Abstract: Starting from a model of rigid interacting C-60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account (i) van der Waals interactions and electric quadrupole interactions between C-60 monomers on different chains as well as (ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions (i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C-60 chains in planes (001). The interactions (ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C-60 monomers interact with induced quadrupoles due to excited electronic d-states of the alkalis. Both interactions (ii) lead to an effective orientation-orientation interaction between the C-60 chains and always favor the ferrorotational structure I2/m, where C-60 chains have a same orientation. The structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a competition between the direct interaction (i) and the alkali-mediated interactions (ii). In Rb- and CsC60 the latter are found to be dominant, the preponderant role being played by the quadrupolar electronic polarizability of the alkali ions. (C) 2002 American Institute of Physics.

Abstract: Polymerized KC60 undergoes a structural phase transition accompanied by a metal-insulator transition around 50 K. To explain the structural aspect, a mechanism involving small orientational deviations of the valence electron density on every C-60 monomer orientational charge density waves (OCDWs) – has already been proposed earlier. In the present work, we address the metal-insulator transition using the OCDW concept. We are inspired by the analogy between a polymer chain exhibiting an OCDW and a linear atomic chain undergoing a static lattice deformation doubling the unit cell: such a deformation implies a band gap at the zone boundary, yielding an insulating state (Peierls instability). Within our view, a similar mechanism occurs in polymerized KC60; the OCDW plays the role of the lattice deformation. We present tight-binding band structure calculations and conclude that the metal-insulator transition can indeed be explained using OCDWs, but that the threedimensionality of the crystal plays an unexpected key role.

Abstract: We study the confinement of a C-60 molecule encapsulated in a cylindrical nanotube as a function of the tube radius. Drawing the Mercator maps of the potential, we find two distinct molecular orientations; for tubes with small radii, R-T less than or similar to 7 angstrom, a fivefold axis of the molecule coincides with the tube long axis, for larger radii, R-T less than or similar to 8 angstrom, a threefold axis of the molecule coincides with the tube long axis. These different orientations are caused by the relative importance of the repulsive and the attractive parts of the van der Waals potentials of the molecule with the tube wall for small and large tubes respectively. Experimental evidence is provided by the apparent splitting of A(g) modes of the C-60 molecule in resonant Raman scattering.

Abstract: A theoretical model is presented for the description of the metal-insulator transition which accompanies the structural phase transition at T approximate to 50 K in polymerized KC60. The model involves orientational charge density waves (along the C-60 polymer chains) which were introduced previously for a description of the structural phase transition. A satisfactory qualitative and quantitative understanding is obtained when the three-dimensionality of the crystal and the presence of the K+ counterions is properly taken into account.

Abstract: The orientation of a C(70) fullerene molecule encapsulated in a single-walled carbon nanotube (SWCNT) depends on the tube radius. First we confirm that chirality effects do not affect the orientation as well by comparing discrete atomistic calculations with the results of a continuous tube approximation for a variety of SWCNTs. The molecular and the tube symmetry are exploited by using symmetry-adapted rotator functions. We accurately determine the optimal molecular orientation as a function of the tube radius; for low (less than or similar to 7 A) and high (greater than or similar to 7.2 A) tube radii, lying and standing molecular orientations are recovered, respectively. In between, we observe a transition regime. In addition, we consider off-axis positions. We perform a one-dimensional liquid description of a chain of on-axis C(70) molecules inside a SWCNT. All results agree well with recent x-ray diffraction experiments.

Abstract: Born's long wave method is used to study the elastic properties of graphite and graphene. Starting from an empirical force constant model derived from full inplane phonon dispersions of graphite [Mohr et al., Phys. Rev. B 76, 035439 (2007)] we calculate the tension coefficients of graphene. Extending the model by interplanar interactions, we calculate the elastic constants of graphite. The agreement of our theoretical values with inelastic x-ray scattering results on elastic constants of graphite [Bosak et al., Phys. Rev. B 75, 153408 (2007)] is very satisfactory.

Abstract: We study the structure and phase behavior of fullerene-cubane C60·C8H8 by Monte Carlo simulation. Using a simple potential model capturing the icosahedral and cubic symmetries of its molecular constituents, we reproduce the experimentally observed phase transition from a cubic to an orthorhombic crystal lattice and the accompanying rotational freezing of the C60 molecules. We elaborate a scheme to identify the low-temperature orientations of individual molecules and to detect a pattern of orientational ordering similar to the arrangement of C60 molecules in solid C60. Our configuration of orientations supports a doubled periodicity along one of the crystal axes.

