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9M(o2p where Vp is the average electron-phonon coupling energy in the (3 x 3) matrix of the subspace associated with the threefold degenerate tlu LUMO bands, and the trace appearing in Eq. (14.6) is taken over the same (3 x 3) space. The sum on p in Eq. (14.6) is over the normal modes of an isolated C«7 ion and the sum on ¡x is over the degeneracy of each mode [14.77], The matrix elements in Eq. (14.6) were calculated by noting the connection of the electron-phonon coupling problem to the Jahn-Teller distortion of a molecule with a degenerate ground state (f]u) in an icosahedral field. It has been argued that the intramolecular Jahn-Teller modes are the ones which directly modulate nearest-neighbor wave function overlaps, so that the screening effect [14.78], which strongly reduces other contributions to the electron-phonon coupling, has a relatively small effect on the intramolecular Jahn-Teller (Hg) modes.

Results for the contribution to V = Vp from each of the Hg modes are given in Table 14.3. The first column gives results obtained from an LDA calculation [14.75] for which the weighted average V and ¿>ph for the eight Hg modes are taken to be 52.0 meV and 950 cm-1, respectively [14.76]. Here ¿ph is an average phonon frequency used in McMillan's formula (see §15.2). A comparison of these values with results obtained

Table 14.3

Contribution of Hg and Ag intramolecular modes to the electron-phonon coupling potential.

Table 14.3

Contribution of Hg and Ag intramolecular modes to the electron-phonon coupling potential.

Mode (p)

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