plet ketone (T1K) of 1 is estimated to be 73 kcal/mol, which is
1À2 kcal lower than observed for acetophenone and propio-
phenone.22
Calculation. We calculated several stationary points on both
the singlet and triplet potential energy surfaces of 1 (Figure 2) to
better understand its photoreactivity and to aid in the character-
ization of the intermediates formed by irradiating 1. The calcu-
lations further allowed us to clarify which excited states are the
precursors to 2 and 3, and this assignment was used to explain
why the photochemistry of 1 is wavelength-dependent. All
calculations were performed using Gaussian03 at a B3LYP level
of theory using 6-31+G(d) as the basis set,23À25 besides the
calculated spectra in Tables 1, 2, and 3, which were calculated
using MOLCAS6.
vinylnitrene 4n with oxygen to form peroxide 4o, which is
presumably unstable and reacts further with acrylonitrile. Photo-
lysis at 366 nm without trapping agents yielded no products
because 4n must undergo intersystem crossing and re-forms 4.
Furthermore, photolyzing 4 with 366 nm light in argon matrixes
did not allow direct detection of 4n because only the formation of
ketene imine 6 was observed (Scheme 3). Murata and co-
workers hypothesized that 4n was formed in a vibrational excited
state in the matrixes and rearranged into 6.
In this paper we report the direct detection of triplet vinylni-
trene 3 via the laser flash photolysis of 1. Irradiation of 1 with a
355 nm laser resulted in the first excited triplet ketone (T1K) of 1
(λmax ∼ 390À410 nm, τ = 90 ns, CH3CN), which forms 3
(λmax ∼ 380À400 nm, τ = 2 μs, CH3CN) selectively. In contrast,
The ground state (S0) geometry of 1 has CdO and CdN
bonds with lengths of 1.23 and 1.25 Å, respectively, which are
typical for carbonyl and iminyl moieties. Contrarily, the CÀN
bond in the azirine ring is 1.56 Å and is thus somewhat longer
and weaker than a normal CÀN bond, which is generally around
1.47 Å. Presumably, the electron-withdrawing effect of the car-
bonyl group weakens the CÀN bond.
irradiation with a 266 nm laser results mainly in 2 (λmax
∼
380 nm, τ = 6 μs, CH3CN). We used density functional theory
(DFT) calculations to aid in the elucidation of the mechanism for
forming 3. The reactivity of 3 is unique and different from
stabilized nitrenes such as triplet alkyl- and phenylnitrenes
because 3 has a significant 1,3-carbon iminyl biradical character
Time-dependent density functional theory (TD-DFT/
B3LYP/6-31+G(d))26À30 calculation on the optimized S0 struc-
ture of 1 shows that its lowest energy electronic transitions are at
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Figure 2. Stationary points on the triplet and singlet surfaces of 1. The calculated energies are in kcal/mol. The energies for (a) 1, 2, 7 and TS-3 were
obtained from B3LYP/6-31+G(d) calculations, (b) T1K of 1 (67 kcal/mol), T1A of 1, TS-1, 3, TS-2 and TI of 7 were obtained from UB3LYP/6-31+G(d)
calculations, (c) S1K and S1A of 1 were obtained from TD-DFT(B3LYP/6-31+G(d)) calculations on the S0 geometry of 1 as obtained from B3LYP/6-31
+G(d) calculation. (d) T1K (73 kcal/mol) and T2K of 1 were obtained from TD-DFT(UB3LYP/6-31+G(d)) calculations on the S0 geometry of 1 as
obtained from B3LYP/6-31+G(d) calculation.
molecular orbitals indicates that the T1K of 1 is mainly dominated
by a (n,π*) configuration, whereas T2K has a (π,π*) configuration.
The energies of T1K and T2K in 1 are similar and consistent with
the values measured for acetophenone.31
We also optimized T1K of 1 using UB3LYP/6-31+G(d)
and found that the CdN and the aromatic CdC bonds are
not significantly changed in comparison to the S0 of 1. In con-
trast, the CdO bond is lengthened to 1.32 Å, which is
consistent with the dominant (n,π*) configuration of the T1K
Figure 3. Relative energy of minimal energy conformers A and B of 3.
of 1.32À34 Significantly, in the T1K of 1, the CÀN bond length is
1.58 Å. This is slightly longer than the corresponding CÀN
bond in the S0 of 1, 1.56 Å, which indicates that the CÀN bond
Scheme 5. Bond Length and Spin Density As Obtained from
B3LYP/6-31+G(d) Calculations of Triplet 3
is even weaker in the T1K of 1. The energy of the optimized T1K
of 1 is 67 kcal/mol above its S0, which is notably lower than for
the TD-DFT calculation. B3LYP optimizations, however, gen-
erally underestimate the energy of triplet ketones with a (n,π*)
configuration, whereas it estimated the energy of triplet ketones
with (π,π*) configuration more accurately.35À37
Similarly, we optimized the triplet excited state of the azirine
chromophore (T1A) in 1 and found that it is located 72 kcal/mol
above the S0 of 1. The most significant difference between the
S0 and T1A of 1 is that the CdN bond is longer in the T1A of 1
(1.48 Å) than in the S0 state (1.25 Å), which indicates that this
bond is better described as a single bond. More importantly,
however, the CÀN bond in T1A of 1 is only 1.48 Å, and thus the
CÀN bond in T1A of 1 is significantly shorter than for the S0 and
T1K states of 1, 1.56 and 1.58 Å. Therefore, the calculations show
that T1A of 1 is not a likely precursor for 3.
