A theoretical explanation of the organic ferromagnetism in the β-phase of para-nitrophenyl nitronyl nitroxide

Volume 207, number 1

CHEMICAL PHYSICS LETTERS

14May 1993

A theoretical explanation of the organic ferromagnetism in the P-phase of para-nitrophenyl nitronyl nitroxide M. Okumura Department

ofChemistry,Faculty of Science, Hokkaido University, Sapporo 060, Japan

K. Yamaguchi, M. Nakano and W. Mori Department of Chemistry, Fatuity of Science, Osaka University, Toyonaka, Osaka 560, Japan

Received 16 September 1992; in final form 20 February 1993

Molecular orbital calculations have been carried out for clusters of para-nitrophenyl nitronyl nitroxide (pNPNN) extracted from the experimental crystal structure of its p-phase. Three-dimensional effective exchange integrals (&,) are found to be positive (ferromagnetic). The ferromagnetic transition temperature is estimated by a generalized Langevin-Weiss model combined with the calculated Jab, being consistent with the observed value. A theoretical explanation is presented for the long-range ferromagnetic ordering in the pNPNN crystal. Implications of the calculated results are also discussed in relation to a theoretical possibility of organic ferromagnetism of other substituted phenyl nitronyl nitroxides.

1. Introduction Previously, the ab initio orbital (MO) method and extended McConnell model (EMM) were applied to calculations of intermolecular effective exchange integrals (Jab) for clusters of various nitroxides such as diphenyl nitroxide (DPNO) [ 1 ] and phenyl nitronyl nitroxides (PNNO) with donor or acceptor groups [2,3]. It was found that the Jab values are positive (ferromagnetic) for the idealized stacked structures of clusters of these species. The spin-wave theory [4,5] was also applied to estimate the magnetic transition temperatures (T,) for low-dimensional crystals of these species on the assumption that the interchain interaction (Ji”k,) is 0.1 K* cm although it might be largely sensitive to crystal structures. The estimated T, values were roughly consistent with T, values determined for several crystal phases of p-nitrophenyl nitronyl nitroxide (pNPNN) by measurements [ 6-91 of heat capacity and magnetic susceptibility. Judging from T,=O.60 K for the ferromagnetic pphase of pNPNN, Ji,,,, should be a small positive quantity which gives rise to the difficulty of theoretical estimation. First-principle calculations of its

sign and magnitude are, however, crucial for theoretical elucidation and understanding of the mechanism of its organic ferromagnetism. Here, in order to determine both intra- and inter-plane effective exchange integrals (J), molecular orbital calculations [ lo- 13] are carried out for pNPNN clusters, whose geometries are taken from the X-ray structure [ 7 ] of the P-phase crystal. Since the calculated J values are not so anisotropic, a generalized Langevin-Weiss (GLW) model [ 14,151 is used to estimate its ferromagnetic transition temperature (T,). A theoretical explanation is presented for the long-range ferromagnetic ordering in the p-NPNN crystal. Implications of the calculated results are also discussed in relation to a theoretical possibility of organic ferromagnetism of other substituted PNNOs.

2. Langevin-Weiss model for the ferromagnetic phase transition There are two steps for theoretical estimations of the ferromagnetic transition temperature: ( 1) the calculation of the intermolecular effective exchange integrals and (2) the Langevin-Weiss mean-field

0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.

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calculation. As shown in recent neutron diffraction [ 161 and ENDOR [ 17 ] experiments, the dynamic spin polarization (SP) effect [l-3] plays an important role for the ferromagnetic effective exchange interactions between nitroxide radicals. Therefore, as a first step of theoretical elucidation of organic ferromagnetism, the spin-polarized unrestricted Hartree-Fock (UHF) calculation [ LO]is performed for both the low-spin (LS) and high-spin (HS) clusters of nitroxides. The spin projection is performed for the LS UHF solution which entails the HS contaminants arising from the large SP effect. The approximate but size-consistent spin projection procedure, which is referred to as APUHF, has already been described in detail elsewhere [ 10,111 in relation to the first-principle calculations of J in the Heisenberg model for organic radicals. The APUHF method has been successfully applied to calculate the J values for clusters of free radical species [ 12,131. Therefore it is utilized here to evaluate both intraand inter-chain effective exchange integrals for p NPNN clusters with the X-ray structures [ 71. In order to estimate T,, the so-called LangevinWeiss mean-field theory is applied to molecular crystals of free radicals as illustrated in fig. 1. From fig. 1, a localized spin S, on a molecule (a) interacts with other spins S,, on the neighbouring free radicals (b, c, ...). giving rise to the effective exchange interaction as

