Reactive Intermediate Chemistry

4. EXPERIMENTAL ESTIMATION OF S–T GAPS

One of the main issues in carbene chemistry is to measure the S–T gap, especially in large systems such as DPCs. We have seen that high-level theory can predict the S–T gap of these large systems fairly precisely. However, these computations mostly estimate values in the gas phase. It has been shown that the S–T gap is sensitive to the solvent polarity (see Section 4.3). Therefore, accurate measurements of carbene singlet–triplet energy gaps are both fundamentally and mechanistically very important. As the absolute rate constants for the reactions involving carbenes are available, attempts to estimate the gap become a more tempting issue. In this section, we will see how those values are determined.

4.1. Preequilibrium Mechanism

The quenching of a triplet carbene reaction with methanol is frequently used as the standard means of probing the singlet–triplet gap. It is widely believed that singlet carbenes insert readily into the O H bonds of methanol, while the triplet states undergo hydrogen abstraction from the C H bonds.41 The behavior of diarylcarbenes appears to violate this rule.

The LFP of diphenyldiazomethane ( DDM ) in a variety of solvents produces triplet diphenylcarbene (3DPC, 314a), whose transient absorption is readily monitored. The optical absorption spectrum of 3DPC is quenched by methanol and yields the product of O H insertion, suggesting that 3DPC is quenched by the

O H bond of methanol. The quenching rate constant (kT) is determined to be 6:8 106 M 1s 1 in benzene.37

The results are interpreted in terms of a preequilibrium mechanism42 in which 3DPC equilibrates with 1DPC before it can interact with O H bond to give benzhydryl methyl ether. According to this mechanism, the observed rate constant for the reaction of 3DPC with methanol is

At relatively low concentration of methanol, with kST > kS [MeOH], kobs reduces to

If one assumes that the rate constant of 1DPC with methanol is at the diffusion controlled rate (kS ¼ 5 109 M 1s 1), measurement of kobs immediately yields the lower limit of K to be 0.002. Since GST ¼ RT ln K, the maximum free energy separation between 1DPC and 3DPC can be calculated to be 3.9 kcal/mol. If one assumes that the only entropic difference between the spin states is due to multiplicity (R ln 3), then HST is estimated to be 3 kcal/mol for DPC in benzene.

396 TRIPLET CARBENES

This approach is further elaborated by measuring unknown rate constants, kST, kTS, and kS.43 Since only the triplet ground state of DPC could be observed spectroscopically, as the singlet is invisible, estimations of GST are obtained with a combination of picoand nanosecond TRUV–vis measurements, chemical quenching, and triplet sensitized experiments. Thus, picosecond laser induced fluorescence is used to measure the rate of formation of 3DPC upon photolysis of DDM and, hence,

traps, respectively, to determine other rate constants. The rate constant of 3DPC with isoprene is obtained by nanosecond LFP by monitoring the decay of the transient signal due to 3DPC as a function of [isoprene]. Finally, the rate constants kS and kTS are estimated by competitive quenching experiments obtained by photolysis of two different carbene precursors in the presence of both isoprene and methanol. Kinetic and thermodynamic parameters obtained from the competitive quenching experiments are in good agreement under the various quenching conditions. The values of HST are sensitive to solvent polarity and are much larger in isooctane (3.8– 4.1 kcal/mol) than in acetonitrile (2.2–2.8 kcal/mol) (see Section 4.3).

This method is criticized later (see Section 4.2), but has been employed to estimate GST for several diarylcarbenes systematically (Table 9.5). For example, widening of the carbene angle is predicted to enhance GST. Opening of the angle is achieved by sterically crowding the ortho position of diphenylcarbenes.44 The quenching rate constant by methanol is shown to decrease as more methyl groups are introduced at the ortho position of diphenylcarbenes (19a–c). The GST parameter is estimated to increase on going from DPC to (2,4,6-trimethylphenyl)- (2-methylphenyl)carbene (19b). Methanol (1.2 M) fails to quench the transient absorption of triplet dimesitylcarbene (19c), indicating a triplet quenching rate constant of <2 103 M 1s 1. The quenching rate constant of the singlet state by methanol is estimated by a Stern–Volmer study of the yield of triplet signal as a function of methanol concentration, to be 1:4 109 M 1s 1 (this value is to be compared with the rate constant of 114a of 1:3 1010 M 1s 1 under the same conditions). Apparently, steric hinderance slows down the singlet reaction, but not enough to account for the observed lack of triplet carbene reactivity with methanol. These results indicate that there is a large HST and that kTS is comparatively small.

