Efficient, long-range correlation from occupied wavefunctions only

We use continuum mechanics [Tao \emph{et al}, PRL{\bf 103},086401] to approximate the dynamic density response of interacting many-electron systems. Thence we develop a numerically efficient exchange-correlation energy functional based on the Random Phase Approximation (dRPA). The resulting binding energy curve $E(D)$ for thin parallel metal slabs at separation $D$ better agrees with full dRPA calculations than does the Local Density Approximation. We also reproduce the correct non-retarded van der Waals (vdW) power law E(D)\aeq -C_{5/2}D^{-5/2} as $D\to\infty$, unlike most vdW functionals.Comment: 4 pages, 1 figur

The flexible nature of exchange, correlation and Hartree physics: resolving "delocalization" errors in a 'correlation free' density functional

By exploiting freedoms in the definitions of 'correlation', 'exchange' and 'Hartree' physics in ensemble systems we better generalise the notion of 'exact exchange' (EXX) to systems with fractional occupations functions of the frontier orbitals, arising in the dissociation limit of some molecules. We introduce the Linear EXX ("LEXX") theory whose pair distribution and energy are explicitly \emph{piecewise linear} in the occupations $f^{\sigma}_{i}$. {\hi}We provide explicit expressions for these functions for frontier $s$ and $p$ shells. Used in an optimised effective potential (OEP) approach it yields energies bounded by the piecewise linear 'ensemble EXX' (EEXX) energy and standard fractional optimised EXX energy: $E^{EEXX}\leq E^{LEXX} \leq E^{EXX}$. Analysis of the LEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer so that "ghost" Hartree interactions appear between \emph{opposite} spin electrons in the usual formula. The energy $E^{LEXX}$ contains a cancellation term for the spin ghost case. It is evaluated for H, Li and Na fractional ions with clear derivative discontinuities for all cases. The $p$-shell form reproduces accurate correlation-free energies of B-F and Al-Cl. We further test LEXX plus correlation energy calculations on fractional ions of C and F and again shows both derivative discontinuities and good agreement with exact results

Dispersion corrections in graphenic systems: a simple and effective model of binding

We combine high-level theoretical and \emph{ab initio} understanding of graphite to develop a simple, parametrised force-field model of interlayer binding in graphite, including the difficult non-pairwise-additive coupled-fluctuation dispersion interactions. The model is given as a simple additive correction to standard density functional theory (DFT) calculations, of form $\Delta U(D)=f(D)[U^{vdW}(D)-U^{DFT}(D)]$ where $D$ is the interlayer distance. The functions are parametrised by matching contact properties, and long-range dispersion to known values, and the model is found to accurately match high-level \emph{ab initio} results for graphite across a wide range of $D$ values. We employ the correction on the difficult bigraphene binding and graphite exfoliation problems, as well as lithium intercalated graphite LiC$_6$. We predict the binding energy of bigraphene to be 0.27 J/m^2, and the exfoliation energy of graphite to be 0.31 J/m^2, respectively slightly less and slightly more than the bulk layer binding energy 0.295 J/m^2/layer. Material properties of LiC$_6$ are found to be essentially unchanged compared to the local density approximation. This is appropriate in view of the relative unimportance of dispersion interactions for LiC$_6$ layer binding

Disk M Dwarf Luminosity Function From HST Star Counts

We study a sample of 257 Galactic disk M dwarfs (8<M_V<18.5) found in images obtained using HST. These include 192 stars in 22 fields imaged with the repaired WFC2 with mean limiting mag I=23.7 and 65 stars in 162 fields imaged with the pre-repair Planetary Camera with mean limiting mag V=21.3. We find that the disk luminosity function (LF) drops sharply for M_V>12 (M<0.25 \ms), decreasing by a factor \gsim 3 by M_V~14 (M~0.14\ms). This decrease in the LF is in good agreement with the ground-based photometric study of nearby stars by Stobie et al. (1989), and in mild conflict with the most recent LF measurements based on local parallax stars by Reid et al. (1995). The local LF of the faint Galactic disk stars can be transformed into a local mass function using an empirical mass-M_V relation. The mass function can be represented analytically over the mass range 0.1\ms<M<1.6\ms by \log(\phi)=-1.35-1.34\log(M/\ms)-1.85 [\log(M/\ms)]^2 where \phi is the number density per logarithmic unit of mass. The total column density of M stars is only \Sigma_M=11.8\pm 1.8\ms\pc^{-2}, implying a total `observed' disk column density of \Sigma_\obs~=39\ms\pc^{-2}, lower than previously believed, and also lower than all estimates with which we are familiar of the dynamically inferred mass of the disk. The measured scale length for the M-star disk is 3.0\pm 0.4 kpc. The optical depth to microlensing toward the LMC by the observed stars in the Milky Way disk is \tau~1x10^{-8}, compared to the observed optical depth found in ongoing experiments \tau_\obs~ 10^{-7}. The M-stars show evidence for a population with characteristics intermediate between thin disk and spheroid populations. Approximating what may be a continuum of populations by two separate component, we find characteristic exponential scale heights of ~210 pc and ~740 pc.Comment: 30 pages, uuencoded postscript, includes 3 figures, 2 table

How many-body effects modify the van der Waals interaction between graphene sheets

Undoped graphene (Gr) sheets at low temperatures are known, via Random Phase Approximation (RPA) calculations, to exhibit unusual van der Waals (vdW) forces. Here we show that graphene is the first known system where effects beyond the RPA make qualitative changes to the vdW force. For large separations, $D \gtrsim 10$nm where only the $\pi_z$ vdW forces remain, we find the Gr-Gr vdW interaction is substantially reduced from the RPA prediction. Its $D$ dependence is very sensitive to the form of the long-wavelength many-body enhancement of the velocity of the massless Dirac fermions, and may provide independent confirmation of the latter via direct force measurements.Comment: 3 Figures: PACS 73.22.Pr, 71.10.Pm, 61.48.Gh, 34.20.C

Enrollment in the 2003/2004 MILC Program: Does Timing Matter?

Agricultural and Food Policy, Marketing,

Improving U.S. Housing Finance Through Reform of Fannie Mae and Freddie Mac: Assessing the Options

Presents criteria for evaluating proposals for reforming the two government-sponsored enterprises. Outlines the key arguments for their structural strengths and weaknesses, a framework and goals for reform, and features of specific proposals to date

van der Waals dispersion power laws for cleavage, exfoliation and stretching in multi-scale, layered systems

Layered and nanotubular systems that are metallic or graphitic are known to exhibit unusual dispersive van der Waals (vdW) power laws under some circumstances. In this letter we investigate the vdW power laws of bulk and finite layered systems and their interactions with other layered systems and atoms in the electromagnetically non-retarded case. The investigation reveals substantial difference between `cleavage' and `exfoliation' of graphite and metals where cleavage obeys a $C_2 D^{-2}$ vdW power law while exfoliation obeys a $C_3 \log(D/D_0) D^{-3}$ law for graphitics and a $C_{5/2} D^{-5/2}$ law for layered metals. This leads to questions of relevance in the interpretation of experimental results for these systems which have previously assumed more trival differences. Furthermore we gather further insight into the effect of scale on the vdW power laws of systems that simultaneously exhibit macroscopic and nanoscopic dimensions. We show that, for metallic and graphitic layered systems, the known "unusual" power laws can be reduced to standard or near standard power laws when the effective scale of one or more dimension is changed. This allows better identification of the systems for which the commonly employed `sum of $C_6 D^{-6}$' type vdW methods might be valid such as layered bulk to layered bulk and layered bulk to atom