14 May 1993

L = - 2 x Jab&'sb ,

(1)

where Jab denotes the effective exchange integral between spins a and b. The spin St, is replaced by the expectation value (S,,) = (S) under the mean-field approximation. Then eq. ( 1) can be rewritten by E,,= -2 c Jab
(2a)

=N-‘Lwd-* 2 C Jab

, x ( -MP* w )*wElSa

(2b)

=AM*w&

UC)

,

where N is the number of free radicals in the crystal and AM(M= -Ngp&S} ) denotes the Weiss molecular magnetic field. The A factor is defined by A=N-‘(gpB)-22

C Jab.

(3)

Under the above situation, the magnetization of a molecular crystal is described by the Brillouin function [ 181, and it disappears at the critical temperature (T,), leading to the so-called Langevin-Weiss relation (4a) =2S(S+1)

c&/3,

(4b)

where S is l/2 for a free radical. Eq. (4b) is applied to theoretical estimations of T, for the @-phaseof pNPNN and molecular crystals of other free radicals.

3. Comparison between ab initio and semiempirical APUMP approximations

Fig. 1. Schematic illustration of the Langevin-Weiss molecular magnetic fields. The neighbouring radicals (b, c, ...) exert the magnetic fields on the central radical (a) via the effective exchange interactions (J).

Ab initio calculations are difficult to perform for clusters of pNPNN even at the APUHF STO-3G level [ 21. Therefore, use of the semiempirical ( INDO ) version [ 10] seems inevitable for such large systems as clusters of pNPNN. However, in order to examine the reliability of the INDO approximation, we have made a comparison between the J values calculated for previously examined face-to-face dimers (see fig. 1 in ref. [2] ) of the simple nitroxide HzNO by the INDO and ab initio approximations. The results are summarized in table 1. Table 1 shows that the INDO approximation can reproduce correctly the negative (antiferromagnetic) sign of the J values for the dimer, but it underestimates their

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14 May 1993

Table 1 Variations of& values (cm-‘) with the intermolecular distance for HlNO dimer Distance

3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00

(A)

INDO APUHF

-22.3907 - 6.8460 - 2.0523 - 0.6059 -0.1756 -0.0505 -0.0132 - 0.0044 -0.ooi4 - 0.0004 - 0.0002

4.31G

STOJG APUHF

APUMP

APUHF

APUMPZ

-36.0902 - 10.7985 -3.0514 -0.8124 -0.1976 - 0.0439 -0.0108 -0.0022 0.0000 0.0000 0.0000

-49.2848 - 15.0549 -3.0514 - 1.2074 -0.3073 -0.0659 -0.0176 -0.0044 - 0.0002 0.0000 0.0000

-273.3450 - 115.7880 -54.7276 -24.6013 - 10.3825 -2.0612 - 1.4708 -0.4830 -0.1537 -0.0439 -0.0114

-369.5370 - 177.3580 -82.3547 -36.5765 - 15.3637 -6.0583 -2.2392 -0.7903 -0.2634 -0.0878 -0.0220

magnitude in the weak interaction region ( > 3.0 A) as compared with those of the APUMPZ 4-3 1G method. The magnitude of Jcalculated by the INDO method decreases in an exponential manner with increasing intermolecular distance, showing the same tendency revealed by the ab initio calculations [ 2,131. Judging from the computational results, the INDO approximation is useful enough for a qualitative purpose. However, severe SCF convergence conditions ( lO-‘O for both total energy and density) are required for the calculations, since the J values are given by the difference in the large total energies of the HS and LS states. The reproducibility of each total energy (au) obtained by the quadrupole precision on an IBM RISC 6000 computer is confirmed to be in the order of 10-lo.

