Structural and Magnetic Properties of Gd3N@ C80

23637

2006, 110, 23637-23640 Published on Web 11/03/2006

Structural and Magnetic Properties of Gd3N@C80 Jing Lu,*,†,‡ Renat F. Sabirianov,‡,§ Wai Ning Mei,‡,§ Yi Gao,§ Chun-gang Duan,⊥ and Xiaocheng Zeng§,| Mesoscopic Physics Laboratory, Department of Physics, Peking UniVersity, Beijing 100871, P R China, Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266, Nebraska Center for Material and Nanoscience, UniVersity of Nebraska at Lincoln, Lincoln, Nebraska, 68588, Department of Chemistry, UniVersity of Nebraska at Lincoln, Lincoln, Nebraska 68588, and Department of Physics, UniVersity of Nebraska at Lincoln, Lincoln, Nebraska 68588 ReceiVed: September 23, 2006; In Final Form: October 19, 2006

Using relativistic and on-site correlation-corrected density functional theory, we have investigated the structural and magnetic properties of recently synthesized Gd3N@C80. The most stable structure of Gd3N@C80 has the three magnetic Gd ions pointing to the centers of hexagons in C80. The magnetic ground state of this structure has the three coplanar spins (S ) 7/2) offset by 120° angles. At the same time, the state with the highest multiplicity, where all the spins are parallel aligned, is found only about 4.5 meV higher in energy. Therefore, at room temperature, we expect Gd3N@C80 to be paramagnetic with the spin fluctuating between different multiplicities. As a result, Gd3N@C80 may exhibit greater proton relaxivity than Gd@C60 and Gd@C82 and serve as a possible candidate for the next generation of commercially available magnetic resonance imaging contrast agents.

Computational Details

in DMOL package.9 The electronic configuration of Gd is 4s24p64d104f75s25p65d16s2. The calculated ground-state spin multiplicity of the Gd2 dimer is M ) 19, which is in accordance with the previous all-electron relativistic density functional theory calculation.10 The calculated bond length (3.00 Å) and binding energy (2.03 eV) of the Gd2 dimer are comparable with the previously calculated bond length (2.90 Å)10 and experimental binding energy (1.784 ( 0.35 eV).11 The structure of Gd3N@C80 has been determined by the X-ray diffraction technique based on Gd3N@C80‚NiII(OEP)‚ 1.5(benzene) crystal.4 The Gd3N unit is found to be pyramidal within the Ih cage. We label this Gd3N@C80 configuration as configuration I, where the three Gd atoms are positioned over the centers of hexagons in the fullerene cage. We also consider four other configurations of Gd3N inside a free Ih C80: (II) optimization of the X-ray determined structure; (III) one Gd atom points toward one C atom and the other two Gd atoms point toward an off-center position of a hexagon, respectively; (IV) one Gd atom points toward one hexagonal center and two Gd atoms point to two C-C 6-6 double bonds, respectively; and (V) the three Gd atoms point toward three C-C 5-6 single bonds, respectively. The convergence tolerance of force on each atom of configurations II-V is 0.05 eV/ Å.

Double numerical atomic orbital basis set plus polarization function (DNP) is used. The calculations are performed

Results and Discussion

* Corresponding author. E-mail: [email protected]. † Peking University. ‡ Department of Physics, University of Nebraska at Omaha. § Nebraska Center for Material and Nanoscience, University of Nebraska at Lincoln. | Department of Chemistry, University of Nebraska at Lincoln. ⊥ Department of Physics, University of Nebraska at Lincoln.

