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Reactive Intermediate Chemistry

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DIRECT OBSERVATION OF TRIPLET CARBENES

385

3.1. Spectroscopic Characterization of Triplet Carbenes in Matrices at Low Temperature

Matrix isolation coupled with some conventional spectroscopic method [usually electron paramagnetic resonance (EPR), ultraviolet (UV), and infrared (IR)]12 is used to detect and characterize the species of interest. There are several advantages in studying the chemical behavior of reactive species under matrix-isolation conditions. Thus, the inert material of the matrix essentially shuts down any intermolecular reactions giving the opportunity to examine the intrinsic reactivity of the reactive intermediate. By annealing the matrix, it is possible to see if low-barrier isomerizations are available to the investigated species. Doping the matrix with some reagent and/or using less inert material for the matrix (e.g., oxygen or methane) gives insight into several intermolecular chemical pathways that may be available. Finally, molecules in an inert matrix can be essentially considered as isolated, making the comparison of experimental and computational data more straightforward.

3.1.1. EPR Spectroscopy. The structure of triplet carbenes is unequivocally characterized by EPR zero-field splitting (ZFS) parameters, which are analyzed by D and E values. In a simple model, the ZFS parameters D and E for a triplet depend on the distance between electrons with parallel spins as given by equation (4):

D

 

 

r2 3z2

 

 

1

;

E

 

 

y2 x2

 

4

 

/

 

r5

 

r5

/

 

r5

 

Þ

 

 

 

ð

where r is the distance between the two spins, x, y, and z are the components of r along the x, y, and z axis, respectively. The parameter D measures the magnetic dipole interaction along the z axis and is related to the average 1/r3 as shown above. A high value of D implies a large spin–spin interaction and proximity of the two spins. The parameter E, on the other hand, is a measure of the difference between similar magnetic dipole interactions along the x and y axes. A molecule with three

different axes should have a finite E, whereas this quantity vanishes for linear molecules with degenerate p orbitals.14–16

More plainly, the more the two electrons are delocalized in carbenes with a conjugated p system, the smaller the value of the D will be. On the other hand, increasing the bond angle at the carbene center leads to a higher p-orbital contribution and a smaller value for E. Although the values D and E depend on the electronic distribution, it has been shown that there is a good correlation between the E=D ratio and the bond angle at the divalent carbon atom.

However, be aware that the ratio of E=D is not always a reliable guide to the structure of triplet carbenes. For example, diphenylcarbene and fluorenylidene have very different geometries but almost exactly the same D and E values.15a If one really wants to learn about the geometry, one must label the carbene carbon with 13C and measure the hyperfine coupling constants.

386 TRIPLET CARBENES

The temperature dependence of the intensity of the EPR signals for a triplet carbene can provide some information about the ordering and energetics of the lowest singlet and triplet spin states. No EPR signal from the triplet carbene will be observed for a carbene with a singlet ground state far below the triplet. When the energy difference between the singlet and triplet spin state is small, then an EPR spectrum can be observed regardless of the ground-state multiplicity. However, the intensity of magnetization (I) should deviate from the behavior predicted by the Curies law17 according to Eq. 5.

I ¼

C

½3 þ expð EST=RTÞ& 1

ð5Þ

T

This law means that the intensity becomes smaller as the temperature is raised. Deviations from linearity could indicate a temperature-dependent equilibrium between a triplet and a singlet. Conversely, a linear Curie plot is taken as evidence for a triplet ground state far below the singlet, but such observations require that the carbene be stable to a certain extent at elevated temperature.