Conversely, decreasing the bond angle by bringing the rings closer should destabilize the triplet. This aim is achieved by producing a series of cyclophane diarylcarbenes in which phenyl rings are linked by an alkyl chain of 9–12 methylene units (20).45 The bond angle is contracted by shortening the tether in these cyclophane diarylcarbenes. As one may expect, kobs jumps by a factor of 320 upon decreasing the bridge length from 12 to 9. Assuming that kS is diffusion controlled, K is thought to be the sole determining factor for the variation in the observed rates with chain length.

398 TRIPLET CARBENES

Similar attempts to estimate GST have been carried out for p-substituted DPCs (14) by measuring the rate constant with methanol.47 The data are in line with the predictions. Modest retarding rate effects are found with p acceptor substituents in the 4-position of DPCs. Such groups help to delocalize an unpaired electron of the triplet carbene, while destabilizing the singlet state. Conversely, electron-donating substituents accelerate the rate of triplet carbene reaction with methanol (Table 9.5).

Effects of electronic factors on GST have been examined more systematically for a series of cyclic aromatic carbenes incorporated into a presumably planar ring of five or six atoms. The carbene bond angle in those examples is not expected to change much and the diversity of chemical behavior must then be primarily associated with electronic changes. The parameter GST of each carbene has been estimated from the rate constants for reactions of the electronic states and are summarized in Table 9.6.48

TABLE 9.6. Equlibrium Constant (Keq) and GST Estimated for Cyclic Aromatic Carbenes

O

24 (XA)

aMesylate ¼ Mes, FL ¼ fluorenylidene, DMFL ¼ dimethoxyfluorenylidene.

bCyclohexane ¼ c-C6H12, n-C5H12 ¼ n-Pentane.

cKeq ¼ kST=KTS.

For example, the reaction of mesityl(bora)anthrylidene (BA, 22) with 2-propanol gives only a 17% yield of an O H insertion product. The remainder of the products arise from radical-recombination processes attributable to the triplet carbene. No ether is formed when the diazo precursor is photolyzed in the presence of triplet

DPC. These observations mean that BA is not easily accessed from BA, probably because of a large GST. Although kST and kTS could not be directly obtained, an estimate is possible based on the available data. The fact that sensitized photolysis give no ether product indicates that kTS < kT [2-propanol]. The latter term is obtained by LFP and thus kTS <2 106 s 1. From a Stern–Volmer plot of ether yield versus 2-propanol concentration, kST=kS is obtained from the slope. Coupling this result with a rise time of <100 ps for 3BA limits kST to at most 1 1010 s 1 and yields a rate constant of kS ¼ 6:6 108 M 1s 1 for reaction of 1BA with 2-propanol.

This gives K > 4,000, or GST >5:2 kcal/mol.49

On the other hand, the reaction of xanthylidene (XA, 24) with tert-butyl alcohol gave an ether almost exclusively. An LFP study showed that the reaction proceeded at a nearly diffusion-controlled rate (3:4 109 M 1s 1). In contrast to the behavior of BA, triplet sensitized formation of XA in the presence of alcohol gives exactly the same results as does the direct irradiation. More interestingly, XA does not react measurably with O2. The lifetime of 1XA is the same in O2 saturated cyclohexane as it is in solutions that have been deoxygenated. If 3XA were in rapid equilibrium with 1XA, then O2 should shorten the apparent lifetime of 1XA by reacting with the triplet. These observations, coupled with the fact that XA generated in matrix at low temperature shows no EPR signals, suggest that XA has a singlet ground state with the triplet significantly higher in energy. An estimate of GST for XA can be obtained based on its reactivity with O2. With the knowledge that triplet carbenes react irreversibly with O2 with a rate constant close to the diffusion limit (kdiff ), Keq can be expressed as

where kobsO2 is the rate constant for the reaction of 1XA in oxygen-saturated solution, and kobsN2 is the rate constant in the absence of O2. Since no significant difference in these rate constants can be detected, a limit, set in part by the experimental uncertainty, indicates Keq > 1 104. This value corresponds to GST < 5 kcal/mol.50

