J. Phys. Chem. 1996, 100, 4775-4780
4775
Is Ferromagnetic Spin Coupling Constant within Homologous Di- and Triradicals? Shuhua Li, Jing Ma, and Yuansheng Jiang* Department of Chemistry, Nanjing UniVersity, Nanjing, 210093, People’s Republic of China ReceiVed: August 8, 1995; In Final Form: December 7, 1995X
By means of the powerful Lanczos algorithm, the nonempirical valence bond (VB) model has been applied to investigate the low-lying electronic states for three typical types of homologous π-conjugated di- and triradicals. For small radicals including trimethylenemethane, cyclopentadienyltrimethylenemethane, mbenzoquinodimethane, and trimethylenebenzene, our VB results are in remarkable agreement with those obtained from previous sophisticated ab initio molecular orbital calculations. By using the energy difference between the high-spin ground and first excited states for these molecules, the strength of ferromagnetic coupling in these diradicals and their homologous triradicals has been discussed in detail. Our results reveal that ferromagnetic coupling in diradicals TMM and BQDM will decrease to different extent in their homologous triradicals. However, ferromagnetic coupling strength between two “unpaired” electrons in DCPP is found to be 9 times larger than that in its component diradical CPTMM.
Introduction The rational design and synthesis of organic magnetic materials is an area of active research today.1 One strategy being currently pursued2,3 is shown schematically in Figure 1. A high-spin material can be constructed by two building blocks: the spin-containing unit (SC) and the ferromagnetic coupling unit (FC). The SC is simply any structure that provides the unpaired electrons, and the FC is a general structural unit that ferromagnetically couples any two or more SCs. As has been stressed previously,4 the key element to the design of new magnetic materials is the FC. To evaluate the effectiveness of a FC, one usually studies a relevant diradical with triplet ground state, which is composed of two simple radicals (the SCs) linked through the FC. The singlet-triplet (S-T) energy gap identifies the strength of the spin coupling through the FC. Therefore, numerous experimental and theoretical works have been performed to assess the S-T energy gaps in diradicals.5-13 However, for designing polymer or solid ferromagnets, we must answer another key question, i.e., whether strong ferromagnetic coupling in diradicals can be maintained in extended systems with more than two unpaired electrons; for example, is “J” constant within homologous di-, tri-, and polyradicals?14,15 In the present work, we probe this problem by investigating the spin coupling in three typical π-conjugated diradicals TMM, BQDM, and CPTMM and their homologous triradicals16 (Figure 2). Among them, TMM is the simplest π-conjugated diradical, BQDM has been the subject of extensively experimental and theoretical studies in recent years,6,12,17 and CPTMM is a member of nonalternant, non-Kekule´ hydrocarbons. Although for TMM, BQDM, and CPTMM the S-T splittings have been obtained by performing sophisticated ab initio calculations within the molecular orbital (MO) theory,5,6,8 less work has been done for their homologous triradicals due to the size of these molecules except for TMB, which has been studied at the unrestricted Hartree-Fock (UHF) level. Here we employed the nonempirical valence bond (VB) approach, first introduced by Said et al.,17 which has proven to provide very reliable results for the low-lying states of organic π-conjugated hydrocarbons.18,19 With the aid of the powerful computational algorithm X
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4775$12.00/0
Figure 1. Schematic for design of high-spin molecules and materials. The arrow reprsents the SCs.
Figure 2. Selected diradicals and their homologous triradicals.
