Restricted Three Body Problems at the Nanoscale

Chan, Yue; Thamwattana, Ngamta; Hill, James M.

doi:10.1007/s00601-009-0070-3

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…3, this mathematical problem has limited physical significance, and we can approximate the potential by integrating over the buckyball sphere. Like Chan et al [11] we, therefore, generate an effective potential experienced by a "test" carbon atom located at a point r by integrating over the spherical surface to obtain…”

Section: Quantum Mechanical Approachmentioning

confidence: 99%

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Quantum Bound States in a C–C60 System

Adam

Sofianos

2015

Few-Body Syst

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We investigate the quantum mechanical system of a carbon "test atom" in the proximity of a C60 molecule, both inside and outside the fullerene "cage". Two sets of bound states are found to exist, a deeply bound set inside the cage and another weakly bound set outside it. Tunnelling between these regions is highly unlikely to happen because of the extreme height and width of the potential barrier. However, we predict that a layer of atoms could be adsorbed onto C60 by forming a quantum mechanical bound state, with the adsorbed atoms being concentrated above the "panels" of the buckyball, consistent with "bucky onions" observed experimentally. Until now analysis of such fullerene systems has been via classical mechanics, but a quantum approach reveals new insights. BackgroundSince 1970, when Henson proposed the buckminsterfullerene structure [1], major strides have been made in the field. The compound was first identified by Iijima in 1980 [2] and synthesized in 1985 [3], the latter work resulting in the 1996 Nobel Prize for Chemistry. Fullerenes have attracted wide interest over the past 30 years, for both fundamental and practical reasons, in fields as diverse as geology [4], astronomy [5] and medicine [6]. Very recently the field has diversified yet further, with the synthesis of an all boron fullerene [7].Although it may be surmised that systems containing C60 molecules are too "large" to sustain quantum effects, the observation of Arndt et al. [8], namely the measurement of a quantum interference pattern produced by C60 molecules passing through a diffraction grating, contradicts this. Despite the large number of degrees of freedom (180 for a single C60 molecule) and the associated high probability of decoherence, diffraction was observed. Molecules of the size and complexity of C60 evidently lie in a zone between classical and quantum systems. Although this fact is indeed of fundamental interest, our motivation for undertaking this investigation was to determine whether the Schrödinger equation would yield useful insights into the properties of simple C60 cluster systems. The mechanics of such systems is traditionally analyzed via classical techniques based on the Euler-Lagrange equations (see, for example, Refs. [9][10][11]). The extension to finite temperature and thereby thermodynamical functions is made via the Nosé-Hoover Hamiltonian [12,13].The advantage that a quantum mechanical approach has over corresponding classical techniques is that, for bound states, the condition of normalization imposes tremendous restrictions on the solutions to the Schrödinger Electronic supplementary material The online version of this article (

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Section: Quantum Mechanical Approachmentioning

confidence: 99%

“…The mechanics of such systems is traditionally analyzed via classical techniques based on the Euler-Lagrange equations (see, for example, Refs. [9][10][11]). The extension to finite temperature and thereby thermodynamical functions is made via the Nosé-Hoover Hamiltonian [12,13].…”

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confidence: 97%

Quantum Bound States in a C–C60 System

Adam

Sofianos

2015

Few-Body Syst

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“…Chan et al [9] conducted a research of two-body problems at the nanoscale, including fullerene-fullerene and fullerene-carbon nanotube. Chan et al [10] looked at the placements of three C 60 fullerenes, a carbon atom, and two C 60 fullerenes in the circular planar constrained three-body issue. The maximum angular frequency of two and three fullerene systems reaches the terahertz range, according to their findings.…”

Section: General Introductionmentioning

confidence: 99%

On the restricted three-body model of the dynamical behaviour of masses of C70 fullerenes at the nanoscale

Singh

Tyokyaa²

2022

Heliyon

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The present study investigates the positions and stability of 𝐶 70 fullerenes. Numerically, the positions and stability have been computed 𝐶 70 fullerene at the nanoscale to show the effects of the parameters involved with the help of software MATHEMATICA. The total molecular energy evidenced refers to the total pairwise molecular interactions between two C 70 fullerenes, which is an approximation of a continuous approach. The attractive Vand der Waals forces between only molecules provide the centripetal forces between three fullerenes. The total pairwise molecular interactions between two C 70 fullerenes, which is an approximation of a continuous approach, is termed the total molecular energy evidenced. The attractive Vand der Waals forces between single molecules create the centripetal forces between three fullerenes. We have predicted the collective potential function, mutual force and angular velocity. The stationary points are collinearly lying on the 𝜉 − 𝑎𝑥𝑖𝑠 which are symmetric about the 𝜂 − 𝑎𝑥𝑖𝑠 as the molecules of the carbon atoms in the nucleus are evenly distributed. There is at least one complex root with the positive real part for each set of values, it has been discovered. The stationary points are thus unstable in the Lyapunov sense.

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Static and Restricted Rigid Rotor Configurations of Three Classical 12-6-Lennard-Jones Particles

Rupp

2015

Few-Body Syst

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Restricted Three Body Problems at the Nanoscale

Cited by 5 publications

References 19 publications

Quantum Bound States in a C–C60 System

Quantum Bound States in a C–C60 System

On the restricted three-body model of the dynamical behaviour of masses of C70 fullerenes at the nanoscale

Static and Restricted Rigid Rotor Configurations of Three Classical 12-6-Lennard-Jones Particles

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