We found two minimal energy conformers for 3, A and B, that
are located 20 and 24 kcal/mol above the S0 of 1 (Figure 3). The
CÀN and the CdC bond lengths of 3 are comparable to the
values reported by Parasuk and Cramer for CH2dCH—N:
nitrene calculated by complete active space self consistent field
(CASSCF) theory (Scheme 5).11 We calculated the spin density
for 3, which suggests that 3 has significant 1,3-carbon iminyl
biradical character, as the N atom has a spin density of only
1.38 and the C(2) atom of 0.66. The calculated rotational
barrier between 3A and 3B is rather significant with a value of
338 nm (f = 0.0004) and 268 nm (f = 0.0149) and are due to
electronic transitions out of the lone pair on the carbonyl group
and the phenyl group into π*-orbitals. In comparison, the bands
at 252 nm (f = 0.3825) and 243 nm (f = 0.0267) are due to
electronic transitions in the azirine and the arylketone moieties.
Thus, irradiation of 1 at longer wavelengths selectively excited
only the ketone moiety in 1, whereas both the azirine and the
arylketone absorb at lower wavelengths.
We used calculations to identify the various triplet excited
states in 1 that are localized at different chromophores to identify
the precursor to 3. For example, TD-DFT (B3LYP/6-31+G(d))
calculations on the S0 geometry of 1 located the first and the
second excited state of the triplet ketone (T1K and T2K) in 1,
which were 73 and 78 kcal/mol above the S0 of 1. Analysis of the
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Figure 4. Calculated energy as a function of rotation around the C3ÀC2ÀC1ÀN bond in 3 (UB3LYP/6-31+G(d).
Scheme 6. Triplet Peroyxide Radicals 8 and 9a, and Oxygen Ylides 9b and 9c
11 kcal/mol due to the conjugation between the vinylnitrene and
carbonyl moieties (Figure 4).
We calculated the following points on the singlet potential
surface of 1 to identify the excited state that results in 2. TD-DFT
calculations show that the first excited singlet ketone (S1K) in 1 is
85 kcal/mol above S0 and has an (n,π*) configuration, whereas
the first excited singlet state of the azirine moiety (S1A) in 1 is 113
kcal/mol above S0. The energy of S1A in 1 obtained by TD-DFT
fits well with what Bornemann and Klessinger have calculated for
the energy for S1A of 2H-azirine using CASSCF calculations.41
The calculated singlet transition state for 2 forming 2P is
located 2 kcal/mol above 2, which indicates that 2 can easily
form 2P.
The calculated triplet transition state (TS-1, Figure 2) for
breaking the CÀN bond in T1K of 1 to form 3 is only 1 kcal/mol
above the optimized structure of the T1K. Intrinsic reaction
coordinate38À40 calculations correlate the T1K of 1 and 3 to this
transition state. Thus, formation of 3 is easily accessible from the
T1K of 1, due to the weak CÀN bond.
We also optimized the radical formed by trapping 3 with
oxygen and found that 8 is 9 kcal/mol more stable than 3 and an
oxygen molecule (Scheme 6). The addition of oxygen to 3
shortens the CÀN bond length to 1.26 Å and lengthens the
C1ÀC2 bond to 1.53 Å because the carbonyl and vinylnitrene
groups are no longer in conjugation. The calculated triplet
transition state for oxygen adding to 3 to form 8 is located 7
kcal/mol above 3 and an oxygen molecule. In comparison,
addition of oxygen to the imine radical yields a peroxy radical
(9a) that is 2 kcal/mol less stable than 3 and an oxygen molecule.
The triplet transition state for forming 9a is 15 kcal/mol above 3
and an oxygen molecule. Thus, the calculations show that
trapping of 3 with an oxygen to form 8 can easily be done at
ambient temperature and that the formation of 8 is strongly
favored over 9a. Optimization of 8 as a singlet results in 9b and
acetonitrile, which suggests that intersystem crossing of 8 to the
singlet surface would yield these products. Similarly, optimiza-
tion of 9a as a singlet results in 9c.
The singlet transition state for breaking the CÀC bond in 1 to
form 2 was calculated to be 49 kcal/mol above the S0 of 1, and
intrinsic reaction coordinates (IRC) calculations correlate this
transition state with the S0 of 1 and 2. Thus, upon direct
population of the S1A of 1, it can decay to a vibrationally
hot ground state of 1 and form 2. In comparison, the S1K of 1
can be expected to intersystem cross to the triplet ketone with a
similar rate constant as has been reported for acetophenone
(1011 À1).42À44
s
The absorption spectra of T1K 1, 2, and 3 were calculated by
CASPT2 theory using atomic natural orbital (ANO-S) type basis
sets contracted to single valence polarized basis sets (SVP). The
CASSCF wave function was obtained using the state averaging
technique, where all states were equally weighted. The active space
includes the ten valence p orbitals adding either unpaired electrons
or the lone pair of the nitrogen and oxygen.
Laser Flash Photolysis. The transient spectra obtained by laser
flash photolysis of 1 with a 355 nm laser (15 ns)45 gave a broad
transient with λmax between 390 and 410 nm for nitrogen purged
solutions (Figure 5). The change in the transient spectra over
time and the fact that the kinetics could not be fit to a mono-
exponential function suggested that more than one transient was
formed. The kinetics were adequately fit to the sum of two
exponentials, taking into account a residual absorption, which
We optimized the structure of ketene imine 7, which has CdC
and CdN bonds that are 1.34 and 1.21 Å, respectively. The
optimized triplet imine (TI) of 7 is located 48 kcal/mol above the
S0 of 7. The major difference between TI and S0 of 7 is that the
CdC and CdN bonds (1.42 and 1.26 Å) are longer in the triplet
state. The calculated triplet transition state for 3 to form TI of 7 is
located 67 kcal/mol above 3. Thus, thermal rearrangement of 3
into 7 via TI of 7 is not likely in solution. It is possible, however,
that 3 can intersystem cross to form 7.