we recently introduced,15,20 we can solve the nonempirical VB model exactly for these molecules; thus, the reliable energy gaps between the high-spin ground and first excited states and optimized geometries can be obtained. It should be acknowledged that Said et al. have already studied the compounds TMM and BQDM in their original paper,17 and our subsequent calculations reproduced their results, but we presented the results of these two molecules for the purpose of systematization and comparison. On the basis of these energy gaps, we compared the strength of ferromagnetic coupling in these diradicals and their homologous triradicals and gained an insight into to what extent spin couplings in diradicals are maintained in their homologous triradicals, respectively. For simplicity, in the following we call ferromagnetic coupling through corresponding FCs in radicals ferromagnetic coupling in radicals for short. Method 1. Nonempirical Valence Bond Model. Said et al.17 proposed a very simple nonempirical valence bond (also called © 1996 American Chemical Society
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Heisenberg-type) Hamiltonian which has been extracted from ab initio extended basis set CI calculations on ethylene lowest singlet and triplet states. The two parameters of the model incorporate the σ and π energy dependence to the bond length and bond twisting. This model has been proved to give very reliable predictions on the low-lying states of conjugated hydrocarbons at a low expense.18,19 This effective VB Hamiltonian can be written as
H ) ∑[Rij + gij(ai ahj ajahi + ahi aj ahj ai +
+
+
TABLE 1: Energy Difference between the Ground and First Excited States for TMM and TMP and Reduced Spin-Coupling Constants molecule
state
energya
∆Eb
coupling constant (J)c
TMMd (D3h)
3A ′ 2 1A 1 1B 2 4B 2 2 A1
-0.152 50 -0.097 67 -0.097 43 -0.299 14 -0.275 44
34.4 34.5
17.2 17.2
14.9
14.9
TMP (C2V)
+
a
i-j
ai+ahj +ahj ai - ahi +aj+ajahi )] (1)
In units of atomic units. b Energy (in kcal/mol) relative to the respective ground state. c In units of kcal/mol. d In the distorted singlet state TMM has C2V symmetry.
where Rij is a scalar characterizing the σ-bond force field and gij is the effective exchange coupling between bonded atoms i and j. The interatomic distance rij and the torsional angle θij dependence of Rij and gij are given in ref 17. When the VB Hamiltonian (1) is applied to a polyatomic molecule in a definite conformation, the total energy can be expressed as
E ) ∑(Rij - 2gijPijs)
(2)
i-j
where Pijs is the probability of finding a π singlet arrangement between the bonded atoms i and j, and it is related to a given eigenstate Ψ of the Hamiltonian (1).
Pijs ) 1/2〈Ψ|(ai+ahj + - ahi +aj+)(ahj ai - ajahi )|Ψ〉
(3)
2. Computational Details. The VB Hamiltonian (1) operates solely on the basis of neutral Slater determinants, which consists of all possible ways of distributing spin-up or spindown to these singly occupied orbitals consistent with the required total spin of the molecule state. The dimensions of this space increase rapidly with increasing the size of molecule, so the efficient technique for the diagonalization of large matrices is essential to the solution of this Hamiltonian. In our previous works,15,20 we have demonstrated that the Lanczos method21 is applicable to the treatment of the semiempirical VB model. We will employ this technique to solve the nonempirical VB Hamiltonian (1) exactly and calculate the VB low-lying states. Then the geometry optimization according to eq 2 may proceed from bond to bond,
∂g ∂Pijs ∂Pkls ∂E ∂Rij s ij ) - 2Pij - 2gij + ∑2gkl ∂rij ∂rij ∂rij ∂rij ∂rij kl
(4)
(and an analogous equation for the twist angle around the ij bond). Since the wave function is almost stationary near the energy minimum, one may neglect the derivative of the wave function characteristic and use17
∂gij ∂E ∂Rij = - 2Pijs ∂rij ∂rij ∂rij
(5)
Figure 3. Optimized geometries of the ground and first excited states for TMM and TMP. The planar structures are assumed for the lowlying states of these two molecules. The corresponding bond lengths in parentheses come from ref 5. The bond lengths are in angstroms.
