-A Comparative Study with Trimethylenemethane-

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Dowd synthesized TMM and observed its ESR spectrum in a frozen matrix [2]. A recent photoelectron spectroscopic study on TMM radical anion reports the direct determination of the singlet-triplet energy splitting [3]. Thus the triplet ground state of TMM has been established both theoretically and experimentally. The essential origin of the high-spin state is twofold-degenerate NBMOs.

Since Mataga [4] and Ovchinikov [5] suggested the possibility of organic ferromagnets based on MO (Molecular Orbital) and VB (Valence Bond) method, respectively, many high-spin hydrocarbons have been synthesized [6, 7]. High-spin states often have been found in heteroatom-containing systems and their stabilities have been established by molecular orbital studies [8 - 10]. In particular, there has been increasing interest in nitrogen-centered radicals such as aminium radicals because they can be isolated as cationic radical salts in solid states. Recent studies on magnetic properties of aminium radicals are aimed to realize not only high-spin organic molecules but also organic ferromagnets [11 - 14].

In our previous work [14], we designed polyguanide- and polyuret-based ferromagnets taking account of the non-Kekule character of nitrogen-centered radicals. In this paper we investigate the spin states of non-Kekule-type molecule triiminiummethane ion (TIM

TIM

In order to clarify the spin states of TIM

Figure 1. Molecular structures (a) TMM and (b) TIM^{3+}. The resonance structures represent the non-Kekule character of these molecules.

Because TIM

While the triplet state probably prefers D

The zeroth-order approximate wavefunctions of the energetically low-lying states created by the frontier two electrons are also shown in Figure 2. These wavefunctions satisfy the spin symmetries.

We note that the wavefunctions of the

In the actual computations, we employed semiempirical MO method PM3 [18] because our main interest is qualitative high-spin stability of TIM

Considering the basic perspective as mentioned above, we calculated the optimized geometries and the relative energies of low-lying electronic states of TIM

In order to obtain the optimized geometries and the relative energies we employed CI (Configuration Interaction) method because the electronic states are degenerate. The reference configurations were created by ROHF (Restricted Open-Shell Hartree-Fock) wavefunctions and the active spaces were spanned by four p-orbitals including two NBMOs. The geometrical optimizations were carried out under constraints of D

Figure 2. Schematic non-bonding molecular orbitals (NBMOs) of TMM and possible wavefunctions created by frontier two electrons. The symmetry classifications are given for D_{3h} (C_{2v}) point group.

Figure 3. Optimized geometries and relative energies of TMM and TIM^{3+} at the PM3-CI level of theory.

We direct our attention to the singlet-triplet energy splittings of planar TMM because photoelectron spectroscopy of TMM anion radical has determined the ^{1}A_{1}-^{3}A_{2}' energy splitting to be 16.1 ±0.1 kcal/mol [3]. Our calculation estimated the ^{1}A_{1}-^{3}A_{2}' energy splitting to be 14.2 kcal/mol. This value is close enough to the experimental result. Recent ab initio studies also have predicted that the lowest planar singlet state is Jahn-Teller distorted ^{1}A_{1} and the twisted ^{1}B_{1} state lies 0-6 kcal /mol below the ^{1}A_{1} state [3, 17]. We feel that PM3-CI calculation is sufficient for not only qualitative but also quantitative estimation of the high-spin stabilities. Our main interest is, however, the qualitative description of high-spin stability of TIM^{3+} as an analogy of TMM, as emphasized above.

Let us consider the spin states of TIM^{3+}. The triplet ground state ^{3}A_{2}' with a D_{3h} geometry was predicted to lie below any singlet state similar to TMM. The singlet states ^{1}B_{1}, ^{1}B_{2} and ^{1}A_{1} were nearly degenerate. The lowest singlet state was predicted to be ^{1}B_{1} and have a C_{2v} geometry in which one of the amino groups was twisted. This state was predicted to lie 9.1 kcal/mol above the ^{3}A_{2}' state. The 1B_{2} state with an open-shell configuration was predicted to have a planar C_{2v} geometry in which one of the C-N bonds was longer than those of the other two. In contrast to the ^{1}B_{2} state, the ^{1}A_{1} state with a closed-shell configuration was predicted to have a planar C_{2v} geometry in which one of the C-N bonds was shorter than those of the other two. The singlet-triplet splitting energies were about 3 kcal/mol lower than those of TMM.

