Relaxation of exciton and photoinduced dimerization in crystalline ${\mathrm{C}}_{60}$

We numerically investigate the lattice relaxation of photogenerated exciton in crystalline ${\mathrm{C}}_{60}$ so as to clarify the mechanism of the photoinduced dimerization processes in this material. In our theory, we deal with the π electrons together with the interatomic effective potentials. Calculations are mainly based on the mean-field theory for interelectron interactions but are also reinforced by taking the electron-hole correlation into account, so that we can obtain the exciton effect. Using a cluster model, we calculate the adiabatic potential energy surfaces of the excitons relevant to the photoinduced dimerization processes occurring in a face-centered-cubic crystal of ${\mathrm{C}}_{60}.$ The potential surfaces of the Frenkel excitons turned out to be quite uneven with several energy minimum points during the structural changes from the Franck-Condon state to the dimerized state. This leads to the conclusion that various structural defects exist at low temperatures even in the single crystal, as an intrinsic property of this molecular crystal with a complicated intermolecular interaction. From the analysis of the potential surfaces of the charge-transfer (CT) excitons, it is confirmed that the CT exciton relaxes down to its self-trapped state, wherein the adjacent two molecules get close together. This implies that the CT between adjacent two molecules is one of mechanisms that triggers the photodimerization or the photopolymerization. The oscillator strength distributions are also calculated for various intermediate structures along the lattice relaxation path. As the dimerization reaction proceeds, the oscillator strength grows in the energy region below the fundamental absorption edge, and the lowest-energy peak, originally at about 1.9 eV, finally shifts down to about 1.7 eV in the final dimerized structure. These results clarify the electronic origins of the luminescence observed in the ${\mathrm{C}}_{60}$ single crystal. Moreover, the origins of the photoinduced absorption spectra observed by Bazhenov, Gorbunov, and Volkodav are elucidated by characteristics of the adiabatic potential energy surfaces obtained here.