3.1.1.1. Triplet Carbene Structure and ZFS Parameters. The ZFS parameters are thus shown to provide information on the molecular and electronic structures of triplet carbenes. We will see next how the parameters change systematically by examining a series of triplet carbenes.

a. EFFECTS OF CARBENIC SUBSTITUENTS. Some D and E values for typical triplet carbenes are collected in Table 9.3. The ZFS parameters for methylene,18 the parent compound of all carbenes, clearly indicate that it has a bent structure. The bond angle is estimated to be 136 ,18a which is in good agreement with most theoretical calculations.1

Introduction of aryl groups on methylene results in a significant decrease in D values; thus D values decrease from 0.69 to 0.515 on going from methylene (2) to phenylcarbene (1e).19 The D values decrease further as the aromatic ring is changed from phenyl (1e) to naphthyl (12) to anthryl (13).20 These trends are interpreted in terms of increase in spin delocalization into the aromatic rings. It is interesting to note here that there are only small changes in E=D values among those monoarylcarbenes, indicating that the central bond angle of the carbenes are not affected significantly by a change in those aromatic rings.

b. EFFECTS OF REMOTE SUBSTITUENTS. Effects of para substituents on the EPR spectrum of triplet diphenylcarbenes (3DPCs, 314) have been investigated (Table 9.4, Scheme 9.2).21 Two trends become obvious when the D values are compared for di-para substituted DPCs. First, substitution generally causes a decrease in D over that in the parent molecule. This effect is obviously due to extended p delocalization of spin density. To estimate the relative abilities of substituents to delocalize the spin, sigma-dot substituent constants (s ) have been proposed.22 Among the various approaches to the definition of a s scale, Arnold’s sa scale

 

 

 

 

 

DIRECT OBSERVATION OF TRIPLET CARBENES

387

TABLE 9.3. The ZFS Parametersa for Some Typical Triplet Carbenes

 

 

 

 

 

 

 

D

E

 

 

 

 

 

 

 

 

—————————

 

 

 

Carbenes

(cm 1)

 

E=D

Reference

H

 

 

 

H

0.69

0.003

0.004b

 

18

 

 

 

 

 

 

 

 

 

(3)

 

 

 

 

 

 

 

 

 

 

 

H

 

0.04873c

 

 

 

 

 

 

 

0.5150

0.0251

 

19

 

 

 

(1e)

 

 

 

 

 

 

 

 

 

 

H

 

 

 

 

 

 

 

 

 

(Z) 0.4347

0.0208

0.0424

 

20

 

 

 

 

 

 

 

 

 

 

 

(E) 0.4555

0.0202

0.0433

 

 

 

 

 

 

 

 

 

 

( α -12)

 

 

 

 

 

 

 

 

 

 

H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Z) 0.4926

0.0209

0.0424

 

20

 

 

( β -12)

(E) 0.4711

0.0243

0.0516

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H

 

 

 

 

 

 

 

 

 

0.3008

0.0132

0.0439

 

19

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(13)

aMeasured in benzophenone at 77 K unless otherwise noted. bMeasured in xenon at 4.2 K.

cMeasured in p-dichlorobenzene.

is the most suitable for the analysis of the substituent effect on the D values of DPCs, since the scale is a nonkinetic measure of radical stabilizing effects based on hyperfine coupling constants in the benzylic radical.22 Actually, the D values correlate reasonably well with the sa scale.23

Second, the decrease in D is largest when 3DPC is substituted with one para electron-withdrawing group (e.g., NO2) and one para0 electron-donating group (e.g., NMe2). The decrease in D in these unsymmetrically disubstituted 3DPCs is always larger than that predicted taking the sum of the effects in the monosubstituted derivatives. These observations are explained in terms of merostabilization, a

388 TRIPLET CARBENES

TABLE 9.4. The ZFS Parametersa for Para, Para0-Disubstituted

Diphenylcarbenes (14)

Carbenes

Substituents

 

D

E

 

————————

————————

14

X

Y

(cm 1)

a

H

H

0.4088

0.0170

 

b

H

OMe

0.4043

0.0191

 

c

OMe

OMe

0.4022

0.0189

 

d

H

CN

0.3906

0.0193

 

e

CN

CN

0.3879

0.0178

 

f

H

NMe2

0.3876

0.0168b

g

NMe2

NMe2

0.3748

0.0180c

h

H

NO2

0.3778

0.0173d

i

NO2

NO2

0.3773

0.0177b

j

CN

NMe2

0.3518

0.0163d

k

NO2

NMe2

0.3351

0.0164b

 

 

 

 

 

 

aMeasured in 4:1 methylcyclohexane: isopentane matrix at 77 K unless otherwise noted.

bMeasured in tetrahydrofuran (THF) matrix.

cMeasured in 4:1 methylcyclohexane: THF matrix. d Solid salt was used.

term first suggested by Katritzky and co-workers24 to describe increased delocalization in radicals for which reasonable charge-separated resonance structures can be drawn (Scheme 9.2). These charge-separated resonance structures contribute only in unsymmetrically disubstituted DPCs containing strong electron-withdrawing and donating groups.

