3,304 research outputs found

### 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

### 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

### 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

### 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

### 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

### Quantum Continuum Mechanics Made Simple

In this paper we further explore and develop the quantum continuum mechanics
(CM) of [Tao \emph{et al}, PRL{\bf 103},086401] with the aim of making it
simpler to use in practice. Our simplifications relate to the non-interacting
part of the CM equations, and primarily refer to practical implementations in
which the groundstate stress tensor is approximated by its Kohn-Sham version.
We use the simplified approach to directly prove the exactness of CM for
one-electron systems via an orthonormal formulation. This proof sheds light on
certain physical considerations contained in the CM theory and their
implication on CM-based approximations. The one-electron proof then motivates
an approximation to the CM (exact under certain conditions) expanded on the
wavefunctions of the Kohn-Sham (KS) equations. Particular attention is paid to
the relationships between transitions from occupied to unoccupied KS orbitals
and their approximations under the CM. We also demonstrate the simplified CM
semi-analytically on an example system

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