Static dielectric response of icosahedral fullerenes from C60 to C2160 by an all electron density functional theory

The static dielectric response of C60, C180, C240, C540, C720, C960, C1500, and C2160 fullerenes is characterized by an all-electron density-functional method. First, the screened polarizabilities of C60, C180, C240, and C540, are determined by the finite-field method using Gaussian basis set containing 35 basis functions per atom. In the second set of calculations, the unscreened polarizabilities are calculated for fullerenes C60 through C2160 from the self-consistent Kohn-Sham orbitals and eigen-values using the sum-over-states method. The approximate screened polarizabilities, obtained by applying a correction determined within linear response theory show excellent agreement with the finite-field polarizabilities. The static dipole polarizability per atom in C2160 is (4 Angstrom^3) three times larger than that in C60 (1.344 Angstrom^3). Our results reduce the uncertainty in various theoretical models used previously to describe the dielectric response of fullerenes and show that quantum size effects in polarizability are significantly smaller than previously thought.Comment: RevTex, 3 figure

Electronic structure, vibrational stability, infra-red, and Raman spectra of B24N24 cages

We examine the vibrational stability of three candidate structures for the B24N24 cage and report their infra-red (IR) and Raman spectra. The candidate structures considered are a round cage with octahedral O symmetry, a cage with S_4 symmetry that satisfies the isolated square rule, and a cage of S_8 symmetry, which combines the caps of the (4,4) nanotube, and contains two extra squares and octagons. The calculations are performed within density functional theory, at the all electron level, with large basis sets, and within the generalized gradient approximation. The vertical ionization potential (VIP) and static dipole polarizability are also reported. The S_4 and S_8 cages are energetically nearly degenerate and are favored over the O cage which has six extra octagons and squares. The IR and Raman spectra of the three clusters show notable differences providing thereby a way to identify and possibly synthesize the cages.Comment: (Uses Elsevier style file; To appear in Chemical Physics Letters

Jahn-Teller instability in C6H6+ and C6H6- revisited

The benzene cation (C6H6+) has a doublet (e_{1g}) ground state in hexagonal ring (D_{6h}) geometry. Therefore a Jahn-Teller (JT) distortion will lower the energy. The present theoretical study yields a model Huckel-type Hamiltonian that includes the JT coupling of the e_{1g} electronic ground state with the two e_{2g} vibrational modes: in-plane ring-bending and C-C bond-stretching. We obtain the JT couplings from density functional theory (DFT), which gives a JT energy lowering of 970 cm^{-1} in agreement with previous quantum chemistry calculations. We find a non-adiabatic solution for vibrational spectra and predict frequencies shifts of both the benzene cation and anion, and give a reinterpretation of the available experimental data.Comment: 6 pages, 3 figure

Theoretical infra-red, Raman, and Optical spectra of the B36N36 cage

The B36N36 fullerene-like cage structure was proposed as candidate structure for the single-shell boron-nitride cages observed in electron-beam irradiation experiment. We have performed all electron density functional calculations, with large polarized Gaussian basis sets, on the B36N36 cage. We show that the cage is energetically and vibrationally stable. The infra-red, Raman and optical spectra are calculated. The predicted spectra, in combination with experimentally measured spectra, will be useful in conclusive assignment of the proposed B36N36 cage. The vertical and adiabatic ionization potentials as well as static dipole polarizability are also reported.Comment: RevTex, 4 pages, 4 figures (TO appear in Physical Review A (Breif Report)

The Hamiltonian of the V15_{15} Spin System from first-principles Density-Functional Calculations

We report first-principles all-electron density-functional based studies of the electronic structure, magnetic ordering and anisotropy for the V$_{15}$ molecular magnet. From these calculations, we determine a Heisenberg Hamiltonian with four antiferromagnetic and one {\em ferromagnetic} coupling. We perform direct diagonalization to determine the temperature dependence of the susceptibility. This Hamiltonian reproduces the experimentally observed spin $S$=1/2 ground state and low-lying $S$=3/2 excited state. A small anisotropy term is necessary to account for the temperature independent part of the magnetization curve.Comment: 4 pages in RevTeX format + 2 ps-figures, accepted by PRL Feb. 2001 (previous version was an older version of the paper

