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

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

A theoretical and semiemprical correction to the long-range dispersion power law of stretched graphite

In recent years intercalated and pillared graphitic systems have come under increasing scrutiny because of their potential for modern energy technologies. While traditional \emph{ab initio} methods such as the LDA give accurate geometries for graphite they are poorer at predicting physicial properties such as cohesive energies and elastic constants perpendicular to the layers because of the strong dependence on long-range dispersion forces. `Stretching' the layers via pillars or intercalation further highlights these weaknesses. We use the ideas developed by [J. F. Dobson et al, Phys. Rev. Lett. {\bf 96}, 073201 (2006)] as a starting point to show that the asymptotic $C_3 D^{-3}$ dependence of the cohesive energy on layer spacing $D$ in bigraphene is universal to all graphitic systems with evenly spaced layers. At spacings appropriate to intercalates, this differs from and begins to dominate the $C_4 D^{-4}$ power law for dispersion that has been widely used previously. The corrected power law (and a calculated $C_3$ coefficient) is then unsuccesfully employed in the semiempirical approach of [M. Hasegawa and K. Nishidate, Phys. Rev. B {\bf 70}, 205431 (2004)] (HN). A modified, physicially motivated semiempirical method including some $C_4 D^{-4}$ effects allows the HN method to be used successfully and gives an absolute increase of about $2-3$ to the predicted cohesive energy, while still maintaining the correct $C_3 D^{-3}$ asymptotics

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

Nonuniversality of the dispersion interaction: analytic benchmarks for van der Waals energy functionals

We highlight the non-universality of the asymptotic behavior of dispersion forces, such that a sum of inverse sixth power contributions is often inadequate. We analytically evaluate the cross-correlation energy Ec between two pi-conjugated layers separated by a large distance D within the electromagnetically non-retarded Random Phase Approximation, via a tight-binding model. For two perfect semimetallic graphene sheets at T=0K we find Ec = C D^{-3}, in contrast to the "insulating" D^{-4} dependence predicted by currently accepted approximations. We also treat the case where one graphene layer is replaced by a thin metal, a model relevant to the exfoliation of graphite. Our general considerations also apply to nanotubes, nanowires and layered metals.Comment: 4 pages, 0 fig

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

Architectural implications for context adaptive smart spaces

Buildings and spaces are complex entities containing complex social structures and interactions. A smart space is a composite of the users that inhabit it, the IT infrastructure that supports it, and the sensors and appliances that service it. Rather than separating the IT from the buildings and from the appliances that inhabit them and treating them as separate systems, pervasive computing combines them and allows them to interact. We outline a reactive context architecture that supports this vision of integrated smart spaces and explore some implications for building large-scale pervasive systems

Within-field variability of plant and soil parameters

The variability of ground truth data collected for vegetation experiments was investigated. Two fields of wheat and one field of corn were sampled on two different dates. The variability of crop and soil parameters within a field, between two fields of the same type, and within a field over time were compared statistically. The number of samples from each test site required in order to be able to determine with confidence the mean and standard deviations for a given variable was determined. Eight samples were found to be adequate for plant height determinations, while twenty samples were required for plant moisture and soil moisture characterization. Eighteen samples were necessary for detecting within field variability over time and for between field variability for the same crop. The necessary sample sites vary according to the physiological growth stage of the crop and recent weather events that affect the moisture and/or height characteristics of the field in question