The structures of Gd3N@C80 in different configurations are displayed in Figure 1, and the relevant properties are summarized in Table 1. Configuration II with C3 symmetry has the lowest energy among all of the optimized configurations, and the three Gd atoms remain positioned over the centers of the hexagons in the fullerene cage as in configuration I. The other

Introduction Water-soluble Gd-based monometallofullerenes {Gd@C82(OH)x, Gd@C60[C(COOH)10], Gd@C60(OH)x} have attracted recent interest1-3 as a possible new generation of magnetic resonance imaging (MRI) contrast agents because they not only can produce proton relaxivities several times and even tens times greater than commercially available MRI contrast agents but also are safer than the latter because the toxic Gd ions are completely encaged inside the fullerenes and do not dissociate under physiological conditions. If more Gd atoms are encapsulated and ferromagnetically coupled [or have a higher spin multiplicity than the single Gd3+ ion (S ) 7/2)] inside fullerenes, then proton relaxivities larger than that of Gd@C82/Gd@C60 may be obtained. This idea stimulates the recent synthesis and characterization of [email protected] However, the key issue of how the three magnetic Gd ions are coupled to one another inside C80 remains unclear. In this article, we have investigated for the first time the magnetic properties of Gd3N@C80 by using all-electron relativistic density functional theory within the generalized gradient approximation8 (RGGA).

10.1021/jp0662395 CCC: $33.50

© 2006 American Chemical Society

23638 J. Phys. Chem. B, Vol. 110, No. 47, 2006

Letters

TABLE 1: Symmetry (within Tolerance of 0.002 Å), the Energy E (meV) with Respect to the Lowest Energy Configuration (Configuration II), the Spin Exchange Interaction Energy Difference between the M ) 8 and M ) 22 Spin Multiplicity of the Same Configuration, ∆E ) E(M ) 8) - E(M ) 22) (meV), the Exchange Parameter J1 (meV), the HOMO-LUMO Gap ∆ (eV), the Gd-N, Gd-Gd, and Shortest Gd-C Distances (Å), and the ∠Gd-N-Gd Angles (deg) in Different Configurations of Gd3N@C80 a configs

symm



∆E

coupling

J1

∆b

dGd-N

dGd-Gd

dGd-C

∠Gd-N-Gd

I (expt)

C1

5935

-21 (-7)c

AFM (AFM)c

-5.25 (-1.75)c

1.21 (1.63)c

C3

0

-14 (-4)c

AFM (AFM)c

-3.5 (-1)c

1.29 (1.52)c

III

C1

52

0.3

FM

0.075

1.33

IV

Cs

76

-8 (-4)c

AFM (AFM)c

-2 (-1)c

1.35 (1.50)c

V

C3

82

5

AFM

1.25

1.27

3.409 3.449 3.593 3.466 3.466 3.467 3.469 3.472 3.478 3.426 3.426 3.488 3.442 3.442 3.443

2.402

II

2.038 2.085 2.117 2.099 2.099 2.100 2.092 2.096 2.101 2.101 2.101 2.105 2.109 2.110 2.110

110.3 111.6 119.7 111.3 111.3 119.4 111.6 111.6 112.3 109.2 112.0 112.0 109.3 109.3 109.4

Gd3N

Cs

183d

FM

2.143 2.143 2.144

3.317 3.317 3.319

0.66

2.422 2.380 2.388 2.387

101.4 101.5 101.5

a For comparison, the corresponding parameters of the optimized Gd3N cluster are given at the bottom. b Experimental value ∆ ) 1.75 eV.6 the GGA + U level. d Between M ) 9 and 24 states.

Figure 1. Structures of Gd3N@C80 in different configurations. Grey ball, C; dark blue ball, N; light blue ball, Gd.

three optimized configurations (III, IV, and V) are 52-82 meV higher in energy. The direct X-ray determined structure, configuration I, is about 6 eV much higher in energy and this is attributed to a major deformation of C80 induced by surrounding complex. In fact, several C-C bonds in configuration I are over 1.5 Å, whereas in other configurations the C-C bond length ranges from 1.431 to 1.462 Å. The calculated binding energy of Gd3N to C80 in configuration II is 9.27 eV, significantly larger than that of the single Gd atom inside the C60 (3.77 eV)12 and C82 (5.64)13 cage. The energy difference between the lowest-energy and higher-lying optimized configurations in Gd3N@C80 is about twice that (34 meV)14 in Sc3N@C80. Therefore, it is harder for the Gd3N cluster to rotate inside C80 than the Sc3N cluster. The encapsulated Sc3N cluster is found to rotate freely at room temperature from the 13C NMR

