For sparse materials like graphitic systems and carbon nanotubes the standard
density functional theory (DFT) faces significant problems because it cannot
accurately describe the van der Waals interactions that are essential to the
carbon-nanostructure materials behavior. While standard implementations of DFT
can describe the strong chemical binding within an isolated, single-walled
carbon nanotube, a new and extended DFT implementation is needed to describe
the binding between nanotubes. We here provide the first steps to such an
extension for parallel and concentric nanotubes through an electron-density
based description of the materials coupling to the electrodynamical field. We
thus find a consistent description of the (fully screened) van der Waals
interactions that bind the nanotubes across the low-electron-density voids
between the nanotubes, in bundles and as multiwalled tubes.Comment: 6 pages, 4 figures (5 figure files

Elsebeth Schröder

Girifalco

Gradshteyn

Hult

Lundqvist

Per Hyldgaard

Rydberg

Schröder

English

arXiv

Crossref

Schr\uf6der, Elsebeth

Hyldgaard, Per

Chalmers Research

The van der Waals Interactions of Concentric Nanotubes

Schröder, Elsebeth

Chalmers Publication Library

Concentric nanotubes are stabilized by a competition between the short-range repulsion and
the long-range van der Waals binding. At the relevant binding distances (3.4 Ångström) we
find that traditional first-principle density-functional theory (DFT) calculations can only par-
tially account for these combined interactions and that an accurate quantum-physics account
of structure and dynamics must also include a calculation of the van der Waals forces. We use
a successful model of the electrodynamical response of the nanotube electron gas to provide
such a combined description in which we reflect the important self-consistent screening effects
arising within the nanotube electron gases. Our description differs significantly from traditional
asymptotic calculations of the van der Waals interactions. Work supported by the Carl Tryggers Foundation, W. and M. Lundgren Foundation, the Swedish Research Council (VR), and
the Swedish Foundation for Strategic Research (SSF)

