Homo

"1Q

Fig. 13.22. Diagram of molecular orbitals and transitions for Cm shown in column A. Proposed diagram for molecular orbitals and transitions for C^ is shown in column B, and for C^ is shown in column C. The transitions in columns B and C are labeled and assigned to the simulated near-IR spectra placed above each diagram with the photon energy scale increasing toward the left [13.134].

distortion for the anion was proposed, which completely removes the degeneracy of the tlu and tlg levels (as shown in column A of Fig. 13.23), i.e., tlu -> a{ + b2 + ¿i, and tlg b2 + bx + a2. Two of the three additional electrons are paired in the al orbital and an unpaired electron occupies the next higher b2 level. Four allowed transitions are identified (a-d), and these labels correspond to the peaks in the simulated spectrum above the level diagram.

Three level schemes were considered for the Cf)0 anion, and we discuss them briefly. In one of these schemes, paired electrons are placed in each of the elu levels forming a ground state similar to the C2m dianion as shown in column C of Fig. 13.22. With four paired electrons filling the eiu level, this ground state would be diamagnetic. The near-IR opti-

A B1 B2

Fig. 13.23. Proposed diagram for molecular orbitals and transitions for C^ is shown in column A. Two possible molecular orbital diagrams for C*m are shown in columns B1 and B2. The transitions in (A), (Bl), and (B2) are labeled and assigned to the simulated near-IR spectra placed above each diagram [13.134].

A B1 B2

Fig. 13.23. Proposed diagram for molecular orbitals and transitions for C^ is shown in column A. Two possible molecular orbital diagrams for C*m are shown in columns B1 and B2. The transitions in (A), (Bl), and (B2) are labeled and assigned to the simulated near-IR spectra placed above each diagram [13.134].

cal spectrum of C^ according to this scheme should resemble that of C260 , which it doesn't. So this scheme was discarded. Schemes (Bl) and (B2) in Fig. 13.23 should both give rise to similar simulated spectra (as shown), differing primarily in the number of mid-energy transitions: (b, c) in Bl and (b) in B2. The EPR spectra for schemes Bl and B2 should differ, since B2 describes a spin triplet and Bl is diamagnetic. The availability of EPR spectra for could perhaps help to distinguish between the Bl and B2 models.

Although the assignments of many of the features in the near-IR spectra for the Cg0 ions are still tentative, this region of the spectrum nevertheless provides unambiguous identification of the oxidation state of the CM molecular anion and is important for this reason alone. However, as the discussion above indicates, the optical results coupled with EPR data (see §16.2.2) can provide valuable information about possible Jahn-Teller distortions of the molecular anion ground state.

First principles LDA-based calculations of the Jahn-Teller distortions in the monoanion [13.142] show that the bonds between the pairs of atoms lying near the equator and parallel to it are shortened and strengthened, and the bonds between those atoms that cross the equator are lengthened and weakened (see Fig. 13.24), resulting in a displacement of the two hemispheres of the spherically shaped molecule before the Jahn-Teller distortion. These bond length changes elongate the C60 molecule normal to the equator and stabilize the a2u orbital, in agreement with the Jahn-Teller splitting indicated in column B of Fig. 13.22 for

Qo- The energy gain calculated for the Jahn-Teller distortion of the CM anion is very small (only ~24 meV) and corresponds to a decrease

Fig. 13.24. Model of the anion showing in black the key atoms whose displacements stabilize the a2u orbital. Thick lines connecting the black belt atoms to the two hemispherical caps denote strengthened (shortened) bonds, while dashed lines connecting alternate black atoms correspond to weakened (lengthened) bonds of the C^ anion referred to the neutral C^ molecule [13.142], in bond length on the order of 0.01 A for the quasiequatorial pairs of carbon atoms. The eigenvalue spectrum corresponding to the Jahn-Teller distortion of the C60 anion from icosahedral Ih symmetry to the lower D5d symmetry is shown in Fig. 13.25, generally consistent with the level ordering used to interpret the optical solution spectra for CM in column B of Fig. 13.22.

13.4.2. Optical Properties o/M6C60

In this section we review the optical properties and the contributions to the dielectric function from electronic interband transitions for the saturation-doped M6C60 compounds, where M = K, Rb, and Cs. These compounds crystallize in the body-centered cubic (bcc) phase, with the M ions residing in each of the six tetrahedral interstitial sites in the bcc lattice (see §8.5.1). Complete electron transfer from the alkali metal atoms to the C60 sublat-tice is thought to occur, resulting in the formation of the hexanion with completely filled tlu orbitals. The M6C60 compounds are therefore expected to be insulators, or semiconductors, depending on the intermolecular coupling which determines the bandwidth of the valence and conduction bands. Because of the many similarities between the optical properties of M6C60 compounds (with filled tlu orbitals) and C60 (filled hu orbitals), we begin our discussion of the optical properties of the M_,.C60 compounds with the MfiC 60 alkali metal family of compounds.

The band gap for M6C60 compounds is between the filled tiu states and the empty tig states, which in C60 are split by ~1 eV [13.143,144] (see §13.3.2). Furthermore, the hexanion is in an Ag symmetry configuration ground state (see Table 12.2) and is therefore stable against a Jahn-Teller

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