The crystal structure, cohesive energy, and electronic properties of bulk phases of the fullerene derivative [6, 6]-phenyl-${\text{C}}_{61}$-butyric-acid-methyl-ester (PCBM) have been calculated using ab initio density-functional theory (DFT) techniques. We have only considered cubic and hexagonal crystal lattices with one PCBM molecule per primitive cell. It was found that the cohesive properties of these systems are determined mainly by two types of mechanisms, namely, the van der Waals interaction and the formation of weak hydrogen bonds. Among the considered crystal structures, the most stable one, which is also the most compact structure, is the simple cubic which has a cohesive energy difference of 1.27 eV with respect to the isolated PCBM molecule. Regarding the electronic properties, the simple-cubic PCBM crystal is found to be a semiconductor with an indirect band gap of 1.21 eV. In addition, we have also investigated the electronic contribution of the phenyl-butyric-acid-methyl-ester tail to the electronic states of the entire system. By analyzing the projected density of states (DOS), we found that the states introduced by the tail are too far from the valence and conduction bands, so that the reduction of the band gap of bulk PCBM compared to PCBM molecule results only from the close packing. In addition, the tail introduces a splitting of the degenerate states of the molecule reducing the gap by about 0.2 eV compared to the ${\text{C}}_{60}$ molecule. On the other hand, it is shown that the simple hexagonal structure presents a layered structure with the separation between layers of $12.6\text{Å}$. Furthermore, in the cohesive curve, there is a nonvanishing cohesive energy for noninteracting layers. The study of the hexagonal monolayers shows a stable structure with a cohesive energy of 0.72 eV, which indicates that PCBM can form two-dimensional systems when the PCBM molecules are deposited on the appropriate substrates. The results provided by this work may be important to improve our understanding concerning the mechanisms of formation of PCBM supramolecular structures, and how they can be modified to reach a desired particular property.

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\gamma]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of $W$ is obtained throughout the domain of representability of $\gamma_{ij}$, including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for $W$. Goals and limitations of the different approximations are discussed.Comment: 25 pages and 8 figures, submitted to Phys. Rev.