A similar experimental determination of GST has been carried out for a series of cyclic diarylcarbenes, and results are summarized in Table 9.6.49–53 The obser-

vations clearly support the theoretical prediction that electron-donating and electron-withdrawing groups have an opposite influence on the magnitude ofGST. For example, for BA(22), which is at one extreme among those carbenes studied, the aromatic LUMO is significantly lowered by the presence of the vacant aromatic orbital of the boron, and thus mixed with the carbene p orbital. This interaction lowers the energy of this nonbonding orbital, thus resulting in an increase in GST. An analogous explanation is applied for analysis of XA (24), another

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extreme carbene, where the occupied aromatic orbital is raised by the electrondonating ability of oxygen and is mixed with the carbene p orbital. In this case, the splitting of the orbitals in the mixed state is sufficiently increased beyond that of a prototype carbene to make GST negative. Other aromatic carbenes (14, 23, and 23a) fall into intermediate positions in this range.

4.2. Surface-Crossing Mechanism

For triplet ground-state carbenes with relatively small GST, chemistry often arises from the higher lying, but more reactive singlet carbene. As mentioned above, this behavior is explained usually in terms of a preequilibrium mechanism, in which the equilibrium between singlet and triplet carbenes is rapid relative to reaction from either multiplicity. This mechanism predicts that the observed barrier (Ea) for a singlet carbene reaction is given by the actual activation barrier of the reaction ( Hz 1–3 kcal/mol) plus the energy required to populate the singlet from the lower energy triplet carbene ( HST ¼ 4:2 and 2.5 kcal/mol in isooctane and acetonitrile, respectively). However, the activation energy for the reaction of 3DPC with methanol is measured to be 3.61 and 1.66 kcal/mol in isooctane and acetonitrile, respectively, which are smaller than that predicted by the preequilibrium mechanism.54

There are a several explanations for this discrepancy. One resolution would be if the entropic difference between 1DPC and 3DPC is larger than Rln3. The polar nature of singlet carbene could result in a more ordered solvent. Any increase inGST would reduce HST. Moreover, kST was not measured under the actual conditions used to determine GST.

However, Griller et al. proposed that 3DPC can react directly with methanol to produce the ether, without intervention of 1DPC.54 This behavior is involves a surface crossing mechanism in which triplet carbene can react directly with alcohols, with surface crossing occurring after the carbene has begun to interact with the O H bond. In the surface crossing mechanism, the triplet carbene surface crosses the singlet carbene ! product surface at a point below the energy of the singlet carbene, leading to an observed Ea that is lower than the sum of Hz and HST.

Therefore it is highly desirable to observe and monitor simultaneously the transient absorption bands due to both singlet and triplet states. This goal is realized in the TRIR studies of 2-naphthyl(methoxycartbonyl)carbenes (17), in which both 117 and 317 are detected in solution and their kinetics studied. Thus, the rate of decay of both a triplet carbene signal (1650 cm 1) and a singlet carbene signal (1584 cm 1) is monitored as a function of methanol concentration. Note that in this case, quenching rate constants observed at 1650 cm 1 (317) and 1584 cm 1 (117) for the reagent corresponds to that of each state. The rate constants are essentially the same within experimental error.40a This behavior is the first direct evidence to support a preequilibrium mechanism. The rate constants observed for the reaction with 2,3-dimethyl-2-butene are also the same, indicating that alkene also reacts with an already equilibrated singlet/triplet mixture of carbene 17.

