VOLUME 84, NUMBER 11 PHYSICAL REVIEW LETTERS 13 MARCH 2000 Dimer to Monomer Phase Transition in Alkali-Metal Fullerides: Magnetic Susceptibility Changes Kwang S. Kim,* Jung Mee Park, Jongseob Kim, Seung Bum Suh, and P. Tarakeshwar National Creative Research Initiative Center for Superfunctional Materials, Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Korea Kee Hag Lee* and Sung Soo Park Department of Chemistry, WonKwang University, Iksan 570-749, Korea (Received 21 May 1999) Ab initio calculations have been employed to investigate the peculiar change in magnetic property (from diamagnetic to paramagnetic) of the dianionic C 60 -dimer phase in a rapidly cooled AC 60 samples (A: alkali metal). We first note that the triplet state of C 60  2 22 which was never considered previously is nearly degenerate with the singlet state, and the transition barrier between the two states is reasonably small. This explains the susceptibility increase with an increase in temperature and the magnetic phase transition in the process of the dimer to monomer phase transition. PACS numbers: 61.48.+c, 31.15.Ar, 31.15.Ew, 71.24.+q Detailed investigation of the structure of alkali-metal fullerides A x C 60 (A  Na, K, Rb, Cs) has revealed the existence of various stable and metastable crystalline phases with AC 60 stoichiometry [1–19]. These phases ex- hibit interesting structural characteristics and electric and magnetic properties. The two stable phases include a face- centered-cubic (fcc) rocksalt structure of freely rotat- ing C 60 2 monomers above 400 K [1,2,10] and an orthorhombic structure containing covalently bonded dianionic polymer chains below 400 K [3–18,20–22]. In the polymer phase, which has the characteristics of quasi-one-dimensional metal, the individual cages are con- nected by a 2 1 2 cycloaddition along the face diago- nal to the fcc unit cell [3,5,8]. A metastable monoclinic dimer phase appears as a result of rapid cooling from 500 K [3,6,9–11,15–17]. In the dimer phase, which behaves like an insulator below 220 K, a transition from diamagnetic to paramagnetic response with a drastic increase in susceptibility occurs without hysteresis around 220–270 K [2,3,6,7], as shown in Fig. 1 [6]. Then, at 290 K the dimer phase changes to the fcc phase, which subsequently transforms to the ortho-I polymer phase [2,3,6]. The origin of the magnetic phase transition from diamagnetic to paramagnetic response is still an enigma [6], and therefore the present investigation details theoretical calculations carried out to explain it. Previous theoretical studies on both neutral and anionic fullerene dimers have been carried out on a number of plausible structures [19–28]. The structures studied by Kürti and Németh [25] are shown in Fig. 2. In the neu- tral case, the doubly bonded d D 2h (“d” denotes double- bonded) structure, which is the 2 1 2 cycloadduct, is lower in energy than the singly bonded s C 2h (“s” denotes single-bonded) structure which is formed by direct cova- lent bonding between two fullerene monomers. In contrast, in the dianionic dimer C 60  2 22 , the s C 2h has been re- ported to be lower in energy than the d D 2h [25–28]. A shortcoming of the existing theoretical studies has been that all calculations have been carried out on the singlet states of these dimers, whereas only the diamagnetic be- havior of these dimers was taken into account. In order to overcome this shortcoming and to provide an explana- tion for the magnetic phase transitions, we have carried out high level theoretical calculations in the higher spin states of C 60  2 22 , since the complete transfer of the va- lence electron from the alkali atom to fullerene cage in AC 60 is possible. To optimize the structures of the dianion C 60  2 22 , we employed different theoretical methods: semiempirical methods [unrestricted parametrized method (UPM3), restricted open shell parametrized method at the UPM3 optimized geometries (ROPM3//UPM3)], ab initio meth- ods [restricted open shell Hartree-Fock methods using STO-3G basis sets (ROHF/STO-3G)], and density func- tional methods (restricted open shell density functional FIG. 1. Spin susceptibility of KC 60 and RbC 60 in the monomeric rocksalt phase above 400 K and in the quenched phase below 300 K (reproduced from Ref. [6]). 0031-9007 00  84(11)  2425(4)$15.00 © 2000 The American Physical Society 2425