c

At

spectrum measurement.15 However, the appearance of three lines below 100 cm-1 in the Raman spectra of Gd3N@C80,6 which are absent in Sc3N@C80 and Y3N@C80, suggests a frustrated Gd3N rotation inside C80. The encapsulated Gd3N cluster remains pyramidal in all configurations as the optimized free-standing Gd3N cluster is. For an optimized free-standing Gd3N cluster, the Gd-N bond length and Gd-Gd distance are 2.139 and 3.318 Å, respectively, and the ∠Gd-N-Gd angle is 101.7 °. When encapsulated inside C80, the Gd-N bonds are slightly shortened to 2.038-2.111 Å, whereas the Gd-Gd distances are slightly elongated to 3.409-3.593 Å. The ∠Gd-N-Gd angle is increased to 109.3119.7°. The Gd3N cluster appears to be squished by C80 along its threefold axis and the three Gd-N bonds. The encapsulated Gd3N cluster is responsible for the magnetic properties of the system. In our DFT magnetic study, we have considered two spin multiplicities for Gd3N@C80: M ) 8 and 22. In the M ) 8 state, one Gd magnetic moment is antiparallel to two other Gd magnetic moments and in the M ) 22 state the three Gd magnetic moments are parallel aligned [ferromagnetically (FM) coupled]. The ground-state spin multiplicity of configurations I, II, and IV is calculated to be M ) 8, and the spin multiplicity of M ) 22 is 21, 14, and 8 meV higher in total energy for configurations I, II, and IV, respectively. Alternatively, configurations III and V have an M ) 22 ground state, and the M ) 8 state is 0.3 and 5 meV higher in total energy, respectively. Hexagonal close-packed (hcp) metal Gd has a ferromagnetic ground state with a Curie transition temperature of 293 K. Like many other DFT calculations, the RGGA/DNP calculation also predicted an antiferromagnetic ground state for hcp Gd. Only inclusion of the on-site correlation of 4f narrow bands can correct this discrepancy and obtain a ferromagnetic ground state for hcp Gd.16 Therefore, the GGA plus the on-site correlation (GGA + U)17 approach is further carried out for three configurations with M ) 8 multiplicity based on the projector augmented wave method implemented in the VASP package.18 Following the previous work for hcp Gd16 and for GdN,19,20 the on-site Column repulsion and exchange is taken as U ) 6.7 eV and J ) 0.7 eV, which have reproduced the Curie

Letters

J. Phys. Chem. B, Vol. 110, No. 47, 2006 23639

Figure 2. One example of compromised coplanar ground-state spin arrangement in configurations I, II, and IV of Gd3N@C80.

transition temperature of Gd16 and GdN well.20 The GGA + U approach does not reverse the magnetic property but the energy difference between the M ) 8 and M ) 22 states is reduced to 7, 4, and 4 meV for configurations I, II and IV, respectively. As far as the magnetic property of Gd-related material is concerned, we believe that the on-site electron correlation effect dominates the relativistic effect, and the smaller energy difference of 4-7 meV between M ) 8 and M ) 22 states appears more reliable and are adopted in the later part of this article. Next, we analyzed the exchange interaction using the Heisenberg spin Hamiltonian