 

 

 

• •

 

 

 

 

 

 

 

X

 

 

 

 

 

Y

 

Me2N

 

 

NO2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+

 

 

 

-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+

 

 

 

+

 

 

 

 

 

 

 

 

 

Me2N

 

 

 

 

N

 

O

 

Me2N

 

 

N

 

O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- O

 

 

 

 

O -

 

 

 

 

 

 

 

 

 

 

Scheme 9.2

3.1.1.2. Geometrical Isomerism. Triplet carbenes in which the divalent carbon atom is substituted with an sp2 hybridized carbon atom may exist in two rotomeric forms that are stable at very low temperatures. In favorable cases, EPR spectra of

DIRECT OBSERVATION OF TRIPLET CARBENES

389

these carbenes exhibit two sets of triplet signals with significantly different ZFS parameters.

The magnitude of the ZFS parameter D is largely determined by the spin–spin dipolar interaction of the two electrons at the divalent carbon atom. Accordingly, the fraction of the p spin density located at the carbenic center can be estimated from the D value of the carbene. In spite of the predominance of this one-center interaction, the spin density at atoms several bonds removed from the divalent carbon atom can also have a significant effect on the ZFS parameters.

This effect was first observed for the pairs of 1- and 2-naphthylcarbenes (12).20 Since then, reports of geometric isomerism in triplet carbenes have appeared with increasing frequency; two sets of triplet signals having similar but nonidentical ZFS parameters are observed.25 The spectra are assigned to the two conformations of the carbene in which the s orbital at the divalent carbon and the aromatic moiety are coplanar. When the distribution of the spin in the p orbital is unsymmetric, the dipole spin–spin interaction of the p electron with the electron localized in the s orbital is different for the two conformations. Consequently, the ZFS parameters will be different and in cases in which the differences are sufficiently large, it is possible to observe the spectra of the two isomers.

The assignment of the ZFS parameters to a specific conformer is made possible by a point spin model,26 with individual contributions, Di, due to p-spin densities, ri, at the individual carbon atoms, Ci, namely,

D

i / ri

ri2 3zi2

 

1

6

 

ri5

r3

Þ

 

ð

where ri is the distance between the divalent carbon Cdi and a carbon, Ci, bearing p-spin density, and zi is the z coordinate of Ci. As mentioned above, carbenes will have noticeable secondary contributions to jD=hcj due to the nearest carbons with p electron spin densities. Take 2-naphthylcarbene (b-12) for instance (Scheme 9.3). The p electron density at the 1-position is twice that at the 3-position (r3 1=2r1). For the (E) isomer, C1 lies close to the z axis so that r is approximately parallel to z. Hence, z1 / r1, and there is a noticeable negative contribution to jD=hcj. A similar inspection of the (Z) isomer shows that C3 lies close to the z axis (z3 ¼ r3), whereas C1 is far from the z axis (z1 > r1). Therefore, the negative contribution to jD=hcj is smaller. Based on these considerations, the (E)-conformer must have the smaller jD=hcj value (see Table 9.3).

