Reactive Intermediate Chemistry

Thus, a disjoint non-Kekule´ compound like TME might well have a singlet ground state, since the singlet is expected to be stabilized by a favorable electron correlation effect. This conclusion seems to conflict with the ESR experiments on TME.

Since then, much further computational work has developed a more complex picture of the TME issue.10,101 Currently, it is believed that both the singlet

and triplet TME are twisted out of the planar configuration; the angle of twist for the triplet is 50 (D2 point group) and that for the singlet is 90 (D2d point group). At the minimum energy triplet geometry, the triplet is predicted to be more stable by 1–1.5 kcal/mol. At a particular computational level (CI þ DV2), the triplet minimum near 50 lies 0.1 kcal/mol below the singlet at 90 , although the authors state that ‘‘the prediction of the relative stability of states lying within 2 kcal/mol

of one another is a difficult proposition.’’ Further computational effort has been devoted to this problem.102,103

5.1. The Singlet–Triplet Separation in Tetramethyleneethane

in the Gas Phase

The TME radical anion can be generated in the gas phase by the reaction of O with 2,3-dimethylbutadiene, and the TME neutral biradical can be formed by electron photodetachment on the mass 80 ion by methods similar to those used in the case of TMM (see Section 4.1.4).104 The spectrum obtained by monitoring the photoelectrons shows transitions of TME to two TME neutrals whose origin bands are separated by 2 kcal/mol. The authors assign the lower energy species to the singlet and the higher energy one to the triplet on the basis of two lines of argument:

(1) the intensities of the two band envelopes are in the ratio of 3:1 in favor of the higher energy species, as is often approximately the case in PES leading to both singlet and triplet states, and (2) the lower energy species (singlet) has a much narrower Franck–Condon vibrational envelope than the higher energy one. This second result is consistent with the electronic structure computations, which predict a bisected geometry (D2d) for both TME and TME singlet but a twisted (by 50 ) geometry for the triplet. Thus, a small geometry change is expected in the reaction TME ! 1TME and a large change for the reaction TME ! 3TME.

These results of course are inconsistent with Dowd’s finding of a triplet ground state from the matrix ESR spectrum. At present, the discrepancy is rationalized 104 with the hypothesis that the triplet is metastable in the matrix and that its conformational conversion to the more stable singlet is slow, thus allowing the observation of the ESR signal and the linear Curie plot. Other cases of what seem to be con-

formationally based triplet metastability in matrix ESR had been observed previously in 1993105,106 and will be discussed later, together with further examples

(see Section 7.2.1).

A six-line ESR spectrum has been observed107 for the triplet state of the TME

derivative 2,3-dimethylene-1,3-cyclohexadiene (36), which first had been generated in low-temperature matrices by Roth et al.108,109

cannot be deduced from this criterion alone is how great the separation of the sing-

let and triplet should be. However, a number of quantum mechanical calculations, both semiempirical114,115 and ab initio116,117 suggest the interesting possibility that

the stabilization of the singlet in the 10-p-electron molecule TMB (singlet lower by 5–7 kcal/mol) should be even greater than that predicted, 1–2 kcal/mol, for the hypothetical planar disjoint 6-p-electron species TME. This prediction makes the TMB molecule an important test of the disjoint criterion, because the computed singlet–triplet (S-T) gap is large enough that even theoreticians would probably agree that a finding of a triplet ground state would clearly be a refutation of theory.

TMB (42) was first generated by Roth el al.118 by photochemical decarbonylation of the ketone 44 in a low-temperature matrix. This preparation was intensely colored, with a main transition at 490 nm and several subsidiary absorptions. Earlier p-CI quantum chemical computations116 had predicted ultraviolet–visible (UV-vis) is transitions for the singlet and triplet states of TMB, and the bands observed by the Roth group were in better agreement with the predictions for the triplet. The preparation also showed a narrow ESR spectrum interpreted by the authors118 as that of a triplet species with D ¼ 0.0042 cm 1 and E ¼ 0.0009 cm 1, which gave a linear Curie plot. The authors assumed that the carriers of the UV–vis and ESR spectra were the same species, namely, triplet TMB. They concluded that TMB is a ground-state triplet, contrary to the disjoint theory and to the computational results described above.

