“…The interpolated distance of 1.37 A agrees to numerical precision with the 1.36 A obtained in an earher LDF calculation [9] using the same methodology but a less sophisticated functional. Various theoretical methods give roughly this same displacement A 4-31G (host) and DZP (guest) Hartree-Fock calculation finds 1.297 A [12], an MNDO calculation finds 1.4 A [13], and a double-numerical basis-set LDF caicluation finds 1.5 A [14] for this equilibrium displacement.…”
Section: Introductionsupporting
confidence: 63%
“…These fitting bases were both augmented with 0.25, 0.37, 0.70, 2.0 and 5.0 p and d exponents on C and 0.1, 0.3 and 0.9 p and d exponents on Li. This same set of exponents and contraction scheme were used in a local density functional (LDF) study of Li@C60 [9]. b.…”
“…The interpolated distance of 1.37 A agrees to numerical precision with the 1.36 A obtained in an earher LDF calculation [9] using the same methodology but a less sophisticated functional. Various theoretical methods give roughly this same displacement A 4-31G (host) and DZP (guest) Hartree-Fock calculation finds 1.297 A [12], an MNDO calculation finds 1.4 A [13], and a double-numerical basis-set LDF caicluation finds 1.5 A [14] for this equilibrium displacement.…”
Section: Introductionsupporting
confidence: 63%
“…These fitting bases were both augmented with 0.25, 0.37, 0.70, 2.0 and 5.0 p and d exponents on C and 0.1, 0.3 and 0.9 p and d exponents on Li. This same set of exponents and contraction scheme were used in a local density functional (LDF) study of Li@C60 [9]. b.…”
“…This finding was further confirmed by Dunlap et al in 1992, which showed that the equilibrium position of Li + and Na + are displaced radially outward by 1.40 Å and 0.70 Å from the center of the cage of Li@C60 and Na@C60, while K + is located in the center of the cage of K@C60. 25 In other studies, interactions of Na atom and Na + ion with C60 molecule were investigated by Hartree−Fock theory, and possibilities of significant charge transfer from the metal to the C60 molecule and subsequent decrease in the HOMO−LUMO gaps of C60 were discovered. 26 Quantum chemical calculations of Li@C60…”
We have investigated the mechanism of alkali metal incorporation into C60 fullerene by density functional theory (DFT) at the UB3LYP/6-31G* level of theory. Calculations were performed to study the insertion pathways of Li(+), Na(+), and K(+) through six- or five-membered rings of fullerene, and the computed energy barriers of metal ion insertion are compared with the available experimental data. Between the two possible insertion pathways, metal ion insertion through [2 + 2 + 2] ring opening of the six-membered ring is found to be more favored than the insertion through the ring opening of the five-membered ring. The size of the ring openings generated by the three metal ions is likely to be correlated with their ionic size, which shows the smallest opening for Li(+) and the largest for K(+) cation. The insertion energy barriers of the ions are found to be increased in the order of Li(+) < Na(+) < K(+) in line with the experimental results. The ring opening made by breaking of C-C bonds during the metal ion insertion in six- or five-membered rings can cause the ring to be rearranged and convert back into a closed fullerene cage to form a stable endohedral metal-fullerene complex.
“…17 In this work, we considered the potassium ions to be encapsulated inside the inner CNT, because K + @C 60 is one of simplest endofullerenes. 46 Figure 2(a) shows the structure of the double-wall CNTs, for which both ends of the outer shell are opened and the core shell is extruded. Legoas et al 21,22 showed that the nano-oscillators are dynamically stable when the difference in radii between the inner and the outer nanotubes is ϳ3.4 Å.…”
This paper demonstrates a gigahertz actuator based on multiwall carbon nanotubes (CNT) encapsulating metallic ions using classical molecular-dynamics simulations. Our results for a vacant CNT oscillator were in good agreement with the results obtained from previous experiments, theories, and simulations. Encapsulated potassium ions accelerated by an applied external electric field could initialize a gigahertz actuator composed of a 7K+@CNT oscillator, in which a CNT encapsulates seven potassium ions. The energetics and operation of a vacant CNT oscillator were similar to those of the 7K+@CNT oscillator except for the binding energies, the correlated collisions, and the mass increase caused by the encapsulated ions. Since the total mass of the 7K+@CNT oscillator was slightly higher than that of the vacant CNT oscillator, the frequency of the vacant CNT oscillator was slightly higher than the frequency of the 7K+@CNT oscillator. The correlated collisions between the ions or between the CNT and the ions slightly affected the oscillation dynamics, such as restoring force and frequency.
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