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Table 1. Vertical Excitation Energies of the Triplet T1K of 31, C1 Symmetrya
state
ΔECASSCF eV
ΔECASPT2 eV
ref weightb
λ nm
f c
major configurationsd
61%: H-3 f L
T1
T2
T3
T4
T5
0.69
0.69
0.68
0.69
0.68
0.27
1.61
1.86
2.22
0.48
1.42
1.69
1.84
2578
875
732
673
0.000160
0.000003
0.000270
0.000500
53%: H f L
31%: H-1 f L+1; 22%: H-5 f L
20%: H f L+1; 34%: H-1 f L
14%: H f L+3; 31%: H-1 f L+1;
19%: H-5 f L
T6
T7
T8
T9
T10
2.67
3.11
3.25
3.53
3.89
2.26
2.72
2.84
2.95
3.22
0.67
0.67
0.67
0.68
0.66
548
456
437
420
384
0.000099
0.000003
0.000032
0.000011
0.000110
65%: H-4 f L+2
30%: H-3 f L; 21%: H-3 f L+3
21%: H-3 f L+1; 31%: H-1 f L+H-3 f L
27%: H-3 f L+2; 30%: H-2 f L+2
16%: H-5 f L+1
a Based on a CASPT2/CASSCF(14,13)/ANO-S wave function at the UB3LYP/6-31+G* geometry to eliminate the intruder states, with a level shift of
0.22 h applied to the CASPT2 wave function. b Weight of the zero order CASSCF in the CASPT2 wave function. c Oscillator strength for electronic
transition. d Electron excitations within the active space.
Table 2. Vertical Excitation Energies of Triplet 33, C1 Symmetry, Calculated by the CASPT2 Methoda
state
ΔECASSCF, eV
ΔECASPT2, eV
ref weightb
λ, nm
f c
major configurationsd
T1
T2
T3
0.68
0.68
0.67
78%: H f L
2.29
3.39
1.69
3.10
734
400
2.2 Â 10À4
1.8 Â 10À2
74%: H-3f H
30%: H-1f L+1
8%: H-2f L+1
T4
T5
T6
T7
3.77
4.30
4.51
4.68
3.78
3.55
3.69
4.25
0.68
0.66
0.67
0.67
328
349
336
292
2.2 Â 10À3
2.0 Â 10À2
1.2 Â 10À2
4.0 Â 10À3
46%: H-2f L+1
18%: [Lf L+2, H-1f H]
14%: H-2fH
22%: [Lf L+2, H-1f H]
30%: H-1f H
12%: H-1f L+1
25%: H-1f L+1
24%: H-2f L+2
a Based on a CASPT2/CASSCF(14,13)/ANO-S wave function at the UB3LYP/6-31+G* geometry, to eliminate the intruder states, with a level shift of
0.2 h applied to the CASPT2 wave function. b Weight of the zero order CASSCF in the CASPT2 wave function. c Oscillator strength for electronic
transition. d Electron excitations within the active space.
Table 3. Vertical Excitation Energies of Singlet 12, C1 Symmetry, Calculated by the CASPT2 Methoda
state
ΔECASSCF, eV
ΔECASPT2, eV
ref weightb
λ, nm
f c
major configurationsd
S0
0.00
4.37
4.67
4.74
4.79
0.00
2.92
3.30
3.91
3.77
0.69
0.66
0.66
0.68
0.64
77% of S0
first
425
376
317
329
2.3 Â 10À2
5.6 Â 10À1
4.4 Â 10À2
9.9 Â 10À2
60%: H-3 f L
52%: HfL
second
third
62%: H f L+3
22%: H-2 f L
18%: H-1 f L+3
16%: H-1 f L + H f L
13%: H-1 f L
fourth
fifth
5.97
4.67
0.63
266
1.3 Â 10À1
a Based on a CASPT2/CASSCF(14,13)/ANO-S wave function at the B3LYP/6-31+G* geometry, to eliminate the intruder states, with a level shift of
0.2 h applied to the CASPT2 wave function. b Weight of the zero order CASSCF in the CASPT2 wave function. c Oscillator strength for electronic
transition. d Electron excitations within the active space.
did not decay over the longest time scale studied (0.2 ms). The
latter absorption presumably corresponds to the absorption of
the product. The rate constants determined at 400 nm were
1.1 Â 107 sÀ1 (τ = ∼90 ns) and 3.7 Â 105 sÀ1 (τ = ∼3 μs)
(Figure 6). For the reaction in methanol, the rate constants
recovered were 4 Â 106 sÀ1 (τ = ∼250 ns) and 2 Â 105 sÀ1 (τ =
∼5 μs). Laser flash photolysis of 1 in oxygen-saturated acetoni-
trile showed the formation of transients with similar spectral
features as observed under nitrogen (Figure 5B). However, the
lifetimes of the transients were shorter under oxygen. The decay
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assignment of the longer-lived transient under nitrogen to the
nitrene is consistent with a quenching rate that is lower than for a
diffusion-controlled process.