However, a repetition of these experiments, supplemented by a variety of other evidence,63,119,120 led to different conclusions. These studies showed that (1) the

purple color and the ESR spectrum are associated with two different species;

(2) the colored species is in fact TMB, but the ESR spectrum is associated not with the TMB triplet but rather with some still unidentified side product; (3) the major irradiation product of the ketone precursor 44 is singlet TMB, as was demon-

strated by solid-state carbon-13 nuclear magnetic resonance 13C NMR spectroscopy. This technique, developed by Zilm and co-workers,121–124 is especially

applicable to the distinction between a singlet and a paramagnetic species, since the latter, a triplet, for example, would give broadened lines in a completely different spectral region, if it can be observed at all, whereas a singlet should show a normal spectrum. The irradiation product from 13CH2-labeled 44 showed a 13C NMR spectrum consisting of a single unbroadened resonance at 113 ppm, a normal position for a CH2 group. The signal intensity correlated well with the intensity of the 490-nm band in the UV–vis spectrum. Thus, the purple species is singlet TMB. No trace of the triplet spin state is formed in the photolysis or after prolonged storage at low temperature. These results are in accord with the theoretical prediction of a singlet ground state for TMB.

There remained the matter of the UV–vis spectra, which as we have seen, agreed better with the calculated116 transitions of the triplet than with those of the singlet. This anomaly was resolved in a new calculation,125 which went beyond the p-CI level used earlier116 and incorporated correlation between the s and p electrons of TMB.

In preparative reactions, alkenes such as fumaronitrile, 1,2-dichloroethylene, styrene, and diethyl fumarate were reported not to capture TMB (photochemically generated by continuous photolysis of ketone 44).126 However, O2 was an efficient trapping agent. The authors126 argued that since other singlet biradicals can be trapped with alkenes, the failure to trap TMB with these reagents pointed to the triplet biradical as the only reactive intermediate. These observations led them to conclude that the singlet–triplet equilibrium must lie strongly on the side of the triplet, in agreement with their interpretation of the ESR spectrum. However, the slow rate of the reaction of TMB singlet with alkenes63 is now attributed to a phase mismatch between the biradical symmetric highest occupied molecular orbital (HOMO) and the alkene antisymmetric lowest unoccupied molecular orbital (LUMO) in the cycloaddition transition state, which prevents a facile cycloaddition.63

Roth et al.126 derived a heat of formation for TMB by kinetically following the reaction of dicyclobutabenzene with O2 in a gas-phase shock tube. They derived a heat of formation for TMB (42) on the assumption that the reaction passed through it as a reactive intermediate. The conclusions must be questioned, however, since a second important assumption of the analysis126 was that the hypothetical biradical– dioxygen reaction occurred at the statistically modified encounter-limited rate, as the authors126 believed to be appropriate for a triplet biradical. With TMB now having been identified as a singlet, this assumption becomes dubious. In fact, in solution, nanosecond time-resolved measurements63 of the rate of disappearance of the flash photochemically generated TMB singlet show that the O2 trapping rate is only about one-thousandth that of the encounter frequency. If, as seems likely, a similar factor exists in the gas-phase reaction, the reported126 value of the heat of formation would require revision.

The O2 trapping experiments also led to an estimate126 that the triplet must lie at

least 5 kcal/mol below the singlet. Again, this finding is inconsistent with other experimental63 and theoretical114–117 findings that all point to a singlet ground state.

Aside from the preceding argument based on the oxygenation kinetics,126 no quantitative experimental estimates of the singlet–triplet separation in TMB have been reported. If a suitable precursor of the TMB radical anion in the gas phase can be made, photodetachment PES of TMB would become a likely way to solve this problem.