Using this computational method, we have optimized the geometries of the ground and first excited states for a series of π-conjugated radicals. In our calculations, the low-lying states of these molecules were assumed to have planar structures for simplicity, and we imposed a tolerance of 10-3 energy gradient norm. This results in an error of 10-3 Å for the bond lengths and less than 10-5 au for the energies. Results and Discussion 1. TMM and TMP. The calculated energies of the ground and first excited states of TMM and TMP are summarized in Table 1, and the optimized geometries are depicted in Figure 3. It is interesting to compare our results with those from Dixon et al.’s ab initio MCSCF calculations5 (as also shown in Figure 3). Clearly, our calculated bond lengths for the triplet ground state and two nearly degenerate distorted singlet states (due to a Jahn-Teller effect) agree very well with theirs; the calculated S-T splitting (3A2′-1A1) is 34.4 kcal/mol, considerably larger than their value of 21.2 kcal/mol. This implies that this method tends to overestimate to some extent the preference for highspin states compared with the post-HF ab initio methods. In fact, our subsequent calculations for other molecules also demonstrate this point. The reason for this may be the neglect of the second nearest neighbor interactions in this nonempirical VB model,17 which would stabilize low-spin states, as shown below in TMM. Despite the inherent drawback in this model,
The dependence on rij of Rij and gij yields a rapid and very efficient energy minimization by imposing the condition S=1
∂E )0 ∂rij which yields an optimized value for rij.
(6)
S=0 *
*
(I)
*
this method is still the best candidate for our qualitative or even semiquantative investigation about the spin-coupling strength
Ferromagnetic Spin Coupling in Di- and Triradicals
J. Phys. Chem., Vol. 100, No. 12, 1996 4777
TABLE 2: Energy Difference between the Ground and First Excited States for CPTMM and DCPP and Reduced Spin-Coupling Constants molecule
state
energya
∆Eb
coupling constant (J)c
CPTMM (C2V)
3B 2 1A 1 4A u 2A g
-0.379 21 -0.375 28 -0.751 43 -0.730 81
2.5
1.2
12.9
12.9
DCPP (Ci) a
b
In units of atomic units. Energy (in kcal/mol) relative to the respective ground state. c In units of kcal/mol.
in these systems we studied. For the electronic states of TMP, it should be noticed that only the central bond lengths in the quartet state are shorter than those in the doublet state, and the external bond lengths nearly remain the same in these two states. The doublet-quartet (D-Q) separation we obtained is 14.9 kcal/ mol. Now we discuss the problem concerning the spin coupling through vinylidene as the FC in TMM and TMP. In dealing with the spin of diradicals, chemists usually start by assuming that a diradical is composed of two “unpaired” electrons coupled through a bridge unit, with a coupling constant J characterized by the spin-coupling unit.14 In accordance with this idea, TMM and TMP can be represented by the following “molecules”, where circles denote “unpaired” electron centers and edges signify the spin coupling through FCs. In general, coupling (II) J
J′
J′
constant J ′ in the triradical may be different from J in the diradical. Using the VB model, one can easily evaluate J and J ′ from the relations ∆EST ) 2J and ∆EDQ ) J ′ for these two topological systems, respectively. The calculated J and J ′ have been collected in Table 1. One can find that the coupling constant in TMP only decreases by a factor of about one-tenth. This may be qualitatively interpreted by comparing the positions of the radical centers in the TMM fragment of TMP with those in a single TMM. Since the positions with larger spin densities can be considered as the radical centers, we can determine these radical sites for free radicals with an odd number of electrons by performing spin density calculations by means of the VB wave functions.22 For the quartet state of TMP, we displayed the calculated spin densities in the following. In contrast with
Figure 4. Optimized geometries of the ground and first excited states for CPTMM and DCPP. The planar structures are assumed for the lowlying states of these two molecules. The corresponding bond lengths in parentheses come from ref 8. The bond lengths are in angstroms.