Predicted Infrared and Raman Spectra for Neutral Ti_8C_12 Isomers

Using a density-functional based algorithm, the full IR and Raman spectra are calculated for the neutral Ti_8C_12 cluster assuming geometries of Th, Td, D2d and C3v symmetry. The Th pentagonal dodecahedron is found to be dynamically unstable. The calculated properties of the relaxed structure having C3v symmetry are found to be in excellent agreement with experimental gas phase infrared results, ionization potential and electron affinity measurements. Consequently, the results presented may be used as a reference for further experimental characterization using vibrational spectroscopy.Comment: 6 pages, 5 figures. Physical Review A, 2002 (in press

Effect of local Coulomb interactions on the electronic structure and exchange interactions in Mn12 magnetic molecules

We have studied the effect of local Coulomb interactions on the electronic structure of the molecular magnet Mn12-acetate within the LDA+U approach. The account of the on-site repulsion results in a finite energy gap and an integer value of the molecule's magnetic moment, both quantities being in a good agreement with the experimental results. The resulting magnetic moments and charge states of non-equivalent manganese ions agree very well with experiments. The calculated values of the intramolecular exchange parameters depend on the molecule's spin configuration, differing by 25-30% between the ferrimagnetic ground state and the completely ferromagnetic configurations. The values of the ground-state exchange coupling parameters are in reasonable agreement with the recent data on the magnetization jumps in megagauss magnetic fields. Simple estimates show that the obtained exchange parameters can be applied, at least qualitatively, to the description of the spin excitations in Mn12-acetate.Comment: RevTeX, LaTeX2e, 4 EPS figure

Static dipole polarizability of C70 fullerene

The electronic and vibrational contributions to the static dipole polarizability of C70 fullerene are determined using the finite-field method within the density functional formalism. Large polarized Gaussian basis sets augmented with diffuse functions are used and the exchange-correlation effects are described within the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA). The calculated polarizability of C70 is 103 Angstrom^3, in excellent agreement with the experimental value of 102 Angstrom^3, and is completely determined by the electronic part, vibrational contribution being negligible. The ratio of polarizabilities of C70 and C60 is 1.26. The comparison of polarizability calculated with only local terms (LDA) in the PBE functional to that obtained with PBE-GGA shows that LDA is sufficient to determine the static dipole polarizability of C70.Comment: IOP style, 1 figur

Investigation of the Jahn-Teller Transition in TiF3 using Density Functional Theory

We use first principles density functional theory to calculate electronic and magnetic properties of TiF3 using the full potential linearized augmented plane wave method. The LDA approximation predicts a fully saturated ferromagnetic metal and finds degenerate energy minima for high and low symmetry structures. The experimentally observed Jahn-Teller phase transition at Tc=370K can not be driven by the electron-phonon interaction alone, which is usually described accurately by LDA. Electron correlations beyond LDA are essential to lift the degeneracy of the singly occupied Ti t2g orbital. Although the on-site Coulomb correlations are important, the direction of the t2g-level splitting is determined by the dipole-dipole interactions. The LDA+U functional predicts an aniferromagnetic insulator with an orbitally ordered ground state. The input parameters U=8.1 eV and J=0.9 eV for the Ti 3d orbital were found by varying the total charge on the TiF$_6^{2-}$ ion using the molecular NRLMOL code. We estimate the Heisenberg exchange constant for spin-1/2 on a cubic lattice to be approximately 24 K. The symmetry lowering energy in LDA+U is about 900 K per TiF3 formula unit.Comment: 7 pages, 9 figures, to appear in Phys. Rev.