7. OTHER TESTS OF CONNECTIVITY THEORIES

7.1. m-Quinone Derivatives

An early attempt36–38 to test the disjoint hypothesis compared the magnetic properties of two isomeric tricyclic m-quinonoid non-Kekule´ molecules: 17, formally a biradical with tetraradical resonance structures, and 18, formally a tetraradical (Section 2.3). These molecules belong to the point groups C2h and C2v, respectively, and it will be mnemonically convenient to use those descriptors in what follows. The test derives from the recognition that the connectivities of the two molecules

NH (46a–c) should have a preference of a few kilocalories per mol for the singlet, but that substitution of a sufficiently strong electron-withdrawing group for the functional hydrogen in the NH compound can reduce the singlet–triplet gap to near zero.

Experiment shows that the furan and thiophene compounds 46a and b and the pyrrole derivatives 46c–e all have singlet ground states, as predicted.127,128 The

N-p-toluenesulfonyl derivative 46f, however, is predicted to have a very small

singlet–triplet gap, with the triplet more stable by 0.4–1.5 kcal/mol, depending on the method of calculation.105,106,130 The calculations suggest that the tuning pro-

cess should reach the crossover point from singlet to triplet in this region, and that consequently 46f might have a detectable triplet state.

The outcome of this study confirms the predicted tuning effect. Irradiation of the diazene 45f at 265 nm gives a well-defined triplet signal in the ESR spectrum that persists in the dark for weeks. Significantly, irradiation of 45f at 365 nm gives a

deep blue preparation that has no detectable ESR signal. Chemical evidence from trapping reactions106,130 shows that both the triplet and singlet species have

the N-tosyl-3,4-dimethylenepyrrole structure. The Curie plot of the triplet has a slight downward curvature at the lowest temperatures, which can be formally fitted to a gap ES ET of 0.02 kcal/mol. This curvature is not because of population of the blue singlet. Were that the case, the amount of triplet present in a blue singlet preparation would have been easily sufficient to detect in the ESR spectrum.130 The predicted crossover to a populatable triplet thus is confirmed. Whether the triplet of 46f is really the ground state becomes an oversimplified question in light of the unexpected persistence of both species, which are stable for weeks at 77 K without interconversion. This long-lived (or persistent) spin isomerism is further discussed in Section 7.2.1.

Another example of tuning the spin state by structural variation within a graded series has been provided by the Dougherty group.131 Ab initio (6-31G* p-CISD) calculations on the model series of pyridinium cations 47–49 suggest that the ordering of the states in each compound is strongly dependent on the position of the pyridinium nitrogen. Although in the corresponding neutral pyridines, all the position isomers show triplet ground states, in the cationic systems, the ground state preference changes from definitely triplet in 47, to near degeneracy in 48, to slightly singlet in 49. Thus, the 3,5- and 2,4-pyridinium units are predicted to be ferromagnetic couplers, but the 2,6-pyridinium unit should be an antiferromagnetic coupler. These simple analogues have not been studied so far, but the predictions have been tested in the series of pyridinium bis-TMM analogues (50–52). The ESR spectra are interpreted131 as indicating quintet, quintet, and triplet ground states for 50, 51, and 52, respectively, and the authors employ these results as support for the theoretical predictions.

7.2.1. Long-Lived (Persistent) Spin Isomerism. The singlet of N-tosyl-3,4- dimethylenepyrrole (46f, Scheme 5.10) is a blue, ESR-silent species that is stable

over many days in cold matrices. The triplet is also stable for days at low temperatures. This type of ‘‘long-lived spin isomerism’’ has been attributed105,106,127,132 to

It should be mentioned that Cambi and Szego137 discovered long-lived spin isomers in the 1930s in the field of transition metal complexes, and they have been extensively investigated since then.138 In some cases, they are sufficiently stable for determination of their crystal structure by X-ray methods. The physical basis for the differences between spin isomers in these complexes seems not to be the result of rotational isomerism but instead to involve differences in the geometrical arrangement of the ligands around the metal atom. In several cases with hexavalent metal centers, these isomers correspond to local minima in the itinerary of distortions from octahedral symmetry. Stereochemical nomenclature is a notoriously contentious area, but at the risk of opprobrium from its cognoscenti, I would venture the suggestion that both the rotational isomerism proposed for the non-Kekule´ systems and the distorted polyhedral isomerism of the complexes could be considered examples of conformational isomerism in which the change in conformation is accompanied by a change in spin state.