The assignment of the transient absorption to the T1K of 1 and
3 was further supported with calculations. TD-DFT calculations
of T1K of 1 places the major electronic transitions at 312 nm ( f =
0.0396), 385 nm ( f = 0.0434), and 446 nm ( f = 0.0205) (Figure
5D). In addition, there are less intense electronic transitions at
longer wavelengths, 485 nm and 491 nm. The TD-DFT calcula-
tions place the major electronic transitions for 3 at 343 nm ( f =
0.0288) and 488 nm ( f = 0.0190) (Figure 5E). Thus, the TD-
DFT calculations predict that T1K of 1 will have maximum
absorption at approximately 385 nm with the absorbance trailing
out towards 500 nm and that 3 will have a broad absorption
between ∼340 and 490 nm. The overlapping TD-DFT spectra of
T1K of 1 and 3 fit well with the spectra in argon-saturated
acetonitrile in Figure 5A that has λmax between 390 and 410
nm. The band at 310 nm is exaggerated because of the absor-
ption of the product 3P (see the Supporting Information),
which does not decay with time, nor is it quenched with oxy-
gen. Furthermore, the transient spectrum obtained in argon-
saturated methanol (Figure 5C) has a broad absorption with
λmax at 410 nm and a less intense product band at 310 nm,
which also matches well with the overlapping TD-DFT spec-
tra of T1K of 1 and 3.
Because the T1K of 1 is quenched in oxygen-saturated aceto-
nitrile, it is possible to obtain the transient absorption of 3
(Figure 5B) without the absorption of T1K of 1. The quenching
of T1K of 1 reduces the intensity of the transient absorption
beside the band at 310 nm that is mainly due to product
formation. The transient absorption of 3 has broad absorption
with λmax between 380 and 400 nm. The CASPT2 calcula-
tions place the major electronic transitions for 3 at 336 nm
( f = 0.0123), 349 nm ( f = 0.0210), and 400 nm ( f = 0.0180)
(Table 2), which match with observed λmax for 3 being bet-
ween 380 and 400 nm. In comparison, the TD-DFT calculation
places the major absorption band for 3 at shorter wavelength or
343 nm, but the TD-DFT calculations predict more precisely
that 3 will have broad absorption that trails out towards longer
wavelengths.
The match between the CASPT2-calculated spectrum of T1K
of 1 (Table 1) and the experimental spectrum is disappointing.
The CASPT2 calculations put the major bands for T1K of 1 at 385
nm ( f = 0.00011) and 548 nm ( f = 0.000099) (Table 1). The
band at 385 nm is in good agreement with the experimental
spectra of T1K of 1 and 3, but the transient absorption around
548 nm is much less intense than the absorption between 380
and 410 nm. In addition, the CASPT2 calculated oscillators for
T1K of 1 are significantly weaker than the ones obtained from the
TD-DFT calculations. However, it is complicated to compare
oscillator strengths computed by different methods.74,75
In addition, TD-DFT calculations show that the absorption of
the T1A of 1 is somewhat similar to the absorption spectra of 3
(Supporting Information). However, the calculated potential
energy surface shows that the T1K of 1 is not likely to decay to
form the T1A of 1 because the latter state is higher in energy, and
it would be expected to be quenched with oxygen with a rate
close to that for diffusion.
Figure 5. Laser flash photolysis of 1 with a 355 nm laser in (A) nitrogen-
saturated acetonitrile collected between 19 and 110 ns after the laser
pulse, (B) oxygen-saturated acetonitrile collected 19 and 110 ns after
the laser pulse, and (C) nitrogen-saturated methanol collected between
0.12 and 0.70 μs after the laser pulse. (D) Calculated electronic
transitions for T1K of 1 using its UB3LYP/6-31+G(d) optimized
geometry. The oscillators (f) for the CASPT2 transitions are multiplied
by 200. (E) Calculated electronic transitions for 3 using its UB3LYP/
6-31+G(d) optimized geometry.
could be fit to a monoexponential function and a residual
constant absorption (Figure 6A). The rate constant for the decay
was determined to be 1.5 Â 107 sÀ1 (τ = ∼67 ns). This value is
similar to the short-lived component under nitrogen. The
concentration of oxygen in acetonitrile is 0.02 M,46 and a
transient that reacts with a rate in excess of 3 Â 109 MÀ1 sÀ1
would have a lifetime shorter than 17 ns and would not be
detectable in the presence of oxygen. Therefore the kinetics
under oxygen could be explained by two scenarios: (1) the short-
lived transient under nitrogen is quenched with a rate close to
diffusion control and the long-lived transient is also quenched by
oxygen but with a lower rate (∼7 Â 108 MÀ1 sÀ1), or (2) the
short-lived transient does not react with oxygen and the long-
lived transient is quenched with a rate close to diffusion control.
Scenario (1), where both transients are quenched by oxygen, is
the most likely one. The triplet states of acetophenones have
been shown to have longer lifetimes in methanol because of a
stabilization of the triplet with (π,π*) configuration with respect
to the reactive state with (n,π*) configuration.47 This solvent
dependence was also observed for 1, suggesting that the short-
lived species under nitrogen is the T1K of 1, which is expected to
be efficiently quenched by oxygen. In addition, phenyl- and
alkylnitrenes were shown to react very slowly with oxygen, with
Laser flash photolysis of 1 in nitrogen-saturated acetonitrile
with a 266 nm laser (15 ns)45 produced a transient spectrum with
two absorption maxima at λmax ∼ 310 and 380 nm at short delays
after the laser pulse (Figure 7). At long delays, a species with an
rates between 104 and 107 MÀ1 sÀ1 1,48À50
Therefore, the
.
