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

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)

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

Calculation of valence electron momentum densities using the projector augmented-wave method

We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H_2O)_2) systems agree well with experiments and computational results obtained with other band-structure and basis set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.Comment: Submitted to Journal of Physics and Chemistry of Solids on September 17 2004. Revised version submitted on December 13 200

Positron and positronium affinities in the work-formalism Hartree-Fock approximation

Positron binding to anions is investigated within the work formalism proposed by Harbola and Sahni for the halide anions and the systems Li^- through O^- excluding Be^- and N^-. The toal ground-state energies of the anion-positron bound systems are empirically found to be an upper bound to the Hartree-Fock energies. The computed expectation values as well as positron and positronium affinities are in good agreement with their restricted Hartree-Fock counterparts. Binding of a positron to neutral species is also investigated using an iterative method.Comment: 12 pages, to appear in Physical Review

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

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states

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

Scheduling periodic tasks in a hard real-time environment

We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks $au_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $au_i$ releases a job of running time $c_i$ at each time $a_i + kcdot p_i,k in mathbb{N}_0$ and a collision occurs if two jobs are simultaneously active on the same machine. We shed some light on the complexity and approximability landscape of this problem. Although the problem cannot be approximated within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i | p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads to a 2-approximation. This result is tight, even asymptotically

A systematic approach to designing reliable VV optimization methodology: Assessment of internal validity of echocardiographic, electrocardiographic and haemodynamic optimization of cardiac resynchronization therapy

AbstractBackgroundIn atrial fibrillation (AF), VV optimization of biventricular pacemakers can be examined in isolation. We used this approach to evaluate internal validity of three VV optimization methods by three criteria.Methods and resultsTwenty patients (16 men, age 75±7) in AF were optimized, at two paced heart rates, by LVOT VTI (flow), non-invasive arterial pressure, and ECG (minimizing QRS duration). Each optimization method was evaluated for: singularity (unique peak of function), reproducibility of optimum, and biological plausibility of the distribution of optima.The reproducibility (standard deviation of the difference, SDD) of the optimal VV delay was 10ms for pressure, versus 8ms (p=ns) for QRS and 34ms (p<0.01) for flow.Singularity of optimum was 85% for pressure, 63% for ECG and 45% for flow (Chi2=10.9, p<0.005).The distribution of pressure optima was biologically plausible, with 80% LV pre-excited (p=0.007). The distributions of ECG (55% LV pre-excitation) and flow (45% LV pre-excitation) optima were no different to random (p=ns).The pressure-derived optimal VV delay is unaffected by the paced rate: SDD between slow and fast heart rate is 9ms, no different from the reproducibility SDD at both heart rates.ConclusionsUsing non-invasive arterial pressure, VV delay optimization by parabolic fitting is achievable with good precision, satisfying all 3 criteria of internal validity. VV optimum is unaffected by heart rate. Neither QRS minimization nor LVOT VTI satisfy all validity criteria, and therefore seem weaker candidate modalities for VV optimization. AF, unlinking interventricular from atrioventricular delay, uniquely exposes resynchronization concepts to experimental scrutiny