(X+

4. Calculations of J values and T, for the l&phase of pNPNN Fig. 2 illustrates the crystal structure of the b-phase of pNPNN with the Fdd2 space symmetry [ 71. From fig. 2, twelve nearest-neighbour p-NPNN molecules exist around the central pNPNN: namely, the coordination number z [ 181 in the GLW model is 12. They are classified into three groups, which are denoted by the white, shaded and black circles. The effective exchange integrals between the central p NPNN and the nearest neighbours in each group are equivalent, and therefore one of them is explicitly

Fig. 2. The crystal structure of the P-phase of pNPNN with the Fdd2 space symmetry. The four equivalent pNPNN are denoted by the white, shaded and black circles. J,. (n=2-4) denotes the effective exchange interaction.

defined as J,,, (n = 2-4 ) without loss of generality as shown in fig. 2. The lattice distances yI, between the lattice points 1 and rz (n = 2-4) are given by the lattice constants (a, b, c) as follows: (5a) 3

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r,,=a(a2+b2+c2)“2=6.37

CHEMICAL PHYSICS LETTERS

A,

(5b)

r14=~(a2+b2+9c2)1/2=10.04A,

(5c)

where a= 12.36, b= 19.36 and c= 10.97 A. The magnitude of J,, is sensitive, instead of rln, to remote intermolecular interactions since pNPNN is a long organic molecule (see below), The situation is in sharp contrast to that in inorganic magnetic solids

[181. In order to clarify the reliability of the nearestneighbour approximation, we have also examined the exchange interactions in the extended oligomers as illustrated as illustrated in fig. 3. The oligomers (dimer to pentamer) are examined in order to elucidate the sign and magnitude of Ji2 in the UCplane in fig. 3A, whereas the zig-zag oligomers, which are responsible for the so-called diamond lattices, are also examined in figs. 3B and 3C. The lattice points of 3(x, y, z), 3’(x, y+ 4, z+ f ) and 3”‘(x, y+ I, z+ 1 ) in fig. 3B lie in the bc plane and those of 4(x+ 1,y,z-i), 4’(x,y,z+l) and 4”‘(x-f,y,zS;) in fig. 3C are on the ac plane. ’ The LS and HS UHF solutions for the clusters with the experimental structures in the B-phase ofpNPNN [ 71 are constructed by taking the fragment (monomer) orbitals as the initial guess of the SCF calculations. The effective exchange integrals for the clusters of p-NPNN are calculated from their total energies of the HS and LS states by the INDO UHF method [ 11-131. Since the p-NPNN monomer in figs. 2 and 3 is nonplanar, the magnitudes of spin densities on the carbon atoms of nitrophenyl group are smaller than the corresponding values of the planar p-NPNN ex-

4 PI

b

Fig. 3. The oligomers (A) of p-NPNN within the ac plane and those ( (B) and (C) ) extended over the interplanes forming the so-called diamond lattice. The exchange interactions in these clusters are responsible for the most important magnetic interactions in the P-phase of p-NPNN.

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14May 1993

amined previously [ 31. This means that the nonplanarity of pNPNN reduces the spin polarization of the nitrophenyl group by nitronyl nitroxide. However, the orbital splitting pattern in fig. 3 of ref. [ 31 is not altered, showing the large SP effect. The alternating spin density populations in the nitrophenyl ring are indeed in accord with the results of the recent neutron diffraction experiments by Schweizer et al, [ 161 and ENDOR experiments by Takui et al.

[171* The radical orbitals of clusters arising from the

SOMO of the monomer radical are nearly degenerate in energy, and the situation is the same for other cluster orbitals consisting of the HOMO or LUMO of the monomer. This indicates that the intermolecular interactions are small in the case of the g-phase ofp-NPNN and the magnetic behavior of the crystal can be well described by a localized spin model [ 18 1. In fact, the experiments by Yamauchi et al. [ 191 and Kinoshita and co-workers [ 6-91 have shown that the Heisenberg model is well applicable to the analysis of the magnetic behaviors in molecular crystals of nitroxides such as diphenyl nitroxide (DPNO) and p-NPNN. Table 2 summarizes the total energies, total spin angular momenta ( S2) and Jr, values for clusters of p-NPNN by the APUHF INDO method. The ( S2> values should be about 1.O and 2.0, respectively, for the singlet and triplet UHF solutions of the pure diradicals without spin polarizations of nonradical orbital pairs. The deviations of (S’) values from the normal values are about 1.9 for both states of the pNPNN dimer, showing the exceptionally large SP effect. From table 2, the J12 values for the clusters in fig. 3A were calculated to be in the range 0.17-0.20 cm-’ at the experimental geometry. From the crystal structure in fig. 3A, it is concluded that the ferromagnetic interaction is operative within the UCplane in accord with the experiment [ 6-9 1. The oxygen atom (0 1) of the nitronyl nitroxide group ofpNPNN interacts with the nitro group (Nl02-03) of its nearest neighbour in the ac plane as illustrated in fig. 4A. Judging from the populations of spin densities, the so-called McConnell-type spindensity-product term (SDPII in our terminology [ 121) between the Ol-Nl pair should exhibit the small antiferromagnetic interaction, in accord with the previous conclusion that the face-to-face dimer