H ) -J1

Si‚Sj ∑ i>j

where J1 is the exchange parameter and Si and Sj are spins on the sites of i and j. The spin exchange energy is J1 and -3J1 for spin multiplicity M ) 8 and 22, respectively, and the energy difference between M ) 8 and 22 is ∆E ) E(M ) 8) -E(M ) 22) ) 4J1. We obtained J1 ) -1.75, -1, 0.075, -1, and 1.25 meV for configurations I-V, respectively. Within the framework of DFT, the spin vectors are forced to be collinear. If this limitation is lifted and the spin vectors are free to assume any spatial orientation, then M ) 8 is no longer the ground state of configurations I, II, and IV. The ground state is described classically by a compromised coplanar spin arrangement where the angle between adjacent spin vectors is 120° [the three spins are thus antiferromagnetically (AFM) coupled and M ) 0], and the total spin exchange energy is 1.5J1.21 One example of such a coplanar spin arrangement is shown in Figure 2. The spin exchange energy difference between the ground state and the highest spin excited state (M ) 22) is thus 4.5J1 and the value is -7.88, -4.5, and -4.5 meV for configurations I, II, and IV, respectively. The medical use of an MRI contrast agent is at room temperature (about 26 meV), at which these three systems will be paramagnetic with the magnetic moment oscillating rapidly between different spin multiplicities. In view of the rather weak ferromagnetic exchange interaction (J1 ) 0.075-1.25 meV) in configurations III and V, we expect that the two systems are also paramagnetic or superparamagnetic at room temperature. It should be emphasized that the ferromagnetic phase is not a requisite for Gd ion clusters to generate a larger proton relaxivity than that of a single Gd ion. A recent experiment22 reported that the paramagnetic or superparamagnetic Gd ion clusters inside single-wall carbon nanotubes (SWNTs) with an extrapolated Curie temperature of -1.32 K generated a proton relaxivity several times larger than that of Gd@C60/[email protected] The paramagnetic Gd3N@C80 is probably able to generate a proton relaxivity greater than that of Gd@C60/Gd@C82 as Gdencapsulated SWNTs do because of the certain occurrence possibility of higher spin multiplicity, including M ) 22. The main drawback of Gd-encapsulated SWNTs, in our opinion, is that the Gd ions, which tunnel into the inside of SWNTs presumably through the sidewall defect,22 may leak from these defects and become a health hazard. On the contrary, a perfect

Figure 3. Electronic density in the plane passing through the three Gd ions in configuration II of Gd3N@C80.

C80 cage can keep the Gd ions from leaking, and Gd3N@C80 is more suitable for medical purposes. The calculated energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of Gd3N@C80 is ∆ ) 1.21-1.35 eV at the RGGA level. It is well known that the pure DFT calculations tend to underestimate the HOMO-LUMO gap of a semiconductor. It is interesting to witness that when applying the GGA + U scheme to configurations I, II, and IV, the HOMO-LUMO gap value shifted to 1.63, 1.52, and 1.50 eV, respectively, which are in better agreement with the measured value of 1.75 eV.6 This improvement indicates the importance of the on-site electron repulsion in determining the correct HOMO-LUMO gap of Gd3N@C80. This large HOMO-LUMO gap accounts for the extraordinary kinetic chemical stability and experimental isolation of [email protected] There are only two electrons in its fourfold degenerate HOMOs of the Ih isomer of C80. The formation of a large HOMO-LUMO gap in Gd3N@C80 implies that six electrons are transferred from the Gd3N to the HOMOs of C80. The Mulliken charges on Gd and N atoms are about +1.00 and -1.13 in Gd3N@C80 (II), and the total charge transfer from Gd3N to C80 is only 1.87e. It was shown recently23 that the natural population analysis is more suitable for determining charge transfer of a donor-acceptor system than Mulliken population analysis. A natural population analysis is thus carried out by using the CEP-121G basis set for C and Gd atoms implemented in Gaussian 03 package.24 The resulting electronic configuration is 6s0.24f7.0455d0.39 for the Gd atom and 2s1.932p5.56 for the N atom, and the natural charges on Gd and N atoms are +2.37 and -2.49, respectively. The total charge transfer from Gd3N to C80 is 4.62e. The occupation of 0.39e on the Gd 5d orbitals is ascribed to a contribution of back-donation of the occupied orbitals of the fullerene cage.12,13 After this correction, the charge transfer from Gd3N to C80 is about 5.88e, a result close to the expectation. Bond formation between Gd3N and C80 was proposed based on the observed frustrated Gd3N rotation.6 Figure 3 displays the calculated electron density in a plane containing the three Gd ions. There is no significant electron accumulation and thus no strong covalent bond formation between Gd and proximal C atoms. The interaction between Gd and C80 is primarily ionic in character as in the cases of Gd@C82 and [email protected],13 The calculated dipole moment of Gd3N@C80 (II) is 0.95 Debye, nearly half that of [email protected] In addition to the charge transfer, the orbital hybridization between the guest transition-metal/lanthanide atoms and fullerene

