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The diatomics-in-molecules ͑DIM͒ method for the construction of polyatomic potential-energy functions from the potential energies of atomic and diatomic fragments is generalized to obtain a description of potentialenergy functions of both quasistationary and bound states of polyatomic anions. The formulation is based on the combination of the DIM method with the projection-operator approach of scattering theory. The proposed theory allows the construction of diabatic discrete states, electron-molecule scattering continua, and discretecontinuum coupling elements from the corresponding data of the fragments. The polyatomic projectionoperator description obtained in this way provides the basis for a rigorous treatment of the nuclear dynamics in short-lived electron-molecule collision complexes and ion-molecule collisions in terms of energy-dependent, complex, and nonlocal effective potentials. More approximate local complex potential-energy surfaces of quasistationary states of polyatomic anions also can be obtained with the generalized DIM method via the determination of the poles of the multichannel electron-molecule scattering matrix in the fixed-nuclei limit. Although the focus of the present work is on anions, the proposed theory is also applicable to quasistationary states of neutral and positively charged polyatomic systems including clusters. To illustrate the concepts, the generalized DIM method is applied to obtain the potential-energy functions of the ground and first excited states of the H 3 Ϫ anion, making use of information that is available for the bound and resonance states of H Ϫ and H 2 Ϫ .

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The electronic structures and the total photoionization cross sections of the fullerene C60 and its positive ions C60 n+ (n=1, 2, 3) are calculated for the photon energy range from the ionization thresholds up to 80 eV and compared with the recent experimental data and other calculations. The theoretical approach is based on the local density approximation, the random phase approximation and the jellium models. In contrast to the previous studies, the Perdew–Wang parametrization for the exchange-correlation energy functional is used at present, which leads to more accurate electronic structures and cross sections. Two jellium models are thoroughly tested: the sphere jellium model and the spherical layer jellium model with a finite thickness. It is shown that the spherical layer jellium model provides more reliable results than the sphere model. Two giant resonances are found in the photoionization spectra of all fullerenes treated. The position and the shape of the resonances are determined in agreement with the experimental data.