Phonons, electron-phonon, and electron-plasmon coupling in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mn>60</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>compounds

We have performed ab initio calculations for the ${\mathit{A}}_{\mathit{g}}$ and ${\mathit{H}}_{\mathit{g}}$ intramolecular phonon frequencies, using a full-potential linear muffin-tin-orbital (LMTO) method. The deviation from experiment is typically 5%. We have further calculated the electron-phonon coupling for these modes, as well as for some alkali-metal and libration modes, using both tight-binding and ab initio, full-potential LMTO methods. The tight-binding calculations illustrate that for the intramolecular modes the tedious Brillouin-zone sums can be replaced by calculations for a free molecule, while for the libration modes a simplification of this type is not possible. The ab initio calculations show a strong coupling to the two highest and, to a lesser extent, to the second lowest ${\mathit{H}}_{\mathit{g}}$ intramolecular modes, while the coupling is weak to the librations and the studied alkali-metal modes. The total coupling to the ${\mathit{H}}_{\mathit{g}}$ intramolecular modes is \ensuremath{\lambda}=0.068N(0), where N(0) is the density of states (states/eV spin ${\mathrm{C}}_{60}$), which corresponds to \ensuremath{\lambda}\ensuremath{\sim}0.6--0.7 for the alkali-metal-doped ${\mathrm{C}}_{60}$ compounds. The difference in coupling between superconductivity and photoemission, where the molecule is charged during the emission process, is studied for the ${\mathit{A}}_{\mathit{g}}$ modes. Furthermore, the electron-plasmon coupling is calculated in a tight-binding formalism. This coupling (g/${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$${)}^{2}$\ensuremath{\sim}1 is found to be substantial. The calculated electron-phonon couplings are finally tested by calculating the superconductivity transition temperature using the Eliashberg equation and the temperature-dependent resistivity. These calculations show that the calculated couplings are of the right order of magnitude, but probably somewhat small, and that the coupling to librations and intermolecular modes should be weak.