The limitations of Slater's element-dependent exchange functional from analytic density functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density and the one body effective potential of density functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method,where variationality then refers to the error in each two electron integral and not to the total energy. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in the Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in the system. Of several ways of choosing the scaling factors (Slater's exchange parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and the exact atomic, alpha_EA, values. The performance of this simple analytic model with both sets for atomization energies of G2 set of 148 molecules is better than the local density approximation or the HF theory, although the errors in atomization energy are larger than the target chemical accuracy. To improve peformance for atomization energies, the SR method is reparametrized to give atomization energies of 148 molecules to be comparbale to those obtained by one of the most widely used generalized gradient approximations. The mean absolute error in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 Angstrom. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.Comment: 33 pages, Uses RevTex, to appear in The Journal of Chemical Physic

Accurate molecular energies by extrapolation of atomic energies using an analytic quantum mechanical model

Using a new analytic quantum mechanical method based on Slater's Xalpha method, we show that a fairly accurate estimate of the total energy of a molecule can be obtained from the exact energies of its constituent atoms. The mean absolute error in the total energies thus determined for the G2 set of 56 molecules is about 16 kcal/mol, comparable to or better than some popular pure and hybrid density functional models.Comment: 5 pages, REVTE

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)

On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in Physical Review Letter

Localization Properties of Electronic States in Polaron Model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling are completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.Comment: 6 pages, 6 figure

Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer

The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A field-induced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure

The oldest X-ray supernovae: X-ray emission from 1941C, 1959D, 1968D

We have studied the X-ray emission from four historical Type-II supernovae (the newly-discovered 1941C in NGC 4631 and 1959D in NGC 7331; and 1968D, 1980K in NGC 6946), using Chandra ACIS-S imaging. In particular, the first three are the oldest ever found in the X-ray band, and provide constraints on the properties of the stellar wind and circumstellar matter encountered by the expanding shock at more advanced stages in the transition towards the remnant phase. We estimate emitted luminosities ~ 5 x 10^{37} erg/s for SN 1941C, ~ a few x 10^{37} erg/s for SN 1959D, ~ 2 x 10^{38} erg/s for SN 1968D, and ~ 4 x 10^{37} erg/s for SN 1980K, in the 0.3-8 keV band. X-ray spectral fits to SN 1968D suggest the presence of a harder component, possibly a power law with photon index ~ 2, contributing ~ 10^{37} erg/s in the 2-10 keV band. We speculate that it may be evidence of non-thermal emission from a Crab-like young pulsar.Comment: 6 pages, accepted by ApJ. Revised version with a couple of added references. Thanks to A. Kong and E. Schlegel for their comments. Credit to Holt et al. (2003) for the X-ray discovery of SN 1968D, overlooked in other recent catalog

Topological Phases in Graphitic Cones

The electronic structure of graphitic cones exhibits distinctive topological features associated with the apical disclinations. Aharonov-Bohm magnetoconductance oscillations (period Phi_0) are completely absent in rings fabricated from cones with a single pentagonal disclination. Close to the apex, the local density of states changes qualitatively, either developing a cusp which drops to zero at the Fermi energy, or forming a region of nonzero density across the Fermi energy, a local metalization of graphene.Comment: 4 pages, RevTeX 4, 3 PostScript figure

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM

White Dwarf Rotation as a Function of Mass and a Dichotomy of Mode Linewidths: Kepler Observations of 27 Pulsating DA White Dwarfs Through K2 Campaign 8

We present photometry and spectroscopy for 27 pulsating hydrogen-atmosphere white dwarfs (DAVs, a.k.a. ZZ Ceti stars) observed by the Kepler space telescope up to K2 Campaign 8, an extensive compilation of observations with unprecedented duration (>75 days) and duty cycle (>90%). The space-based photometry reveals pulsation properties previously inaccessible to ground-based observations. We observe a sharp dichotomy in oscillation mode linewidths at roughly 800 s, such that white dwarf pulsations with periods exceeding 800 s have substantially broader mode linewidths, more reminiscent of a damped harmonic oscillator than a heat-driven pulsator. Extended Kepler coverage also permits extensive mode identification: We identify the spherical degree of 61 out of 154 unique radial orders, providing direct constraints of the rotation period for 20 of these 27 DAVs, more than doubling the number of white dwarfs with rotation periods determined via asteroseismology. We also obtain spectroscopy from 4m-class telescopes for all DAVs with Kepler photometry. Using these homogeneously analyzed spectra we estimate the overall mass of all 27 DAVs, which allows us to measure white dwarf rotation as a function of mass, constraining the endpoints of angular momentum in low- and intermediate-mass stars. We find that 0.51-to-0.73-solar-mass white dwarfs, which evolved from 1.7-to-3.0-solar-mass ZAMS progenitors, have a mean rotation period of 35 hr with a standard deviation of 28 hr, with notable exceptions for higher-mass white dwarfs. Finally, we announce an online repository for our Kepler data and follow-up spectroscopy, which we collect at http://www.k2wd.org.Comment: 33 pages, 31 figures, 5 tables; accepted for publication in ApJS. All raw and reduced data are collected at http://www.k2wd.or