23640 J. Phys. Chem. B, Vol. 110, No. 47, 2006

Figure 4. Isosurfaces (the isovalue is 0.03 au) of the HOMO (left) and LUMO (right) in configuration II of Gd3N@C80. Red and green are used to indicate the positive and negative sign of the wavefunctions, respectively.

is another common characteristic of monometallofullerenes25-28 and we find that it remains in Gd3N@C80. The HOMO and LUMO of Gd3N@C80 (II) are shown in the left and right parts of Figure 4, respectively. The HOMO of Gd3N@C80 is derived from one of the C80 HOMOs but has a small amount of component on the N atom. Alternatively, the LUMO of Gd3N@C80, which is chiefly localized on the two Gd atoms, exhibits remarkable component on C80. Finally, we examine the electronic structures of two potential Gd-based metallofullerenes that contain more than one Gd atom, Gd2@C80 and Gd3C2@C80, which are analogs of experimentally reported La2@C8029 and Sc3C2@C80,30 respectively. The ground state of Gd2@C80 at the RGGA level is antiferromagnetic, and the fourfold degenerate HOMOs of C80 are only occupied by seven electrons. In an early DFT work,31 the ground state of Gd2@C80 is predicted to be ferromagnetic. The ground state of Gd3C2@C80 at the RGGA level is also antiferromagnetic and the fourfold degenerate LUMOs of C80 are occupied by 1 electron. Therefore, the main shortcoming of Gd2@C80 and Gd3C2@C80 is that they have a high reactivity due to the partially occupied HOMOs or LUMOs of C80 and are presumably difficult to synthesize and isolate. Conclusions By using density functional theory calculations, we found that the most stable configuration of Gd3N@C80 has the three Gd ions pointing to the centers of hexagons in C80, a result in agreement with the X-ray diffraction experiment. The three magnetic Gd ions are weakly antiferromagnetically coupled, and the ferromagnetic state is only 4.5 meV slightly higher in energy; thus, these two states should coexist at room temperature. If a water-soluble derivative is synthesized, then Gd3N@C80 is likely to show greater proton relaxivity than Gd@C60/Gd@C82 and serve as a candidate for the next generation of commercial magnetic resonance imaging contrast agents. Acknowledgment. This work was supported by Nebraska Research Initiative (No. 4132050400) of the USA, the NSFC (Grant No. 10474123, 10434010, and 90606023), National 973 projects (No. 2002CB613505) of MOST of China, and 211, 985 and Creative Team Projects of MOE of China. Supporting Information Available: Visualized important structure parameters of optimized Gd3N cluster and Gd3N@C80 II and the coordinates of Gd3N@C80 II. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kato, K.; Kanazawa, Y.; Okumura, M.; Taninaka, A.; Yokawa, T.; Shinohara, H. J. Am. Chem. Soc. 2003, 125, 4391.