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Figure 6. Kinetic traces monitored after irradiating 1 with a 355 nm laser (A) at 400 nm in N2-saturated acetonitrile over a window of 2 μs and (B) at
410 nm in oxygen-saturated methanol over a window of 50 μs. (A) The black line corresponds to the fit to the sum of two exponentials with a finite final
absorbance value. The inset shows the kinetics in O2-saturated acetonitrile over a window of 1 μs. The black line corresponds to the fit to a
monoexponential decay with a finite final absorbance value. (B) The black line corresponds to the fit to the sum of two exponentials with a finite final
absorbance value.
Figure 7. Laser flash photolysis of 1 with a 266 nm laser collected between (A) 0.19 and 1.3 μs (red trace) and between (B) 18 and 39 μs (black trace)
after the laser pulse. The inset shows the transients of 1 with a 266 nm excitation in N2-saturated acetonitrile collected between 0.19 and 1.3 μs (red
trace) and between 1.6 and 5.3 μs (blue trace), and in O2-saturated acetonitrile collected between 0.74 and 3.3 μs (green trace). (C) Calculated
electronic transition for 2 using CASPT2 (gas phase) and TD-DFT (acetonitrile) calculations.
absorption maximum at 290 nm was observed. In comparison, in
oxygen-saturated acetonitrile, laser flash photolysis of 1 produces
a transient spectrum that has absorption maxima at λmax ∼ 300
and 380 nm. In oxygen-saturated solution, the absorption at
380 nm is formed faster than the resolution of the laser and it
decays with a rate constant of 1.6 Â 105 sÀ1 (τ ∼ 6 μs)
(Figure 8), whereas at the 290 nm absorption, it does not decay
over a time scale of 200 μs. The latter absorption was assigned to
the absorption of the product. We assign the absorption band at
380 nm to 2 as validated by calculations. The calculated UV
spectra of 2 using B3LYP TD-DFT in acetonitrile put the major
electron transition in 2 at 343 nm (f = 0.508) and 331 nm ( f =
0.065) due to promotion of electrons out of the CdN bond and
the lone pair of the oxygen into the π*-antibonding orbitals.
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Figure 8. Kinetic traces monitored after irradiating with 266 nm laser
over a window of 50 μs, (A) monitoring at 390 nm in N2-saturated
acetonitrile and (B) monitoring at 380 nm O2-saturated acetonitrile.
Scheme 7. Ylides 5A, 5B, and 5C
Figure 9. (A) Difference IR spectrum recorded after irradiation of
1 through a 340 nm filter. (B) Calculated IR spectrum for 7 (B3LYP/
6-31+G(d)) scaled with 0.9613.
reactions. The λmax for 5A, 5B, and 5C was reported between 345
and 410 nm (Scheme 7), which is similar to the transient absorp-
tion of 2.
Thus, the laser flash photolysis experiments for 1 showed that
irradiation of 1 with 355 nm light produces the T1K of 1, which
decays into 3. Irradiation with 266 nm light results mainly in the
formation of 2 and a smaller amount of T1K of 1 and 3.
Matrix Isolations. We deposited 1 into argon matrixes at 14 K.
The carbonyl group in 1 has an intense band at 1681 cmÀ1, and
the imine band has a weak intensity at 1805 cmÀ1 (Figure 9).
Irradiation of the matrix with a mercury arc lamp through a
340 nm filter caused the intensity of the bands at 1805, 1681,
1357, 1353, 1230, 1221, 1218, 1040, 1027, 991, and 718 cmÀ1 to
be reduced. Simultaneously, a set of new bands were formed, and
the most intense bands were located at 2083, 2080, 1643, 1411,
1406, 1013, 762, 706, and 580 cmÀ1. We assign these new bands
to ketene imine 7, on the basis of its calculated IR spectra. The
most intense peak in the IR spectra of 7 is the stretching of the
cumulenic double bond CdCdN at 2083 cmÀ1, which fits well
with the calculated stretch at 2080 cmÀ1 after scaling by a factor
of 0.9613.54 The calculated stretch for the carbonyl group in 7 is
located at 1625 cmÀ1 after scaling, which is also in a good
agreement with the observed peak at 1643 cmÀ1. In the cal-
culated IR spectrum of ketene imine 7, the bending of the CÀH
on the ketene imine and the bending in the methyl group are
coupled and are located at 1407 and 1397 cmÀ1, after scaling. We
assign the vibrational bands at 1411 and 1406 cmÀ1 to these
vibrational bending frequencies. The band at 1013 cmÀ1 is
assigned to the bending of the CÀH bond that is coupled with
the stretching of the aromatic of the CdC bonds. These are
calculated to be at 993 cmÀ1, after scaling. Finally, we assign
the vibration band at 580 cmÀ1 to the bending of the ketene
imine band, which is calculated to be at 567 cmÀ1, after
scaling.
In comparison, the CASPT2 calculations place the major electron
transition at 376 nm (f = 0.56), which corresponds to an excellent
fit with the observed spectra. The absorption at 300 nm that does
not decay significantly was assigned to the photoproduct.
In nitrogen-saturated acetonitrile, we observe a broadening of
the transient spectrum at short delays, presumably due to the
transient absorption of T1K of 1 and of 3 in addition to 2 and the
absorption of the photoproduct. The absorptions of the T1K of 1
and of 3 were shown to be broad, and therefore identifying the
individual transients was not possible. Thus, the decay at 390 nm
in nitrogen-saturated acetonitrile can be fitted as a sum of two
exponentials, with lifetimes of 6 and 2 μs, which can be attributed
to 2 and 3, respectively. It is important to note that the amplitude
of the signals for T1K of 1 and 3 are small because, with the
excitation at 266 nm, the formation of 2 occurs concomitantly. In
oxygen-saturated acetonitrile, a short-lived transient (k = 1.5 Â
107 sÀ1 or τ ∼ 67 ns) was observed, which is consistent with the
shortening of the lifetime of 3 observed for the excitation of 1
with 355 nm.
