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We present a first-principles investigation of the excited-state propertiesof electron acceptors in organic photovoltaics including C$_{60}$, C$_{70}$,[6,6]-phenyl-C$_{61}$-butyric-acid-methyl-ester ([C$_{60}$]PCBM), andbis-[C$_{60}$]PCBM using many-body perturbation theory within the Hedin's$G_0W_0$ approximation and an efficient Lanczos approach. Calculated verticalionization potentials (VIP) and vertical electron affinities (VEA) of C$_{60}$and C$_{70}$ agree very well with experimental values measured in gas phase.The density of states of all three molecules is also compared to photoemissionand inverse photoemission spectra measured on thin-films, exhibiting a closeagreement - a rigid energy-gap renormalization owing to intermolecularinteractions in the thin-films. In addition, it is shown that the low-lyingunoccupied states of [C$_{60}$]PCBM are all derived from the highest-occupiedmolecular orbitals and the lowest-unoccupied molecular orbitals of fullereneC$_{60}$. The functional side group in [C$_{60}$]PCBM introduces a slightelectron transfer to the fullerene cage, resulting in small decreases of bothVIP and VEA. This small change of VEA provides a solid justification for theincrease of open-circuit voltage when replacing fullerene C$_{60}$ with[C$_{60}$]PCBM as the electron acceptor in bulk heterojunction polymer solarcells.

physical review. b, condensed matter and materials physics

First-principles investigation of organic photovoltaic materials  C$_{60}$, C$_{70}$, [C$_{60}$]PCBM, and bis-[C$_{60}$]PCBM using a many-body  $G_0W_0$-Lanczos approach