THE VAN DER WAALS INTERACTIONS OF CONCENTRIC NANOTUBES
Elsebeth Schro¨der and Per Hyldgaard
Dept. of Applied Physics, Chalmers University of Technology and Go¨teborg University,
SE–412 96 Gothenburg, Sweden
E-mail: schroder@fy.chalmers.se
Concentric nanotubes are stabilized by a competition between the short-range repulsion and
the long-range van der Waals binding. At the relevant binding distances (3.4 A˚ngstro¨m) we
find that traditional first-principle density-functional theory (DFT) calculations can only par-
tially account for these combined interactions and that an accurate quantum-physics account
of structure and dynamics must also include a calculation of the van der Waals forces. We use
a successful model of the electrodynamical response of the nanotube electron gas to provide
such a combined description in which we reflect the important self-consistent screening effects
arising within the nanotube electron gases. Our description differs significantly from traditional
asymptotic calculations of the van der Waals interactions. Work supported by the Carl Tryg-
gers Foundation, W. and M. Lundgren Foundation, the Swedish Research Council (VR), and
the Swedish Foundation for Strategic Research (SSF).
Introduction
Soft and sparse material systems constitute a significant challenge for quantum-physical theory
as their structure complicates the necessary calculations. While density-functional theory (DFT)
provides an accurate account of most hard and dense materials, the present implementations of
the DFT tool meets with important, fundamental problems when applied to the soft materials
important for both life and most of our daily-life activities.
The quantum-physical computations are complicated in the soft and sparse materials because
these combine both chemically-bonded ‘molecular regions’ of high electron density and ‘inter-
molecular voids’ across which physical interactions are mediated exclusively through the electro-
magnetic field, reflecting nonlocal correlations of the electron density—the van-der-Waals type
of interactions. The difficulties in combining accurate accounts of both the local and nonlocal
electron correlations has shifted the emphasis to other, less accurate, phenomenological descrip-
tions (often implemented in molecular-dynamics simulations). However, recent advances [1–3]
indicate that the remarkable accuracy of hard-materials DFT calculations can be extended to
soft condensed matter.
Here we investigate the quantum-physical interactions within the concentric-nanotube sys-
tem, Fig. 1. This system constitutes—like graphite [3]—an ideal example of the soft and sparse
materials computational problem due to the clear separation of intratube, local, chemical bind-
ings and nonlocal, physical, intertube interactions. For this system we combine first-principle
DFT calculations with a successful, if approximate, description of the physical intertube forces.
The nonlocal intertube physical interactions
The multiwalled nanotube, i.e., the concentric nanotube system is stabilized by a competition of
the kinetic-energy repulsion and the weak physical attraction mediated by the electromagnetic
fields. Our calculation of this physical intertube attraction is based on accurate first-principle
DFT calculations of the kinetic repulsion and the following approximate treatment of the inter-
tube attraction.
Adapting the successfull model description of Ref. [1] we approximate the local nanotube
response by the bare dynamic susceptibility at (complex) frequency u:
χ0 (n(r), u, u0) =
n(r)
u2 + u20
. (1)
This is a function of the nanotube electron density n(r) (at distance r from the nanotube center)
which we determine directly from first-principle DFT calculations [4]. The frequency cut-off u0
is defined by a separate first-principle calculation of the static nanotube susceptibility.
From this model of the local susceptibility we obtain a corresponding effective susceptibility
tensor χeff which describes the ratio of the locally induced polarization to the externally applied
Figure 1: A quantum-physical description of the interactions within two concentric nanotubes
requires both accurate calculations of the strong, local intratube chemical bindings and of the
weak, nonlocal intertube physical interaction that stabilize the multiwalled nanotube. This inter-
tube interaction arises as a competition of a kinetic-energy repulsion and a van-der-Waals type
attraction. Our standard density-functional theory (DFT) implementations provides an excellent
account of the intratube interactions but not of the intertube forces. We combine first-principle
DFT calculations [4] of the nanotube electron density with a model [1–3] of the electron re-
sponse, to provide a detailed quantum-physical description of the multiwalled nanotube structure
and stability.
electric field. This effective susceptibility is a functional of the electron density:
χeff [n(r)] (u, u0) 6= χ01 + 4piχ0 (2)
but can be calculated from a separate determination of the self-consistent screening within and
between the nanotubes.
Our description differs significantly from the traditional, approximative and asymptotic ac-
count of the van der Waals interaction because of the finite screening effect by the nanotube
electron density. Moreover, our description of the physical intertube attraction offers a direct
integration with the first-principle DFT calculations [4] necessary for an accurate description of
both the intratube chemical binding and the kinetic-energy intertube repulsion.
Conclusion
In summary, we report a quantum-physical calculation that combines both the chemical in-
tratube and physical intertube interactions. Present standard DFT functional calculations alone
can not provide a complete account of the nanotube structure and dynamics but must be sup-
plemented by calculations of the intertube physical interactions. We have adapted a successful
model [1] for these calculations of the physical interactions, based directly on the calculated [4]
nanotube electron density.
References
[1] E. Hult, H. Rydberg, B. I. Lundqvist, and D. C. Langreth, Phys. Rev. B 59, 4708 (1999).
[2] H. Rydberg, B. I. Lundqvist, D. C. Langreth and M. Dion, Phys. Rev. B 62, 6997 (2000).
[3] H. Rydberg, N. Jacobson, P. Hyldgaard, S. I. Simak, B. I. Lundqvist, and D. C. Langreth,
Hard Numbers on Soft Matter, Applied Physics Reports 2001-48.
[4] Computer code DACAPO, http://www.fysik.dtu.dk/CAMPOS/


Concentric nanotubes are stabilized by a competition between the short-range repulsion andthe long-range van der Waals binding. At the relevant binding distances (3.4 \uc5ngstr\uf6m) wefind that traditional first-principle density-functional theory (DFT) calculations can only par-tially account for these combined interactions and that an accurate quantum-physics accountof structure and dynamics must also include a calculation of the van der Waals forces. We usea successful model of the electrodynamical response of the nanotube electron gas to providesuch a combined description in which we reflect the important self-consistent screening effectsarising within the nanotube electron gases. Our description differs significantly from traditionalasymptotic calculations of the van der Waals interactions. Work supported by the Carl Tryggers Foundation, W. and M. Lundgren Foundation, the Swedish Research Council (VR), andthe Swedish Foundation for Strategic Research (SSF)

For sparse materials like graphitic systems and carbon nanotubes the standard density functionaltheory (DFT) faces significant problems because it cannot accurately describe the van der Waalsinteractions that are essential to the carbon-nanostructure materials behavior. While standard implementationsof DFT can describe the strong chemical binding within an isolated, single-walledcarbon nanotube, a new and extended DFT implementation is needed to describe the binding betweennanotubes. We here provide the first steps to such an extension for parallel and concentricnanotubes through an electron-density based description of the materials coupling to the electrodynamicalfield. We thus find a consistent description of the (fully screened) van der Waals interactionsthat bind the nanotubes across the low-electron-density voids between the nanotubes, in bundlesand as multiwalled tubes

Van der Waals interactions of parallel and concentric nanotubes

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