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14 May 1993

Table 2 Total energies (au) and effective exchange integrals J,. (cm-‘) of the cluster of g-phase pNPNN J a\,

Type

Cluster

Spin state

J 12

dimer (l,2)

singlet triplet

-409.693525903420 -409.693526663619

2.97276 3.97276

0.167

trimer (l,2,2’)

doublet quartet

-614.540468996474 -614.540470523797

4.70872 6.70873

0.168

tetramer ( 1,2,2’, 2”)

singlet quintet

-819.387442086842 - 8 19.387444382762

5.94443 9.9444s

0.189

pentamer ( 1(2,2’, 2”, 2’“)

doublet sextet

-1024.234431500865 - 1024.234434565915

7.68001 13.68003

0.202

dimer (l,3)

singlet triplet

-409.694650253543 -409.694650608463

2.97180 3.97180

0.078

trimer (1, 3,3’)

doublet

quartet

-614.5425061757SS -614.542506838785

4.7079 1 6.70790

0.073

tetramer (1,3,3’,3”)

singlet quintet

-819.390302693568 - 8 19.390303664429

5.94443 9.94441

0.080

pentamer ( 1, 3, 3, 3”, 3”‘)

doublet sextet

- 1024.238085557254 - 1024.238086835287

7.68103 13.68101

0.084

dimer (194)

singlet triplet

-409.693971663939 -409.69397 1600252

2.96941 3.96941

-0.014

trimer (l,4,4’)

doublet quartet

-614.541630242885 -614.541630115082

4.70011 6.70011

-0.014

tetramer (1, 4, 41,4”)

singlet quintet

-819.389369831589 -819.389369645712

5.93023 9.93023

-0.016

pentamer ( I, 4,4’, 4”, 4’“)

doublet sextet

- 1024.237144015545 -1024.237143759557

7.66010 13.66010

-0.017

Jl3

J 14

of a planar model system of pNPNN exhibits the antiferromagnetic intermolecular interaction via the 0 1-N 1 contact and the introduction of nonplanarity induces the inversion from the negative Jab to the positive Jab [ 2 1. As shown in fig. 4B, the nonorthogonal conformation between the nitronyl nitroxide and nitro groups is predominantly important for the ferromagnetic intermolecular interaction. The importance of nonorthogonal orbital interactions has been emphasized in the case of transition metal complexes [ 20-221, in relation to the so-called first-order potential exchange [23] between the SOMO-SOMO electrons. However, it is noteworthy that the ferromagnetic exchange in the ac piane ofpNPNN arises from the second-order intermolecular potential exchange between the SOMO electron ofp-

Energy

(S2>

NPNN and the SP x-electron of its nearest neighbour instead of the SOMO electron. The three-dimensional interactions are shown in fig. 5. The effective exchange integral (Jis) for the clusters in fig. 3B is ferromagnetic (about 0.08 cm-‘). The spin density populations indicate that the SDPII terms between the Ol-Cl and Ol-C2 atomic pairs are, respectively, positive and negative as illustrated in fig. 5A. The net interaction after the mutual cancellation remains ferromagnetic in this stacking mode. The ferromagnetic intermolecular interaction between the nitronyl nitroxide group and benzene ring via the SP mechanism is also expected for other PNNO species [ 31. The J,, values for clusters in fig. 3C is slightly antiferromagnetic ( - 0.014 cm- * ) because of the weak van der Waals interaction between methyl and nitro groups as shown in 5

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(A)