Letters (2) Toth, E.; Bolskar, R.; Borel, A.; Gonzalez, G.; Helm, L.; Merbach, A. E.; Sitharaman, B.; Wilson, L. J. J. Am. Chem. Soc. 2005, 127, 799. (3) Sitharaman, B.; Bolskar, R.; Rusakova, I.; Wilson, L. J. Nano Lett. 2004, 4, 2373. (4) Stevenson, S.; Phillips, J. P.; Reid, J. E.; Olmstead, M. M.; Rath, S. P.; Balch, A. L. Chem. Commun. 2004, 2814. (5) Stevenson, S.; Stephen, R. R.; Amos, T. M.; Cardorette, V. R.; Reid, J. E.; Phillips, J. P. J. Am. Chem. Soc. 2005, 127, 12776. (6) Krause, M.; Dunsch, L. Angew. Chem., Int. Ed. 2005, 44, 1557. (7) Ge, Z. X.; Duchamp, J. C.; Cai, T.; Gibson, H. W.; Dorn, H. C. J. Am. Chem. Soc. 2005, 127, 16292. (8) Perdew, J. P.; Wand, Y. Phys. ReV. B 1992, 45, 13244. (9) Delley, B. J. Chem. Phys. 2000, 113, 7756. (10) Dolg, M.; Liu, W.; Kalvoda, S. Int. J. Quantum Chem. 2000, 76, 359. (11) Kant, A.; Lin, S. S. Monatsh. Chem. 1971, 103, 757. (12) Lu, J.; Mei, W. N.; Gao, Y.; Zeng, X. C.; Jing, M. W.; Li, G. P.; Sabirianov, R.; Gao, Z. X.; You, L. P.; Xu, J.; Yu, D. P.; Ye, H. Q. Chem. Phys. Lett. 2006, 425, 82. (13) Senapati, L.; Schrier, J.; Whaley, K. B. Nano Lett. 2004, 4, 2073. (14) Kobayashi, K.; Sano, Y.; Nagase, S. J. Comput. Chem. 2001, 22, 1353. (15) Stevenson, S.; Rice, G.; Glass, T.; Harich, K.; Cromer, F.; Jordan, M. R.; Craft, J.; Hadju, E.; Bible, R.; Olmstead, M. M.; Maitra, K.; Fisher, A. J.; Balch, A. K.; Dorn, H. C. Nature 1999, 401, 55. (16) Kurz, P.; Bihlmayer, G.; Blugel, S. J. Phys.: Condens. Matter 2002, 14, 6353. (17) Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Phys. ReV. B 1995, 52, R5467. (18) Kresse, G.; Joubert, J. Phys. ReV. B 1999, 59, 1758. (19) Duan, C. G.; Sabiryanov, R.; Liu, J. J.; Mei, W. N. Phys. ReV. Lett. 2005, 94, 237201. (20) Duan, C. G.; Sabiryanov, R.; Mei, W. N.; Dowben, P. A.; Jaswal, S. S.; Tsymbal, E. Y. Appl. Phys. Lett. 2006, 88, 182505. (21) Dai, D. D.; Whangbo, M. H. J. Chem. Phys. 2004, 121, 672. (22) Sitharaman, B.; Kissell, K. R.; Hartman, K. B.; Tran, L. A.; Baikalov, A.; Rusakova, I.; Sun, Y.; Khant, H. A.; Ludtke, S. J.; Chiu, W.; Laus, S.; Toth, E.; Helm, L.; Merbach, A. E.; Wilson, L. J. Chem. Commun. 2005, 3915. (23) Yerushalmi, R.; Scherz, A.; Baldridge, K. K. J. Am. Chem. Soc. 2004, 126, 5897. (24) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (25) Lu, J.; Zhang, X.; Zhao, X.; Nagase, S.; Kobayashi, K. Chem. Phys. Lett. 2000, 332, 219. (26) Lu, J.; Zhang, X.; Zhao, X. Chem. Phys. Lett. 2000, 332, 51. (27) Wang, K.; Zhao, J.; Yang, S.; Chen, L.; Li, Q.; Wang, B.; Yang, S.; Yang, J.; Hou, J. G.; Zhu, Q. Phys. ReV. Lett. 2003, 91, 185504. (28) Kessler, B.; Bringer, A.; Cramn, S.; Schlebusch, C.; Eberhardt, W.; Suzuki, S.; Achiba, Y.; Esch, F.; Barnaba, M.; Cocco, D. Phys. ReV. Lett. 1997, 79, 2289. (29) Bethune, D. S.; Johnson, R. D.; Salem, J. R.; Vries, M. S. d.; Yannoni, C. S. Nature 1993, 366, 123. (30) Liduka, Y.; Wakahara, T.; Nakahodo, T.; Tsuchiya, T.; Sakuraba, A.; Maeda, Y.; Akasaka, T.; Yoza, K.; Horn, E.; Kato, T.; Liu, M. T. H.; Mizorogi, N.; Kobayashi, K.; Nagase, S. J. Am. Chem. Soc. 2005, 127, 12500. (31) Kobayashi, K.; Nagase, S. Chem. Phys. Lett. 1996, 262, 227.