the difference of the dominant valence bond structures for these two states. By calculating the projection of a certain valence bond structure on the wave function of both states, we can easily evaluate the relative importance of this valence bond configuration in these two states. Our results (not shown) are consistent with those derived from ab initio calculations.8 The calculated S-T splitting of CPTMM is 2.5 kcal/mol, lower than the ab initio estimate of 4.9 kcal/mol. Obviously, this value is far less than ∆EST we obtained above for TMM. Since CPTMM can be viewed as TMM with one methylene group replaced by cyclopentadienyl, one would like to know why this circumstance occurs. To demonstrate this point qualitatively, we may refer to the Ovchinnikov’s rule, which says that for 〈SZ〉 the lessspin-frustrated spin distributions determine the nature of the ground state. The small ∆EST for CPTMM is due to the fact that
(III)
the radical sites of TMM illustrated in Figure 3, we find that the radical sites in TMP nearly keep their original positions in the single TMMs. This may be responsible for the approximate maintenance of strong ferromagnetic coupling in TMP. 2. CPTMM and DCPP. For two low-lying electronic states of CPTMM and DCPP, we reported their energies in Table 2 and their optimized geometries in Figure 4. For comparison, the optimized structures of CPTMM in the lowest singlet and triplet state obtained by means of MCSCF(8,8) SDmethod8 have also been cited. Surprisingly, the bond lengths obtained with our VB model are fairly close to those obtained by means of the ab initio MCSCF method for both the 3B2 and 1A1 states of CPTMM. As pointed out previously,8 the significant difference between the structures of 3B2 and 1A1 states can be ascribed to
present the same minimal number of spin frustrations. On the contrary for TMM, one finds spin distributions accepting different minimal frustrations for 〈SZ ) 1〉 and 〈SZ ) 0〉, as shown below.
(IV)
Consequently, it is understandable that the S-T energy gap of CPTMM is very low relative to the corresponding value of TMM, and at most CPTMM behaves as a “spin-diluted” TMM.14 It should be pointed out that for larger molecules this simple analysis will gradually lose its effectiveness, because with increasing the size of molecules other spin distributions
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Figure 5. Optimized geometries of the ground and first excited states for BQDM, TMB, and DMPM. The planar structures are assumed for the low-lying states of these three molecules. The corresponding bond lengths in parentheses come from ref 6 for BQDM and ref 9 for TMB. The bond lengths are in angstroms.
except less-spin-frustrated spin configurations may play an important role in the nature of the lowest eigenstate. DCPP is constructed by connecting two CPTMMs in a linear arrangement by sharing a carbon atom, and so far its electronic structures may have not yet been elucidated due to its size. From the calculated results displayed in Figure 4, it is seen that in the ground quartet state (4Au) of DCPP the C-C bond lengths in the cyclopentadienyl are the same as in the triplet state (3B2) of CPTMM and also vary negligibly in the lowest doublet state (2Ag) of DCPP. The geometrical difference between the quartet and lowest doublet states of DCPP emerges significantly in its remainder part, the TMP fragment. That is to say, the large D-Q splitting of DCPP, 12.9 kcal/mol, primarily results from the geometrical difference of the TMP fragment in these two states. To further verify this inference, we presented the calculated spin densities in the quartet state of DCPP in the following. As expected, almost three radical sites all concentrate
(V)
on the TMP part and exhibit the similar distribution as in a separate TMP molecule (see (III)). Due to this similarity, the D-Q energy separation of DCPP is quite close to that of TMP. As done for TMM and TMP, we also calculated spin-coupling constants in CPTMM and DCPP, which are tabulated in the last column of Table 2. To our surprise, we find that the spincoupling constant in DCPP is about 9 times larger than that in
TABLE 3: Energy Difference between the Ground and First Excited States for BQDM, TMB, and DMPM and Reduced Spin-Coupling Constants molecule BQDM (C2V)
3
B2 A1 4A ′′ 2 2A 2 2B 1 4B 2 2A 1 1
TMBd (D3h) DMPM (C2V) a
energya
state
-0.406 03 -0.360 50 -0.439 19 -0.393 58 -0.393 35 -0.801 91 -0.784 99
∆Eb
coupling constant (J)c
28.5
14.2
28.6 28.8
9.5 9.6
10.6
10.6
b
In units of atomic units. Energy (in kcal/mol) relative to the respective ground state. c In units of kcal/mol. d In the distorted doublet states TMB has C2V symmetry.