Transient spectra of several ylides have been reported, and
generally they are long-lived intermediates.51À53 For example,
5A has a lifetime of more than 100 μs, and 5B has a lifetime of
13 ms (Scheme 7). It is reasonable, however, that 2 is shorter-
lived than 5A and 5B because 2 undergoes an intramolecular
reaction to form 2P, whereas 5A and 5B decay by bimolecular
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Irradiation of 1 in argon matrix with a Mineralight 254 nm
UV lamp decreased the intensity of the same azirine vibrational
bands as irradiation via a 340 nm filter. New IR bands at 2955,
2119, 1686, 1417, 1359, 1229, 963, 534, and 483 cmÀ1 were
formed in addition to the IR bands assigned to 7 (Figure S5,
Supporting Information). We assign these additional IR bands
to 2. The most intense bands at 2119 and 2098 cmÀ1 correlate
to the cumulenic double bond CdNdC, which fits well with
the calculated stretch of this band at 2074 cmÀ1 with scaling.
The stretching of the CÀH bonds in the methyl group was
calculated to be at 2917 cmÀ1 with scaling, and this is in accor-
Scheme 8. Possible Reactions of 3 with Oxygen
dance with the experimentally observed band at 2955 cmÀ1
.
The band at 1686 cmÀ1 is attributed to the carbonyl stretch on
the basis of the calculated IR spectrum value of 1671 cmÀ1. In
the calculated IR spectrum of 2, the bending of the CÀH bond
on the ylide carbon and the methyl group are coupled with
vibrational frequencies at 1401 and 1360 cmÀ1, with scaling.
These are in good agreement with the experimentally observed
bands at 1417 and 1359 cmÀ1. The bending of the CÀH bond
on the ylide carbon coupled with the aromatic CÀH bond is
observed at 1229 cmÀ1, which is a good fit with the calculated
value of 1201 cmÀ1, with scaling. The bending of the methyl
group calculated at 993 cmÀ1 with scaling is assigned to the
experimentally observed band at 963 cmÀ1. Finally, the bending
vibrations of the ylide group at 534 and 483 cmÀ1 are supported
by the calculated IR values at 513 and 421 cmÀ1, with scaling.
Thus, irradiation of 1 in matrixes via a 340 nm filter yields 7,
whereas broadband irradiation at ∼250 nm results in the for-
mation of both 7 and 2 because the broad irradiation at lower
wavelengths populates both S1A and S1K of 1. S1A of 1 reacts to
form 2, and the S1K of 1 intersystem crosses to the triplet surface
of 1. We theorize that 3 can intersystem cross in matrixes to form
7 similar to how 3 can intersystem cross at room temperature to
form 3P. Presumably, in matrixes 3 intersystem crosses to re-
form 1, which explains why 1 is not fully converted into 7 in the
matrixes. However, restricted rotation prevents 3 from inter-
system crossing to form 3P.
Laser flash photolysis allowed for the direct detection of 3 and
shows that 3 has a broad absorption with λmax at ∼380À400 nm.
The transient absorption of 3 is shifted to longer wavelengths in
comparison to the transient absorptions of triplet alkylnitrene
(λmax ∼ 320 nm)1,35,55 and phenylnitrene (λmax ∼ 310 nm).56
The major electron transition in phenyl and alkylnitrenes is due
to the promotion of an electron out of the lone pair of the
nitrogen atom into the half-full orbital on the same nitrogen
atom. In comparison, the major electronic transition in 3 involves
transitions out of the lone pair on the oxygen and the CHdC—
N: chromophore into the half full orbital on the nitrogen atom
and the π*-orbitals. Thus, the carbonyl and the vinyl chromo-
phores in 3 are responsible for 3 having a broader absorption
than triplet alkyl- and phenylnitrenes.
Vinylnitrene 3 decays by intersystem crossing to form 3P,
rather than dimerizing with another nitrene molecule as has
been observed for stabilized triplet nitrenes, such as alkyl- and
phenylnitrenes. Forming 3 in an oxygen-saturated solution does
not lead to the formation of any new photoproduct that can be
attributed to intercepting 3 with oxygen. Furthermore, forming 3
in an oxygen-saturated solution in the presence of acrylonitrile
does not yield any new products. As described earlier, Inui and
Murata also found that photolysis of 4 in oxygen-saturated solu-
tions yielded no products.21 However, they found that photolysis
of 4 in the presence of oxygen and acrylonitrile produced 5 and
1-naphthaldehyde, and they proposed that oxygen traps vinylni-
trene 4n to form 4o, which then reacts with acrylonitrile to form
5 and 6. Laser flash photolysis of 1 show that 3 reacts with
molecular oxygen with a rate of 7 Â 108 MÀ1 sÀ1, and thus we
propose that 3 is trapped with oxygen to form 8. Radical 8 does
not, however, produce any new isolatable products (Scheme 8).