1

H

3

H

1

3

(E ) - 12

(Z ) - 12

Scheme 9.3

390 TRIPLET CARBENES

3.1.1.3. Geometrical Changes upon Annealing. Geometrical changes upon annealing the matrix are observed especially for sterically hindered carbenes. For example, the E=D value obtained for di(1-naphthyl)carbene (15) in methyltetrahydrofuran (MTHF) at 15 K is 0.0109/0.3157. A new set of triplet signals with a smaller E=D value (0.0051/0.2609) ascribable to the linear configuration of 315 is observed at the expense of the original peaks when the matrix is annealed to 80 K. This observation is interpreted in terms of steric strain in triplet carbenes.27 Thus, when the carbene is formed in a rigid matrix at low temperature, it should have the bent geometry presumably dictated by that of the precursor. Even if the thermodynamically most stable geometry of the carbene is different from that imposed at birth, the rigidity of the matrix prevents it from assuming its minimum energy geometry. However, when the matrix is softened on annealing, the carbene relaxes to a structure that is closer to linear, as evidenced by the substantial reducing in E. The small reductions in D are also consistent with this picture, as they indicate that the unpaired electrons are more efficiently delocalized in the relaxed geometry. Since E values for 3DPC (14) are essentially insensitive to the matrix, suggesting that the carbene has achieved its relaxed geometry regardless of the environment, the observations indicate that the carbene undergoes expansion of the central C C C angle to gain relief from steric compression in soft matrices or upon an annealing of harder matrices.

Similar dependence of the ZFS parameters on the rigidity of matrices is observed for many other sterically congested triplet carbenes and hence can be considered as an indication of such steric strain.15c

3.1.2. Ultraviolet/Visible Spectroscopy.12,15a,b Unlike the EPR spectrum, the optical spectrum reveals virtually no structural information. Thus, irradiation of a carbene precursor at low temperature creates new absorption features, but it is difficult to assign these bands to a particular structure with certainty. Comparison of the optical and EPR spectrospcopic results obtained under identical conditions can corroborate the simultaneous existence of both the carbene and the absorbing species. The data play an important role in the interpretation of the transient spectroscopic results obtained in time-resolved ultraviolet/visible (UV–vis) spectroscopy. These short time scale experiments help to confirm the spectral assignments made on the basis of the low-temperature measurement.

Spectroscopic studies of DPCs (14a) have been most extensively done in an Ar matrix as well as in organic matrices. The wealth of the data may be due to the fact that a precursor, diphenyldiazomethane, is available that can be prepared and handled in a relatively simple way. Most of DPCs are stable in an organic matrix at liquid nitrogen temperature.

Generally speaking, the spectra of DPCs consist of two features, intense absorption bands in the UV region and weak, broad, and sometimes structured bands in the visible region. There is a qualitative resemblance between the spectra of DPCs and those of diphenylmethyl radicals. As a rule of thumb, DPCs are usually blueshifted by 20–30 nm with respect to the corresponding radicals. For example, DPC has absorptions with maxima near 300 and 465 nm and the diphenylmethyl radical

DIRECT OBSERVATION OF TRIPLET CARBENES

391

exhibits maxima at 336 and 515 nm. If it is assumed that the pz electron is not involved in the transitions, then the p system of DPCs can be considered as that of an odd-alternant hydrocarbon radical having 13 p electrons. In systems of this type, a strong absorption band due to p–p* transition is expected.

As expected, the absorption bands due to polynuclear aromatic carbenes are redshifted as p conjugation is developed. For example, triplet di(1-naphthyl)carbene (15)28 and di(9-anthryl)carbene (16)29 show a rather strong and structured UV– vis absorption bands at 300– 450 and 350–500 nm, respectively.

• •

 

• •

 

 

 

 

15

16

3.1.3. Fluorescence. Triplet DPCs (14) show strong emission in a low-tempera- ture matrix.15a,b For example, for DPC (14a), emission at lmax ¼ 482 nm (t ¼ 123 ns ) with a quantum yield of 0.33 is observed in a methylcyclohexane glass

at 77 K. The emission is assigned to fluorescence arising from a radiative transition from the first excited triplet level to the triplet ground level (T1 T0). Substituted DPCs also show fluorescence, but the subsitution leads to a red-shift in the emission regardless of whether they have electron releasing or withdrawing properties.

Again, there is a resemblance between the emission of DPCs and those of the diphenylmethyl radicals. The emission maximum of DPCs is blue-shifted by 20–50 nm with respect to that of the radicals. For example, diphenylmethyl radical exhibits its emission at 535 nm. Another characteristic difference between these two species is that the lifetime of 3DPC* is significantly shorter than that of the first excited state of the diphenylmethyl radical.30,31

3.1.4. IR Spectroscopy. The IR spectra of triplet carbenes can be obtained by using matrix isolation techniques.32 Fortunately, a matrix IR spectrum consists of a series of sharp bands showing no rotational structure. This relative simplicity is the result of the rigidity of the matrix and the minimization of intermolecular interactions. Thus, it is often possible to discriminate individual species in mixtures with great ease.