According to Ovchinikov's paper [5], any conjugated system is described within a framework of the VB theory and the spin state is analyzed using the Heisenberg Hamiltonian (Equation 1), where *J _{ij}* is the exchange integral (

The expectation value of this Hamiltonian is minimized when all localized spins have opposite direction. Such an alternation of spins is called 'spin polarization' [20]. Therefore, it is worthwhile to calculate the spin distribution of TIM

The p-spin densities coming from the 2p

Figure 4. p-spin densities of the triplet states of (a) TMM and (b) TIM^{3+} at the PM3-UHF//PM3-CI level of theory. <**S**^{2}> is the spin-squared expectation value.

The VB analysis using resonance structures is perhaps most intuitive to explain this situation. Figure 5 shows the resonance structures of TMM (Figure 5(a)), TIM^{3+} (Figure 5(b)) and iminiumdimethylenemethane ion (IDMM^{+} :Figure 5(c)) which is a mono-aza analog of TMM. TMM and TIM^{3+} are isoelectronic and their ground states are described in the left hand side of Figure 5(a) and (b) with D_{3h} geometries and no bond alternation. These resonance structures are consistent with the calculated geometries. We can expect their triplet ground states from the resonance structures containing three biradical contributions described in Figure 5(a) and (b). In TIM^{3+} the spin-paired structure is very unstable because the formal charge of one of the nitrogen atoms is +2 (Figure 5(b)). The main contributor is described not by one resonance structure but by three equivalent biradical structures. Thus the essential character of TIM^{3+} seems to be well described by the most left hand side in Figure 5(b) in which positive charges are delocalized on not only the nitrogen atoms and but also the carbon atom.

Interestingly, IDMM^{+} is predicted to have a singlet ground state [21]. This is explained using resonance structures in the right-most hand in Figure 5(c). The spin-paired structures in which the positive charge is localized on carbon atoms are more stable than that of the biradical structure in the left hand side because the electronegativity of the nitrogen atom is higher than that of the carbon atoms. The summed group charges of the ground state of IDMM^{+} are reported in [21]; amino group; +0.05, central carbon; +0.15, methylene group; +0.40. Thus the ground state of IDMM^{+} is expected to be singlet. Although TIM^{3+} is a tri-aza analogue of TMM, we can expect the triplet ground state because the spin-paired structures are very unstable as mentioned above.

In order to confirm the VB analysis as described above, we calculated the net atomic charges of TMM and TIM^{3+} using the UHF method under the geometries at the PM3-CI level of theory. The charge distributions of triplet TMM and TIM^{3+} obtained by the UHF calculations are shown in Figure 6(a) and (b), respectively. In TMM the net atomic charge is almost zero. On the other hand, the net atomic charge of TIM^{3+} is delocalized on all atoms. The central carbon is also positively charged as well as the nitrogen atoms. This is consistent with the qualitative analysis as mentioned above.

Figure 5. Resonance structures of (a) TMM, (b) TIM^{3+} and (c) IDMM^{+}.

Figure 6. Charge distributions of (a) TMM and (b) TIM^{3+} at the PM3-UHF//PM3-CI level of theory.

[ 2] P. Dowd,

[ 3] P. G. Wenthold, J. Hu, R. R. Squires, W. C. Lineberger,

[ 4] N. Mataga,

[ 5] A. A. Ovchinikov,

[ 6] H. Iwamura,

[ 7] A. Rajca,

[ 8] K. Yoshizawa, M. Hatanaka, A. Ito, K. Tanaka and T. Yamabe,

[ 9] K. Yoshizawa, M. Hatanaka, Y. Matsuzaki, K. Tanaka and T. Yamabe,

[10] K. Yoshizawa, T. Kuga, T. Sato, M. Hatanaka, K. Tanaka and T. Yamabe,

[11] K. Yoshizawa, M. Hatanaka, H. Ago, K. Tanaka and T. Yamabe,

[12] H. Murata, M. Takahashi, K. Namba, N. Takahashi, and H. Nishide,

[13] H. Murata, D. Miyajima, R. Takada and H. Nishide,

[14] M. Hatanaka and R. Shiba,

[15] H. A. Jahn and E. Teller,

[16] H. C. Longuet-Higgins,

[17] C. J. Cramer and B. A. Smith,

[18] J. J. P. Stewart,

[19] J. J. P. Stewart,

[20] K. Yamaguchi, Y. Toyoda and T. Fueno,

[21] J. Li, S. E. Worthington and C. J. Cramer,

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