8. MEASUREMENT AND INTERPRETATION OF MAGNETIZATION AND MAGNETIC SUSCEPTIBILITY

Notable developments in technique139–141 have made possible the elucidation of characteristics of paramagnetic materials that have not been readily accessible with ESR spectroscopy or gas-phase negative ion photodetachment PES. Foremost among these have been improvements in the design and construction of instruments

for direct measurement of magnetization. The theories of magnetic properties are well established,142–144 and many measurements of magnetization using Guoy or

Faraday blances had been made, especially in the field of inorganic chemistry. The advent in recent years of superconducting quantum interference devices (SQUIDs) has improved the accuracy and convenience of such measurements. The direct magnetic methods can be applied to characterization of both smallmolecule non-Kekule´ compounds and oligomeric or polymeric paramagnetic substances. In favorable cases, it is possible to measure the separation between multiplet states and to recognize mixtures of them. We take a brief detour to introduce some of the key points here.

The alignment of paramagnetic molecules in an applied magnetic field is influenced by two opposing factors: the magnetic energy, gmBHz, which tends to align the spin moments with the field, and the energy of thermal motions, kT, which tend to randomize them. At sufficiently high field and low temperature, the magnetic susceptibility w per mole of a paramagnetic sample is derived from the measured magnetization I in a field H by the relationship w ¼ I=H. Several methods of hand-

ling the experimental data have been described, but for our purposes, it will be simplest to use the effective magnetic moment. It can be shown142–144 that for those

molecules in which spin-orbit coupling can be neglected, which will be the case for most of the systems in this chapter, the dependence of w on the total spin S is usefully expressed by the effective magnetic moment meff (Eq. 4), in which mB is the

Bohr magneton, N is the number of moles in the sample, and g is the (dimensionless) electron free-spin factor (g-factor), which has the value 2.0023.

Experimentally, one thus expects that a triplet paramagnet ðS ¼ 1Þ should dis-

play meff ¼ 2:83mB, a quintet ðS ¼ 2Þ 4.90 mB, and so on. A mixture of two states of different spin should have a value intermediate between the two values. For two

such states in equilibrium, the energy gap can be calculated from the value of w and the Weiss temperature y in the Curie–Weiss law (Eq. 5.)139

2,3,8,131,139,145,146 ´

ors to determine spin states and energy gaps in non-Kekule molecules. They are nicely complementary to ESR spectroscopy. For example, although both techniques are in principle capable of determining ES ET, ESR cannot be used if the gap is too large (> 0:5 kcal/mol) or if the two states happen to be energetically degenerate, whereas these difficulties do not apply to direct magnetic measurements. On the other hand, ESR can report crucial structural information about the species, whereas in the direct magnetic measurements, molecules of the same spin multiplicity are indistinguishable. The ESR spectra become difficult to interpret when the total spin grows large, but direct magnetic measurements can afford values of S for multiple spins3 or even for S values as large as 5000 in a highspin polymer.147

9. WHERE THE DISJOINT AND PARITY-BASED PREDICTIONS DIFFER

The non-Kekule´ compounds we have considered so far are all structurally related to TMM and TME, and the disjoint and parity methods for predicting qualitatively the ground-state spin give similar results. However, the two methods do not agree in the case of another type of non-Kekule´ structure, of which the parent compound is the biradical 2,3,4-trimethylenepentane-1,5-diyl (56), commonly called pentamethylenepropane (PMP) (Scheme 5.11).

connectivity

Scheme 5.11