CPTMM. By analogy with TMM and TMP, we have qualitatively interpreted this circumstance. Our results for DCPP may present a novel picture of magnetic interaction, where the spincoupling strength between two “unpaired” electrons can even be amplified in extending diradicals to homologous triradicals in some cases, as exemplified above. 3. BQDM, TMB, and DMPM. The ab initio calculations have been carried out on the ground and first exited states of BQDM and TMB.6,9 To our knowledge, the low-lying states of DMPM are still unknown. To compare the spin-coupling strength in diradical BQDM with those in its homologous triradicals TMB and DMPM in a unified way, we reported our nonempirical VB calculations for these molecules in Figure 5 and Table 3. In the following, we will first make some comparison between our results and the available ab initio MO results6,9 and then discuss the extent to which spin coupling in BQDM will be maintained in TMB and DMPM, respectively. For the 3B2 state of BQDM, almost each C-C bond length predicted by our method is at least 0.02 Å shorter than that optimized with UHF calculations.6 Because the previous works23,24 have demonstrated that large CI or MCSCF calculations are essential to the geometry optimizations of radicals, we might think that C-C bond lengths are probably overesti-
Ferromagnetic Spin Coupling in Di- and Triradicals mated by means of the UHF scheme. While in the 1A1 state of BQDM, our predicted bond lengths are in better agreement with those obtained from the two-configuration SCF (TCSCF) scheme,6 which provides relatively more electron correlation for the singlet states of diradicals. Accordingly, the S-T energy separation we obtained is 28.5 kcal/mol, which is larger than the UHF value of 10 kcal/mol. This difference can be ascribed to the same reason mentioned above. TMB is the typical triradical of current interest, which has been discussed by Yoshizawa et al.9 in detail at the UHF level using the 6-31G basis set. We cited their results in parentheses together with our VB results in Figure 5 for the purpose of comparison. At first sight, we find our VB calculations correctly predicted the symmetries of these low-lying states despite the fact that our geometry optimizations have been carried out without the constraint of symmetry.9 Secondly, for the ground 4A ′′ state, the trend of bond lengths predicted by both 2 approaches is consistent, yet slightly shorter C-C bond lengths have been obtained by the VB approach. Thirdly, since the lowest doublet 2E′′ state in the D3h geometry is subject to the first-order Jahn-Teller distortions which remove the degeneracy, TMB prefers the distorted structures in its lowest doublet state. This inference has also been confirmed by our results. One of the distorted doublets (2A2 state) is found to have an elongated geometry in which one of the three vinylidene C-C bonds is much larger than the other two, whereas for another doublet (2B1 state), it prefers a compressed geometry in which one of vinylidene C-C bonds is 0.06 Å shorter than the other two. The correlation between these predictions and those from Yoshizawa et al.’s ab initio calculations is fairly good; thus, it is expected this correlation will be further improved at the higher level within the MO framework, as has been pointed out above. In addition, the 2A2 state is predicted to be only 0.2 kcal/mol lower in energy than the 2B1 state, implying that these two states are nearly degenerate. This result is not in agreement with the UHF ab initio calculations,9 in which the energy difference between these two states is 22.5 kcal/mol. On the other hand, the D-Q energy gap (4A2′′-2A2) is equal to 28.6 kcal/mol, nearly 2 times the ab initio value of 14.5 kcal/mol at the UMP2/ 6-31G*//UHF/6-31G level. On the basis of the argument described above, TMB can be viewed as a regular triangle molecule with an equal ferromagnetic coupling constant J between two nearest neighbor sites, satisfying ∆EDQ ) 3J. Consequently, the ferromagnetic coupling constant in triradical TMB is predicted to be 9.5 kcal/mol, which is about two-thirds the coupling constant in BQDM. Let us return to the electronic states of DMPM. In the quartet state of this species, the C-C bond lengths in each constituting a BQDM fragment are very close to those corresponding values in the triplet state of the isolated BQDM, provided small deviations occur in those bonds near the bridge carbon atom, but for the lowest doublet state, the geometry of each BQDM fragment is quite different from that of isolated