(4

Fig. 5. Three-dimensional intermolecular interactions between p NPNN. The dotted lines in (A) indicate important interactions. The interatomic distances for the 01-Cl and 01-C2 pairs are 3.219 and 3.247 A, respectively. The van der Waals interactions between the methyl and nitro groups are shown in (B) by the circles,

Fig. 4. Intermolecular interactions between pNPNN in the UC plane. The dotted lines in (A) indicate important interactions. (B) shows the side view for emphasizing the nonorthogonality between the nitro and nitroxide groups. The interatomic distances for theOl-Nl,Ol-02 and 01-03 pairsare 3.368,3.435 and 3.67 1 A, respectively.

5B. However, this weak interaction is overcome with the other ferromagnetic interaction JL3.The net interplane J value is therefore positive (ferromagnetic ). The magnitude ofJIj+J14 is about one third ofJrZ in the ac plane in the case of the P-phase ofp-NPNN. The J values for other radical pairs except for the pairs examined above are negligible. This indicates the adequacy of the quasi three-dimensional Heisenberg-type model. Therefore, the A factor of the Weiss effective molecular magnetic field is approximately given by taking twelve nearest-neighbour pNPNN as fig.

A=2N-‘(gpB)-2(45r

+4J,+4J3)

)

(6)

where 5,z, J,3 and J14 are, respectively, the effective exchange integrals calculated for the dimers ( 1- 2)) ( I - 3) and ( 1 - 4) in fig. 2. Then the ferromagnetic transition temperature (r,) is calculated to be 0.64 K by the use of eq. (4b), in accord with the experiment (0.60 K). This in turn indicates that the ef6

fective exchange interactions instead of the magnetic dipole interactions are predominantly operative in the ferromagnetic spin ordering in the P-phase of pNPNN.

5. Discussion and concluding remarks The semiempirical computations of p-NPNN clusters with their P-phase geometries [ 71 indicate threedimensional ferromagnetic exchange interactions, which are crucial for the occurrence of the long-range magnetic order in the Heisenberg model [ 18,251. Although the spin-polarized APUHF INDO method is crude, it can reproduce the order of T, for the organic ferromagnetism on the basis of the Heisenberg model. This in turn indicates that the SP mechanism is operative for occurrence of the organic ferromagnetism. Judging from the J values in table 2 and computational results in table 2 in ref. [ 31, it is reasonable that the organic ferromagnetism can be expected in the low-temperature region (0.1-0.5 K) for crystals of PNNO with donor or acceptor groups [ 3 1. The SP rule proposed previously [ l-3,25] is applicable to ferromagnetic interactions in clusters of several nitroxides and the crystalline organic ferromagnet [ 6-91 composed by p-NPNN.

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CHEMICAL PHYSICSLETTERS

The effective exchange integrals calculated for clusters with the experimental geometries in the gphase of p_NPNN are small compared with the J values for the dimers of planar PNNO with donor or acceptor groups by the use of the extended McConnell model (EMM) [l-3,25,26]. This may be ascribed to the cancellation of the sum of various positive exchange interactions between the interatomic pairs by the sum of other negative interatomic J values, since the crystal structure of the B-phase of pNPNN is complex and pNPNN is nonplanar within the crystal, All the interacting atomic pairs should be considered in the EMM model; note that the previous EMM model [l-3] takes into account just the overlapping atomic pairs because only the idealized stacking structures arc examined. The reliability of the UHF-based methods followed by the approximate spin projection [ l-3,1 l13 ] was recently examined in detail by comparison with several spin-restricted calculations such as CASSCF and second-order (SO) CI [27]. It was found that both methods provide similar J values if the same basis set is utilized, The utility of the APUHF INDO approximation for qualitative purposes is also confirmed in section 3 and in refs. [ I31. Before the discovery of the organic ferromagnet of p-NPNN [ 6-91, the ab initio and semiempirical APUMP calculations [ l-3,1 l-131 have indeed revealed a theoretical possibility that crystalline organic ferromagnets are feasible if stacking modes of component radicals are well controlled. The present calculations have clarified that the B-phase crystal of p-NPNN is one of such examples which satisfy theoretical requirements [ 13 ] for the occurrence of organic ferromagnetism. Judging from the magnitude of the calculated J values for nitroxides [ l-31, organic ferromagnets with higher r,( >0.60 K) seem feasible if three-dimensional exchange interactions between component nitroxides are well controlled. Recently, Rassat et al. [ 281 have discovered the crystalline organic ferromagnet of nitroxide, which exhibits the transition temperature over 1.OK. Thus both the experimental [6-9,281 and theoretical results [ l-3,1 l-l 31 indicate that the crystal engineering approach for various nitroxides is promising for synthesis of high-T, organic ferromagnets. In conclusion, the present theoretical calculations have revealed a theoretical explanation of the or-