The major difference between 3 and 4n is that 3 has a carboxyl
group that acts as an intramolecular trapping agent. It should be
highlighted that the calculations show 8 is only 9 kcal/mol
more stable than 3 and an oxygen molecule, and thus it is
possible that the reaction is reversible. Generally, most simple
aliphatic (sp3) carbon radicals react exothermically (approxi-
mately À35 kcal/mol) with molecular oxygen, while the forma-
tion of peroxy radicals from vinyl and phenyl (sp2) radicals are
even more exothermic (approximately À45 kcal/mol).57À60
Triplet phenylnitrene derivatives and alkylnitrenes react with
oxygen to form nitro products with much less efficiency than in 3.
The rates for phenylnitrene derivatives reacting with oxygen have
been measured to be between 5 Â 104 and 8 Â 106 MÀ1 sÀ1, and
’ DISCUSSION
The wavelength dependency of the photochemistry of 1 can
be explained as follows: By irradiating above 300 nm, the ketone
chromophore in 1 absorbs the light and forms the S1K of 1, which
intersystem crosses to the T1K of 1. This results in the formation
of 3. The calculations demonstrate that the precursor to 3 is the
T1K of 1 rather than the T1A of 1. The electron withdrawing effect
of the carbonyl group weakens the CÀN bond in the T1K of 1
and makes formation of 3 feasible. Thus, 3 is formed by the
photoinitiated cleavage of the CÀN bond in the T1K of 1 rather
than via triplet sensitization. Similarly, Fausto and co-workers
have demonstrated that 2H-azirine derivatives with electron-
withdrawing substituents are more prone to CÀN bond cleavage
of the azirine ring rather than the CÀC bond cleavage.16,17 In
comparison, when irradiating with light below 300 nm, the
azirine chromophore of 1 absorbs and forms S1A of 1, which
undergoes internal conversion to form a vibrationally hot ground
state that cleaves the CÀC bond in the azirine chromophore to
form 2. However, irradiation with light below 300 nm also
populates S1K of 1 in competition with forming S1A of 1, which
explains why the laser flash photolysis and the matrix isolation
experiments showed formation of 7 and 3 as well as 2.
for alkylnitrene the rate is ∼5 Â 104 MÀ1 sÀ1 1,48À50
.
The
calculated activation barrier for triplet methylnitrene reacting
with oxygen is considerably higher than for 3, which explains why
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Scheme 9. Calculated (B3LYP/6-31+G(d)) CÀN Bond Length and Spin Density of Various Triplet Nitrenes
3 reacts faster with oxygen than do alkylnitrenes.61 Since we
did not observe formation of acetonitrile and 9b or 10, we
conclude that 3 reacts with oxygen at a similar rate as observed
for carbon centered radicals but does not yield stable products
that we can isolate. However, it is also possible that the reac-
tion is reversible.
’ CONCLUSION
In conclusion, we have shown that the laser flash photolysis of
1 with 355 nm laser excitation results in formation of the T1K of 1,
which cleaves to form 3. The T1K of 1 has a maximum absorption
between 390 and 410 nm and a lifetime of ∼90 ns in acetonitrile,
whereas 3 has a broad absorption with λmax between 380 and
400 nm and a lifetime of only a few microseconds. Vinylnitrene 3
decays via intersystem crossing to form 3P. Furthermore, 3 reacts
efficiently with oxygen, but oxygen trapping of 3 does not lead to
any stable products. Thus, the reactivity of 3 highlights that it is
best described as 1,3-carbon iminyl biradical rather than stabi-
lized triplet nitrenes.
We compared the optimized structure of 3 with the optimized
structures of the simple triplet nitrenes shown in Scheme 9. The
structures of these triplet nitrenes were also calculated using
B3LYP/6-31+G(d) calculations.62 The triplet ethyl- and esterni-
trenes have the longest CÀN bonds of 1.40À1.41 Å, which
indicates there is little interaction between the carbonyl groups
and the nitrene moiety in the esternitrene. Similarly, the calcu-
lated spin density on the N atom in the triplet ethyl- and estern-
irenes is the largest because it is localized on the N-atom. In
comparison, triplet phenylnitrene has a shorter CÀN bond of
1.33 Å, which signifies some conjugation between the nitrogen
atom and the phenyl moiety. This is further highlighted by the
calculated spin density. The double bond character of the CÀN
bond and the delocalization of the spin density in CH2dCH—
N: and 3 demonstrate that these triplet nitrenes have significant
1,3-carbon iminyl biradical character, which explains why 3
reacts differently from the other triplet nitrenes in Scheme 9.
Triplet vinylnitrene 3 does not dimerize as triplet alkyl- and
phenylnitrenes, nor does it decay by hydrogen abstraction as
the triplet esternitrene. Instead, it decays by intersystem cross-
ing. Intersystem crossing in alkyl and phenylnitrene is a spin-
forbidden process, which becomes allowed via spinÀorbit and
vibronic coupling.63 Vibronic coupling, however, in triplet
alkyl- and phenylnitrenes is expected to be small, because for
monovalent nitrenes, only a few bending modes of the nitrene
moiety are possible that modify the orbital structure to make
state mixing possible. In contrast, vibronic coupling in 3 can
be expected to be significant due to the conjugation of the
vinylnitrene moiety with the carbonyl group and the 1,3-biradical
character of 3. Furthermore, we have previously shown that
the 1,4 ketyl iminyl radical 11 also decays by intersystem
crossing.64
’ EXPERIMENTAL SECTION
Laser Flash Photolysis. Laser flash photolysis experiments were
done with a neodymium-doped yttrium aluminum garnet (Nd:YAG)
laser (355 and 266 nm, 15 ns).45,64 Stock solutions of 1 in methanol or
acetonitrile were prepared with spectroscopic grade solvents, such that
the solutions had an absorption between 0.2 and 0.8 at 355 or 266 nm.