Like UV–vis spectra, IR spectra do not give concrete evidence for the multiplicity of carbene in question and, hence, comparison with EPR spectra is highly desired. However, IR spectroscopic data encode a lot of structural information and can be analyzed with the help of computational methods, thus aiding in the identification of the observed species. Since geometries of the singlet and triplet carbenes are usually different, their IR spectra are expected to be different. One can often assign a multiplicity of the carbene if one can calculate theoretical

392

TRIPLET CARBENES

 

 

 

 

 

 

 

 

OMe

 

 

 

 

 

 

 

 

O

 

 

 

 

 

OMe

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Singlet

Triplet

O

 

117

 

317

 

 

 

 

(1590, 1625, 1640 cm-1)

(1660 cm-1)

 

 

 

Scheme 9.4

IR bands for the both states. For example, singlet and triplet states of 2-naphthyl- (methoxycarbonyl)carbenes (NMCs, 17) show very different IR spectra (Scheme 9.4)33 (1590, 1625, 1640 cm 1 for 1NMC and 1660 cm 1 for 3NMC). Both states are observable in this case. In the singlet state, the carbomethoxy group assumes a conformation perpendicular to the naphthylcarbene plane to avoid destabilization of the empty carbenic 2p atomic orbital by the electron-withdrawing carbonyl group, while in the triplet, the methoxycarbonyl group is in the same plane to delocalize an unpaired electron. For this reason, there is a barrier between the two states and hence both of them are observable under these conditions.

The other advantage of matrix IR spectroscopy is that one can follow the sub-

sequent reaction (either thermally or photochemically) of triplet carbenes relatively precisely, again with the aid of computational methods.32,34,35 This complementary

approach will reinforce the assignment of triplet species. For example, triplet carbenes react with oxygen even at very low temperature to give oxidation products such as carbonyl oxides (see Section 6), which are easily characterized by comparing the IR spectra with those calculated.

Matrix IR data, like UV–vis, play an important role in the interpretation of the transient spectroscopic results obtained in the time-resolved IR spectroscopy described below (Sections 4.2 and 4.3).

3.2. Time-Resolved Spectroscopy in Solution at Room Temperature

A second way to observe those highly reactive species appeared later than the one developed for low temperatures. The new method provided an important opportunity absent from the low-temperature experiments, that is, the ability to measure their rates of reaction under normal conditions. In the late 1960s, Moritani et al.36 detected transient absorption bands of triplet dibenzocyclopentadienylidene (18) and later in the 1970s, Closs and Rabinow37 observed transient UV–vis absorption bands of 3DPCs (14). Both groups used conventional flash photolysis. However, with this technique, the measurements were restricted to microsecond time resolution. With the advent of the laser flash photolysis (LFP) technique, nanosecond time resolution became widely available, and made the measurement of the absolute rate constants for the reactions involving carbenes and related species very easy.38 The methods provide much useful kinetic information including reactivities and energetics of carbenes, as we will see in this chapter.

DIRECT OBSERVATION OF TRIPLET CARBENES

393

Time-resolved UV–vis spectroscopy is the most common technique and has been widely used, but other time-resolved spectroscopies such as IR and EPR have become available as well.

3.2.1. Time-Resolved UV–Vis (TRUV–Vis) Spectroscopy. In LFP, a solution of a photolabile precursor such as a diazo compound or diazirine is photolyzed with a pulse of a laser to give the transient of interest. Once formed, the transient is monitored by an optical detection system consisting of a xenon lamp, monochromator, and photomultiplier tube. The output of the photomultiplier is fed to a transient digitizer and the signal is finally fed to a computer for storage and kinetic analysis. Reaction kinetics are investigated at a fixed wavelength by monitoring changes in the optical absorption of a transient with time. The spectrum of a transient is reconstructed from measurements of these time profiles at a series of wavelengths.

