Jahn-Teller Spectral Fingerprint in Molecular Photoemission: ${\mathrm{C}}_{60}$

The $h_u$ hole spectral intensity for ${\mathrm{C}}_{60}\to {\mathrm{C}}_{60}^{+}$ molecular photoemission is calculated at finite temperature by a parameter-free Lanczos diagonalization of the electron-vibration Hamiltonian, including the full 8 $H_g$, 6 $G_g$, and 2 $A_g$ mode couplings. The computed spectrum at 800 K is in striking agreement with gas-phase data. The energy separation of the first main shoulder from the main photoemission peak, 230 meV in ${\mathrm{C}}_{60}$, is shown to measure directly and rather generally the strength of the final-state Jahn-Teller coupling.

Figure 1

Experimental PE spectra by Canton et al. [4] and by Brühwiler et al. [3] compared with the calculation based on the ab initio parameters of Ref. 5 ($T=800\mathrm{K}$, $N_{\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{r}}=31$, $N_{\max }={10}^5$, $N_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}=245$). Intensities are normalized to unity. Inset: $T=800\mathrm{K}$ spectra including the single $H_g^{(1)}$ mode, and $H_g^{(7)}$ and $H_g^{(8)}$. All spectra are shifted to move the main peak to zero energy and broadened with a 10 meV HWHM Gaussian. The error bar gives the largest statistical error introduced by random sampling of the initial states.

Figure 2

Vibronic excitation energies for a single $H_g$ mode coupled to the $h_u$ level, as a function of coupling, for a ratio $g^{(2)}/g^{(1)}$ characteristic of the $H_g^{(7/8)}$ modes. The average refers to the multiplet originating from the one-phonon states. Bold: $h_u$ states, the only visible states in $T=0$ PE.

Figure 3

Temperature dependence of the PE, computed including all modes of ${\mathrm{C}}_{60}$ for $T=0$, $T=300\mathrm{K}$, and $T=800\mathrm{K}$. Labels ${\Lambda }_v^{(j)}$ indicate the leading component in the vibronic states. Inset: computed spectra ($T=800\mathrm{K}$) based on the same DF coupling parameters $g_{\Lambda j}^r$ divided by $\sqrt{2}$, original, and multiplied by $\sqrt{2}$, compared to experiment [3].