BQDM in the singlet state, reflecting that the spin polarization of the π electrons on one BQDM fragment induced by another connected one sharing a bridge carbon atom is relatively larger in the doublet state than in the quartet state. The quartet 4B2 state is predicted to be 10.6 kcal/mol lower in energy than the lowest doublet 2A1 state, indicating that the nearest neighbor ferromagnetic coupling constant is also 10.6 kcal/mol according to the above discussions. This implies that about three-fourths of spin coupling strength in BQDM will be maintained in DMPM. Conclusions With the aid of the powerful Lanczos algorithm, this paper has applied the nonempirical VB model extracted from high-
J. Phys. Chem., Vol. 100, No. 12, 1996 4779 quality ab initio MO calculations on ethylene to investigate the low-lying electronic states for three types of homologous π-conjugated di- and triradicals. For the low-lying states of small molecules including TMM, CPTMM, BQDM, and TMB, our VB results are in remarkable agreement with those obtained from previous sophisticated ab initio MO calculations. This again indicates that this nonempirical VB approach can provide very reliable results for the low-lying states of π-conjugated radicals. For the ground quartet and lowest doublet states of TMP, DCPP, and DMPM, we have first reported their electronic structures and given a detailed analysis in terms of a chemically simple concept. On the basis of the energy separations between the high-spin ground and first excited states, ferromagnetic coupling strength in these radicals has been compared and discussed, leading to the conclusions as follows. 1. Ferromagnetic coupling in diradical TMM will decrease by a factor of one-tenth in its “linear” triradical TMP. 2. Ferromagnetic coupling in BQDM can be maintained to a large extent of three-fourths in its “linear” triradical DMPM and two-thirds in its “cyclic” triradical TMB. 3. In “linear” triradical DCPP, ferromagnetic coupling strength will increase severely by 9 times relative to that in its component diradical CPTMM. Among the above conclusion 3 is interesting, which may enrich our understanding of ferromagnetic coupling in extended systems. From the other two conclusions, it can be anticipated that calculated spin-coupling constants in triradicals TMP and DMPM will be dominantly maintained, approaching a definite value, in their homologous polyradicals, even polymer ferromagnets, respectively. In the past decades, a large number of high-spin organic molecules based on the various FCs such as m-phenylene have been synthesized and characterized.3,25-27 However, the mechanism of magnetic coupling in these systems was less known until now. The results presented in this paper may increase our understanding of this problem and may stimulate organic chemists to synthesize stable high-spin molecules and higher temperature organic ferromagnetic materials. Acknowledgment. This work was supported by China NSF. References and Notes (1) (a) Miller, J. S.; Epstein, A. J. In New aspects of organic chemistry; Yoshida, Z., Shiba, T., Ohsiro, Y., Eds.; VCH Publishers: Berlin, 1989; p 237. (b) Iwamura, H. AdVan. Phys. Org. Chem. 1990, 26, 179-253. (2) (a) Dougherty, D. A. Mol. Cryst. Liq. Cryst. 1989, 176, 25-32. (b) Novak, J. A.; Jain, R.; Dougherty, D. A. J. Am. Chem. Soc. 1989, 111, 7618-7619. (c) Dougherty, D. A. Pure Appl. Chem. 1990, 62, 519-524. (d) Kaisaki, D. A.; Chang, W.; Dougherty, D. A. J. Am. Chem. Soc. 1991, 113, 2764-2766. (3) Jacobs, S. J.; Shultz, D. A.; Jain, R.; Novak, J.; Dougherty, D. A. J. Am. Chem. Soc. 1993, 115, 1744-1753. (4) Silverman, S. K.; Dougherty, D. A. J. Phys. Chem. 1993, 97, 13273-13283. (5) Dixon, D. A.; Dunning, T. H., Jr.; Eades, R. A.; Kleier, D. A. J. Am. Chem. Soc. 1981, 103, 2878-2880. (6) Kato, S.; Morokuma, K.; Feller, D. ; Davidson, E. R.; Borden, W. T. J. Am. Chem. Soc. 1983, 105, 1791-1795. (7) Do¨hnert, D.; Koutecky, J. J. Am. Chem. Soc. 1980, 102, 17891796. (8) Nachtigall, P.; Dowd, P.; Jordan, K. D. J. Am. Chem. Soc. 1992, 114, 4747-4752. (9) (a) Yoshizawa, K.; Hatanaka, M.; Matsuzaki, Y.; Tanaka, K.; Yamabe, T. J. Chem. Phys. 1994, 100, 4453-4458. (b) Yoshizawa, K.; Hatanaka, M.; Ito, A.; Tanaka, K.; Yamabe, T. Chem. Phys. Lett. 1993, 202, 483-488. (10) Coolidge, M. B.; Yamashita, K.; Morokuma, K.; Borden, W. T. J. Am. Chem. Soc. 1990, 112, 1751-1754. (11) Ishida, T.; Iwamura, H. J. Am. Chem. Soc. 1991, 113, 4238-4241. (12) See, for example: Platz, M. S. In Diradicals; Borden, W. T., Ed.; Wiley-Interscience: New York, 1982; pp 195-258.