Assignment of the transient absorption spectrum typically is done by reference to the low-temperature spectra described above. It is also important to analyze the chemical reactions of the intermediates. For example, triplet carbenes are known to react with O2 very efficiently to give ketones. So, if the detected intermediate can be observed to react with O2, there is additional evidence for assignment as a triplet carbene (see Section 6.5).

Rate measurements are straightforward if the carbene can be monitored directly. As a rule, the decay of carbene absorption is pseudo-first order due to rearrangement and/or reaction with the solvent. In the presence of a quencher, the decay is accelerated and the rate constant kq is obtained from a plot of kobs versus the concentration of the quencher (Eq. 7). Carbenes that contain a UV chromophore (e.g., DPC ) are readily observed and their decay kinetics during the reaction can be readily followed by LFP.

kobs ¼ ko þ kq½Q&

ð7Þ

However, carbenes such as alkylcarbenes that contain no chromophore are generally transparent in the most useful UV region. Those spectroscopically invisible carbenes can be monitored by the ylide method. Here, the carbenes react with a nucleophile Y: competitively with all other routes to decay to form a strongly absorbing and long-lived ylide (Scheme 9.5). In the presence of an additional

 

 

 

 

 

 

 

 

k0

 

 

Product

 

 

 

hν

 

 

 

 

ky

 

 

R

R

 

 

R + -

 

 

N2

 

 

 

 

 

Y

 

 

 

R

 

 

R

-N2

 

 

 

 

 

R

 

 

 

 

 

 

 

Y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ylide

 

 

 

 

 

 

 

 

kq

 

 

Product

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Scheme 9.5

394 TRIPLET CARBENES

quencher (q), the observed pseudo-first-order rate constant for ylide formation is given by Eq. 8. A plot of kobs versus the concentration of the quencher at the constant concentration of the nucleophile will provide kq. If the growth rate of ylide absorption is too fast to be monitored, relative rates can still be obtained by a Stern–Volmer approach (Eq. 9). In this case, the yield of ylide, measured as the change in optical density ( OD), decreases in the presence of a carbene quencher.

kobs

¼ ko þ ky½Y:& þ kq½Q&

ð8Þ

OD0

 

1

kq½Q&

 

1

k

Q

9

 

 

¼

þ ky½Y:&

¼

Þ

OD

 

 

þ

qt½ &

ð

By plotting 1/ OD as a function of [Q], the ratio of kq=ky[Y:] can be derived. This ratio corresoponds to the kqt term of the Stern–Volmer equation. Here t is the lifetime of the carbene in the absence of quenchers.

When monitoring the transient due to triplet carbenes is difficult because of the inherent weak nature of the bands and/or severe overlapping with the absorption bands of the parent diazo compounds, it is more convenient to follow the dynamics of the triplet carbene by measuring the rate of the products formed by reaction of triplet carbenes with quenchers such as radicals (Section 5.3) and carbonyl oxides (Section 6.5). In this case, note that the observed rate constant (kobs) of a triplet carbene reaction is the sum of the decay rate constants of the triplet. These may include decay via an associated but invisible singlet with which the triplet is in rapid equilibrium. Thus in general,

kobs ¼ kT þ kSK

ð10Þ

where kT and kS are singlet and triplet rate constants and K is the equilibrium constant: the ratio of the singlet equilibrium population to that of triplet. Unfortunately, kobs cannot be dissected further by LFP and this process must be accomplished by product analysis.

3.2.2. Time-Resolved IR Spectroscopy. More recently, time-resolved IR (TRIR) experiments have been used to characterize species with lifetimes of microand even nanoseconds.39 Since IR spectra provide structural information in more detail than UV, this technique will be more powerful than TRUV–vis if one can find a carbene that can be detected and studied by this technique. To date, however, only one carbene has been studied by using TRIR. The matrix IR study shows that the planar triplet and twisted singlet states of 2-naphthyl(methoxycartbonyl) carbenes (NMC, 17) show distinctly different IR bands (see Section 3.1.4). Both 1NMC and 3NMC are detected by TRIR in solution and their kinetics have been

studied. Such experiments provide clear cut data for the reaction kinetics as well as energetics of both states (see Sections 4.2 and 4.3 ).40a,b

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