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We have calculated the quantum quadrupolar interaction due to charge density fluctuations of localized 4f -electrons in γ−Ce by taking into account the angular dependence, the degeneracy of the localized 4f −orbitals and the spin-orbit coupling. The calculated crystal field of 4f electronic states is in good agreement with neutron diffraction measurements. We show that orientational ordering of quantum quadrupoles drives a Fm3m → Pa3 phase transition at ∼ 86 K which we assign with the γ−α transformation. In the Pa3 phase the centers of mass of the Ce atoms still form a face centered cubic lattice. The theory accounts for the first order character of the transition and for the cubic lattice contraction which accompanies the transition. The transition temperature increases linearly with pressure. Our approach does not involve Kondo spin fluctuations as the significant process for the phase transition. PACS. 71.10.-w Theories and models of many electron systems -71.27.+a Strongly correlated electron systems; heavy fermions -71.45.-d Collective effects -64.70.Kb Solid-solid transitions

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The confinement of a C60 molecule encapsulated in a cylindrical nanotube depends on the tube radius. In small tubes with radius RT approximately < 7 A, a fivefold axis of the molecule coincides with the tube axis. The interaction between C60 molecules in the nanotube is then described by a O2-rotor model on a 1D liquid chain with coupling between orientational and displacive correlations. This coupling leads to chain contraction. The structure factor of the 1D liquid is derived. In tubes with a larger radius the molecular centers of mass are displaced off the tube axis. The distinction of two groups of peapods with on- and off-axis molecules suggests an explanation of the apparent splitting of Ag modes of C60 in nanotubes measured by resonant Raman scattering.

Starting from a multipole expansion of intra-molecular Coulomb interactions, we present configuration interaction calculations of the molecular energy terms of the hole configurations (h + u ) m , m = 2 − 5, of C m+ 60 cations, of the electron configurations t n 1u , n = 2 − 4, of the C n− 60 anions, and of the exciton configurations (h + u t − 1u ), (h + u t − 1g ) of the neutral C60 molecule. The ground state of C 2− 60 is either 3 T1g or 1 Ag, depending on the energy separation between t1g and t1u levels. There are three close (∼0.03 eV) low lying triplets 3 T1g, 3 Gg, 3 T2g for C 2+ 60 , and three quartets 4 T1u, 4 Gu, 4 T2u for C 3+ 60 , which can be subjected to the Jahn-Teller effect. The number of low lying nearly degenerate states in largest for m = 3 holes. We have calculated the magnetic moments of the hole and electron configurations and found that they are independent of molecular orientation in respect to an external magnetic field. The coupling of spin and orbital momenta differs from the atomic case. We analyze the electronic dipolar transitions (t1u) 2 → t1ut1g and (t1u) 3 → (t1u) 2 t1g for C 2− 60 and C 3− 60 . Three optical absorption lines ( 3 T1g → 3 Hu, 3 T1u, 3 Au) are found for the ground level of C 2− 60 and only one line ( 4 Au → 4 T1g) for the ground state of C 3− 60 . We compare our results with the experimental data for C n− 60 in solutions and with earlier theoretical studies.

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As a possible mechanism of the ␥-␣ phase transition in pristine cerium a change of the electronic density from a disordered state with symmetry Fm3 m to an ordered state Pa3 has been proposed. Here we include on-site and intersite electron correlations involving one localized 4 f electron and one conduction 5d electron per atom. The model is used to calculate the crystal field of ␥-Ce and the temperature evolution of the mean field of ␣-Ce. The formalism can be applied to crystals where quadrupolar ordering involves several electrons on the same site.