Abstract: Starting from an empirical force constant model of valence interactions and calculating by Ewalds method the ion-ion force constants, we derive the dynamical matrix for a monolayer crystal of hexagonal boron nitride (h-BN). The phonon dispersion relations are calculated. The interplay between valence and Coulomb forces is discussed. It is shown by analytical methods that the longitudinal and the transverse optical (LO and TO) phonon branches for in-plane motion are degenerate at the Γ point of the Brillouin zone. Away from Γ, the LO branch exhibits pronounced overbending. It is found that the nonanalytic Coulomb contribution to the dynamical matrix causes a linear increase of the LO branch with increasing wave vector starting at Γ. This effect is general for two-dimensional (2D) ionic crystals. Performing a long-wavelength expansion of the dynamical matrix, we use Borns perturbation method to calculate the elastic constants (tension coefficients). Since the crystal is noncentrosymmetric, internal displacements due to relative shifts between the two sublattices (B and N) contribute to the elastic constants. These internal displacements are responsible for piezoelectric and dielectric phenomena. The piezoelectric stress constant and the dielectric susceptibility of 2D h-BN are calculated.

Abstract: We have studied the dependence of the binding energy of a cubane dimer on the mutual orientation of and the distance between the composing monomers employing the second-order Møller-Plesset perturbation scheme (MP2) with the cc-pVDZ molecular basis set. We have found that the MP2 contribution from the molecular correlations is responsible for the bound state of the cubane dimer, whereas the Hartree-Fock contribution remains anti-bonding at all intermolecular distances. Starting with two molecules in the standard orientation and centers of mass at (0,0,0) and (0,0,d), respectively, the maximal binding energy is found at d = 5.125 Å and one of the monomers rotated by 45° about the z-axis. This configuration implies that the hydrogen atoms belonging to different monomers tend to repel each other. The results are in agreement with experimental data on the optimal packing of cubane molecules in the solid state.

Abstract: We present Monte Carlo simulations of chains of C70 molecules encapsulated in a single-walled carbon nanotube (SWCNT). For various tube radii R (6.5 Å less-than-or-equals, slant R less-than-or-equals, slant 7.5 Å), we analyze rotational and translational motion of the C70 molecules, as a function of temperature. Apart from reproducing the experimentally well-established lying and standing molecular orientations for small and large tube radii, respectively, we observe, depending on the tube diameter, a variety of molecular motions, orientational flipping of lying molecules, and the migration of molecules resulting in a continual rearrangement of the C70 molecules in clusters of varying lengths. With increasing temperature, the evolution of the pair correlation functions reveals a transition from linear harmonic chain behavior to a hard-sphere liquid, making C70@SWCNT peapods tunable physical realizations of two well-known one-dimensional model systems.

Abstract: A unified theory of phonon dispersions and piezoelectricity in bulk and multilayers of hexagonal boron nitride (h-BN) is derived. The dynamical matrix is calculated on the basis of an empirical force constant model of intralayer valence and interlayer van der Waals interactions. Coulomb interactions are calculated by Ewalds method, adapted for the three-dimensional (3D) and the multilayer case. The deformation of the ionic charge distribution with long-wave lattice displacements is taken into account. Special attention is devoted to the nonanalytic long-range Coulomb contribution to the dynamical matrix which is different for the 3D crystal and the multilayer case. Consequently there is a splitting of the transverse optical (TO) and longitudinal optical (LO) phonon branches of E1u symmetry and a discontinuity of the A2u branch at the Γ point in 3D h-BN. No such splitting and discontinuity at Γ are present in multilayer crystals with a finite number N of layers. There a diverging bundle of N overbending optical phonon branches emerges from Γ. Borns long-wave theory is applied and extended for the study of piezoelectricity in layered crystals. While 3D h-BN and h-BN multilayers with an even number of layers (symmetry D6h) are not piezoelectric, multilayers with an uneven number of Nu layers (symmetry D3h) are piezoelectric; the piezoelectric coefficient e1,11 is inversely proportional to Nu.

Abstract: Taking into account covalent, Coulomb and van der Waals interactions, we construct the dynamical matrix and calculate the phonon dispersion relations for multilayer crystals of hexagonal boron-nitride. Coulomb interactions account for a strong overbending of optical phonons. Applying and extending Born's long-wave theory to the case of multilayer crystals, we calculate the piezoelectric stress constant equation image as a function of the number of layers equation image. In agreement with group theory, we find that equation image for equation image even; for an uneven number equation image of layers we obtain equation image, i.e. the piezoelectric constant decreases as equation image.