Solutions were purged with nitrogen or oxygen for at least 15 min.
Solutions of 1 are relatively photolabile and could be excited only with a
small number of laser shots. For this reason, transient spectra were
collected using a flow system, where a freshly prepared solution was
pumped through a custom-designed Suprasil-cell (7 Â 7 mm) at a rate of
1.5À2.0 mL/min. As a result, a fresh solution was irradiated by each
laser shot. Decays were collected either by using the flow system or by
subjecting the sample in static cells to a small number of laser shots and
checking for the integrity of the sample with UVÀvis spectroscopy. The
kinetic traces were fitted so that the chi square value (the ratio of the
curve fitting error to the standard deviation) is typically less than 0.02%
of standard deviation of the measured data.
Calculations. All geometries were optimized at the B3LYP level of
theoryandwiththe 6-31G+(d) basisset asimplementedin theGaussian03
program.24,25 All transition states were confirmed to have one imaginary
vibrational frequency by analytical determination of the second deriva-
tives of the energy, with respect to internal coordinates. Intrinsic rea-
ction coordinate calculations were used to verify that the located tran-
sition states corresponded to the attributed reactant and product.38,40
The absorption spectra were calculated using TD-DFT.26À30
Excitation energies and transition moments were computed by the
CASPT2/CASSCF method65,66 as implemented in the MOLCAS pro-
gram,67 using ANO-S type basis sets contracted to SVP basis set. The
CASSCF wave functions were obtained using the state-averaging
technique where all states were equally weighted. The active space has
been defined as 13 MOs and 14 electrons, including the lone pair of the
nitrogen atom. The CASPT2 values have been level-shifted by 0.2 h to
avoid near degeneracy in the wave function. The effect of solvation was
calculated using the self-consistent reaction field method with the
integral equation formalism polarization continuum model with metha-
nol as the solvent.68À72
Triplet vinylnitrenes have not been studied intensively be-
cause they are not formed by direct photolysis of azirines or vinyl
azides. Generally, direct photolysis of simple azirines leads to
formation of ylides rather than vinylnitrenes, unless the azirine
has electron withdrawing substituents. Our studies show that
triplet vinylnitrene 3 can be formed selectively, but it reacts
differently from other stabilized triplet nitrenes, such as triplet
phenyl- and alkylnitrenes which decay by dimerization. Even
though 3 is more reactive than phenyl and alkylnitrenes, it does
not react with the solvent as observed for electron deficient
esternitrenes. Thus, triplet vinylnitrene 3 has unique reactivity,
which is limited by intersystem crossing to form 3P.
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Matrix Isolation. Matrix isolation studies were performed using
conventional equipment.73
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Photolysis of 1. Photolysis of 1 in Argon-Saturated Acetonitrile.
A solution of 1 (6.29 mM, 1 mg/mL) in acetonitrile (dry) was placed
into a Pyrex tube, and it was degassed by bubbling Ar for 20 min. The
sample was irradiated with light from a 450 W high-pressure mercury
lamp through a Pyrex filter (>310 nm) for 1 h. After irradiation, the
solvent was evaporated under reduced pressure. 1H NMR spectroscopy
showed that a single photoproduct 3P was formed in 80% yield, and the
starting material 1 was recovered in 20% yield.
Photolysis of 1 in Oxygen-Saturated Acetonitrile. A solution of 1
(6.29 mM, 1 mg/mL) in acetonitrile (dry) was placed into a Pyrex tube,
and O2 was bubbled into the solution for 20 min. The sample was
irradiated with light from a 450 W high-pressure mercury lamp through a
Pyrex filter (>310 nm) for 1 h. After irradiation, the solvent was
1
evaporated under reduced pressure. H NMR spectroscopy showed
that a single photoproduct 3P was formed in 44% yield, and the starting
material was recovered in 56% yield.
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Irradiation of 1 through Pyrex in Oxygen-Saturated Acetonitrile-d3.
An oxygen-saturated solution of 1 in CH3CN-d3 with methyl benzoate
as an internal standard was photolyzed through Pyrex. Analysis of the
reaction mixture with 1H NMR spectroscopy showed formation of 3P
and remaining 1. However, integration of the 1H NMR signals due to 1
and 3P in comparison to the internal standard showed that the absolute
chemical yields decreased with irradiation.
Irradiation of 1 at Longer Wavelength. A solution of 1 (6.29 mM,
1 mg/mL) and acrylonitrile (0.95 M) in acetonitrile (dry) was placed
into a Pyrex tube, and O2 was bubbled into the solution for 20 min. The
sample was irradiated with light from a 450 W high-pressure mercury
lamp through a light filter (>360 nm) for 1 h. After irradiation, the
solvent was evaporated under reduced pressure. 1H NMR spectroscopy
showed that a single photoproduct 3P was formed in 44% yield, and the
starting material 3 was recovered in 56% yield.
’ ASSOCIATED CONTENT
S
Supporting Information. Cartesian coordinates, ener-
b
gies, and vibrational frequencies. This material is available free
of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: Anna.Gudmundsdottir@uc.edu.
’ ACKNOWLEDGMENT
We thank the National Science Foundation and the Ohio
Supercomputer Center for supporting this work. S.R. thanks the
UC Chemistry Department for a Twitchell fellowship. C.B. and
T.C.S.P. thank the Natural Sciences and Engineering Council of
Canada (NSERC) for support in the form of a discovery grant
(C.B.) and a CGS-D fellowship (T.C.S.P.).
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