Previous studies with the TRUV method to estimate GST have employed a combination of product studies and kinetic measurements and have been based

on assumptions concerning the spin-selective reaction of carbenes. However, the TRIR study with 17 allows a direct experimental estimate of a carbene singlet– triplet gap in solution for the first time. In this case, since the relative intensities of singlet and triplet carbene are directly related to the concentration of each state, an equilibrium constant and free energy difference can be directly derived. The well-separated signals observed at 1650 (317) and 1584 cm 1 (117) are used to estimate the ratio of 317/117, which is determined to be 2.1 at 21 C in Freon-113 solution. This value leads to an equilibrium constant of 1:4 0:2 at 21 C and a free energy difference of 0:2 0:1 kcal/mol, with the triplet lower in energy.

4.3. Effect of Solvent on the S–T Energy Gap

This value is significantly lower than that calculated by DFT theory ( HST ¼ 4:52 kcal/mol). It has been shown that singlet DPC is stabilized relative to triplet DPC in polar solvent, presumably as a result of the zwitterionic nature of singlet carbenes.55 The singlet state is polar and will be stabilized in polar solvent whereas the less polar triplet will not experience such stabilization. Thus, it is expected that the singlet–triplet energy gap will decrease as the solvent polarity increases. A possible explanation for the difference between the calculated (gas phase) and experimental (Freon-113 solution) value of HST is that the singlet is preferentially stabilized in solution. This idea has been examined by generating the same carbene in four solvents (hexane, Freon-113, methylene chloride, and acetonitrile) of different polarity.40b The ratio of 317/117 decreases as the solvent polarity increases, andGST decreases from 0.3 to 0.3 kcal/mol on going from hexane to acetonitrile (Table 9.7). There is a good correlation between GST and the solvent polarity

TABLE 9.7. Experimentala and Theoreticalb Thermochemical Parameters for 2-Naphthyl(methoxycarbonyl)carbene (17)40b

aData obtained in the 1680–1540-cm 1 spectral region. The data in parentheses are those obtained in the 1260–1140 cm 1 spectral region.

bThe values shown in [ ] calculated at B3LYP/6-311 þ G**//B3LYP/6-31G* level using the PCM solvation model and corrected to 298 K.

404 TRIPLET CARBENES

photolysis, radical dimer and double-hydrogen abstraction product rather than the insertion product were the major compounds formed.61

A simple and straightforward way to distinguish between a direct insertion process and one going through free radicals is by a cross-over experiment. Cyclohexane and cyclohexane-d12 are often used as the probe for crossover, and hence the reactive multiplicity of the carbenes in question (Scheme 9.8).

d0 + d1 + d11 + d12

Scheme 9.8

Thus, if a mixture of these hydrocarbons reacts with a singlet state, then the addition product will consist entirely of undeuterated (d0) and deuterated(d12) compounds. If some of the reaction occurs by the hydrogen abstraction–recombination route, then some crossed products (d1 and/or d11 compounds) will be formed. By using this technique, it has been shown that, while some of the DPC-cyclohexane adduct (34) is formed by combination of radical pairs, there is no evidence of crossover product present in the FL– cyclohexane adduct (37).59 The results are interpreted by assuming rapid spin state equilibration relative to the reaction of either spin state with solvent. The larger amount of singlet chemistry of FL relative to DPC can then be explained if the S–T gap is smaller in FL than in DPC.

Other differences between singlet (concerted) insertion and triplet (abstraction– recombination) carbene ‘‘insertion’’ are seen in selectivity, stereochemistry, and the kinetic deuterium isotope effect. The triplet states are more selective in C H insertion than the singlets. For example, the triplet shows higher tertiary to primary selectivity than the singlet in the insertion reaction with 2,3-dimethylbutane. Singlet carbene is shown to insert into C H bond with retention of configuration, while racemization is expected for triplet insertion reaction from the abstraction– recombination mechanism. For example, the ratios of diastereomeric insertion product in the reaction of phenylcarbene with racand meso-2,3-dimethylbutanes are 98.5:1.5 and 3.5:96.5, respectively.62

It is generally observed that the isotope effect for abstraction of hydrogen by a

triplet carbene is 2–9, whereas insertion into a carbon–hydrogen bond by a singlet carbene proceeds with an isotope effect of 1–2.49,53,63