14May1993

ganic ferromagnetism observed for the P-phase of pNPNN: ( 1) The ferromagnetic second-order potential exchange interaction between the SOMO electron localized in the nitroxide group of p-NPNN and the spin-polarized x-electron in the para-nitrophenyl group of its nearest neighbour is operative in the ac plane. (2) The ferromagnetic spin-density-product (SDPII)-type interaction [ 2,12,25] between the SOMO electron localized in the nitroxide group of pNPNN and the spin-polarized n-electron in the phenyl group of its nearest neighbour is operative in the three-dimensional interaction. The SP rule [ 1 ] is applicable to the organic ferromagnet composed by pNPNN. (3) The quasi three-dimensional Heisenberg plus Langevin-Weiss model is applicable to qualitative estimation of the ferromagnetic transition temperature, although its refinement is crucial for a quantitative purpose.

Acknowledgement The authors thank Professor K. Awaga (Tokyo University), Professor T. Inabe (Hokkaido University) and Professor N. Suzuki (Osaka University) for helpful discussions. This work was supported by Grant-in Aid for Scientific Research on Priority Areas of Molecular Magnetism (No. 04242 101).

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[8]M. Tamura, Y. Nakazawa, D. Shiomi, K. Nozawa, Y. Hosokoshi, M. Ishikawa, M. Takahashi and M. Kinoshita, Chem. Phys. Letters 186 (1991) 4Ql. [9] Y. Nakazawa, M. Tamura, N. Shirakura, D. Shiomi, M. Takahashi, M. Kinoshita and M. Ishikawa, Phys. Rev., in press. [lO]K. Yamaguchi, Chem. Phys. Letters 33 (1975) 330; 35 (1975) 230. [ 111 K. Yamaguchi, H. Fukui and T. Fueno, Chem. Letters (1986) 625. [ 121 K. Yamaguchi and T. Fueno, Chem. Phys. Letters 159 (1989) 465. [ 13]K. Yamaguchi, H. Naminoto and T. Fueno, Mol. Cryst. Liquid Cryst. 176 (1989) 151. [ 141 M.P. Langevin, .I. Phys. (Paris) 4 (1905) 678. [ 151 P. Weiss, J. Phys. Radium 4 (1907) 661. [ 161J. Schweizer et al., Mol. Cryst. Liquid Cryst., in press. [ 171 T. Takui et al., Mol. Cryst. Liquid Cryst., in press.

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[ 18 ] D.C. Mattis, The theory of magnetism II (Springer, Berlin, 1985). [ 191J. Yamauchi, K. Okada and Y. Deguchi, Bull. Chem. Sot. Japan 60 (1978) 483. [ 201 J.S. Miller and A.J. Epstein, Progr. Inorg. Chem. 20 ( 1976) [2l]~‘Kahn,J.Chem.Soc. FaradayTrans.1171 (1975) 862. [22] K. Yamaguchi, T. Tsunekawa, Y. Toyoda and T. Fueno, Chem. Phys. Letters 143 (1988) 371. [23] P.W. Anderson, SolidState Phys. 14 ( 1963) 99. [24] K. Awaga and Y. Maruyama, J. Chem. Phys. 91 (1989) 2743. [ 251 K. Yamaguchi, Y. Toyoda, M. Nakano and T. Fueno, Synth. Metals 19 (1987) 87. [26] H.M. McConnell, J. Chem. Phys. 39 (1963) 1910. [27] K. Yamaguchi, M. Okumura, W. Mori, J. Maki, K. Takada, T. Noro and K. Tanaka, Chem. Phys. Letters, submitted for publication. [28] A. Rassat et al., Mol. Cryst. Liquid Cryst., in press.