4780 J. Phys. Chem., Vol. 100, No. 12, 1996 (13) Du, P.; Hrovat, D. A.; Borden, W. T.; Lahti, P. M.; Rossi, A. R.; Berson, J. A. J. Am. Chem. Soc. 1986, 108, 5072-5074. (14) Rajca, A. Chem. ReV. 1994, 94, 871-893. (15) Li, S. H.; Ma, J.; Jiang, Y. S. Chem. Phys. Lett., in press. (16) For simplicity, all our studied molecules are identified in terms of their abbreviated names in the text. Their corresponding original names are as follows: trimethylenemethane (TMM), tetramethylenepropane (TMP), cyclopentadienyltrimethylenemethane (CPTMM), 2,4-dicyclopentadienylidenepentane (DCPP), m-benzoquinodimethane (BQDM), 1,3,5-trimethylenebenzene (TMB), and bis-(3-methylenephenyl)methane (DMPM). (17) Said, M.; Maynau, D.; Malrieu, J. P.; Garcia Bach, M. A. J. Am. Chem. Soc. 1984, 106, 571-579. (18) Said, M.; Maynau, D.; Malrieu, J. P. J. Am. Chem. Soc. 1984, 106, 580-587. (19) Cioslowski, J. Theor. Chim. Acta 1989, 75, 271-278. (20) Li, S. H.; Jiang, Y. S. J. Am. Chem. Soc. 1995, 117, 8401-8406. (21) Lanczos, C. J. Res. Natl. Bur. Stand. 1950, 45, 255-297. (22) Maynau, D.; Said, M.; Malrieu, J. P. J. Am. Chem. Soc. 1983, 105, 5244-5252.
Li et al. (23) Borden, W. T. In Diradicals; Borden, W. T., Ed.; WileyInterscience: New York, 1982; pp 1-72. (24) See, for instance: (a) Davidson, E. R.; Borden, W. T. J. Chem. Phys. 1977, 67, 2191-2197. (25) Borden, W. T.; Davidson, E. R.; Feller, D. J. Am. Chem. Soc. 1981, 103, 5725-5731. (c) Lahti, P. M.; Rossi, A.; Berson, J. A. J. Am. Chem. Soc. 1985, 107, 4362-4363. (26) (a) Rajca, A. J. Am. Chem. Soc. 1990, 112, 5891-5892. (b) Rajca, A.; Utamapanya, S.; Xu, J. T. J. Am. Chem. Soc. 1991, 113, 9235-9241. (27) Rajca, A.; Utamapanya, S. J. Am. Chem. Soc. 1993, 115, 23962401. (28) (a) Veciana, J.; Rovira, C.; Ventosa, N.; Crespo, M. I.; Palacio, F. J. Am. Chem. Soc. 1993, 115, 57-64. (b) Veciana, J.; Rovira, C.; Crespo, M. I.; Armet, O.; Domingo, V. M.; Palacio, F. J. Am. Chem. Soc. 1991, 113, 2552-2561.
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