# A study of carbon nanotubes energetics using orbital free method in the frame-work of the density functional theory

( Pp. 29-36)

More about authors

Zavodinsky Victor G.
Doctor of Physics and Mathematics, Professor; leader-researcher at the Khabarovsk Department of the Institute of Applied Mathematicks of the Russian Academy of Sciences. Khabarovsk, Russian Federation. E-mail: vzavod@mail.ru

Institute of Applied Mathematics of the Russian Academy of Sciences

Khabarovsk, Russian Federation Gorkusha Olga A. Candidate of Physics and Mathematics; senior researcher at the Khabarovsk Department of Institute of Applied Mathematics

Institute of Applied Mathematics of the Russian Academy of Sciences

Khabarovsk, Russian Federation Gorkusha Olga A. Candidate of Physics and Mathematics; senior researcher at the Khabarovsk Department of Institute of Applied Mathematics

Abstract:

Dependence of the binding energy of carbon atoms in nanotubes on the tube diameter is studied. The full-electron orbital free modeling method, developed by us in the framework of the density functional theory, was used for calculation of the binding energy. Nanotubes of limited lengths with the armchair ends were investigated. The tube diameter D, was varied from 0,68 nm up to 1,50 nm; numbers of included atoms were changed from 80 up to 320. Three sets of tubes were studied: the tube length was 0,87 nm in the first set, 1,36 nm in second set, and 1,86 nm in the third set. For the first set the energy minimum (-7.50 eV) was found at Dmin = 1,22 nm, for the second set (-7.62 eV) at Dmin = 1.00 nm, and for the third set (-8.01 eV) at Dmin = 1.06 eV.

How to Cite:

Zavodinsky V.G., Gorkusha O.A., (2020), A STUDY OF CARBON NANOTUBES ENERGETICS USING ORBITAL FREE METHOD IN THE FRAME-WORK OF THE DENSITY FUNCTIONAL THEORY. Computational Nanotechnology, 3 => 29-36. DOI: 10.33693/2313-223X-2020-7-3-29-36

Reference list:

Kunsil Lee, Chong Rae Park. Effects of chirality and diameter of single-walled carbon nanotubes on their structural stability and solubility parameters. Royal Society of Chemistry Advances. 2014. No. 4. Pp. 33578-33581.

Chin Li Cheung, Andrea Kurtz, Hongkun Park, Charles M. Lieber. Diameter-controlled synthesis of carbon nanotubes. J. Phys. Chem. B. 2002. No. 106. Pp. 2429-2433.

Eletskiy A.V. Uglerodnye nanotrubki. UFN. 1997. № 167 (9). S. 945-972.

Ching-Hwa Kiang, Goddard III W.A., Beyers R., Bethune D.S. Carbon nanotubes with single-layer walls. In: Carbon nanotubes. M. Endo, S. Iijima, M.S. Dresselhaus (eds). Oxford OX5 l GB, U.K.: Pergamon, Elsevier Science Ltd; The Boulevard, Langford Lane, Kidlington, 1996. Pp. 47-58.

Zavodinsky V.G., Gorkusha O.A., Kuzmenko A.P. Energetics of carbon nanotubes with open edges: Modeling and experiment. Nanosystems: Physics, Chemistry, Mathematics. 2017. No. 8 (5). Pp. 635-640.

Kohn W., Sham J.L. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965. Vol. 140. Pp. A1133-A1138.

Hohenberg H., Kohn W. Inhomogeneous electron gas. Phys. Rev. 1964. Vol. 136. Pp. B864-B871.

Perdew J.P., Zunger A.S. Self-interaction correction to density functional approximation for many-electron systems. Physical Review. 1981. No. 23. Pp. 5048-5079.

Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method. Physical Review. 1980. No. 45. Pp. 566-569.

Perdew J.P., Wang Y. Accurate send simple density functional for the electronic exchange energy. Physical Review. 1986. No. 33. Pp. 8800-8802.

Zavodinsky V.G., Gorkusha O.A. On a possibility to develop a fullpotential orbital-free modeling approach. Nanosystems: Physics, Chemistry, Mathematics, 2019. No. 10 (4). Pp. 402-409.

Zavodinskiy V.G., Gorkusha O.A. Polnoelektronnyy bezorbital nyy metod modelirovaniya atomnykh sistem: pervyy shag. Computational Nanotechnology. 2019. T. 6. № 3. C. 80-85.

Polnoelektronnyy paket dlya modelirovaniya atomov i molekul. URL: http://elk.sourceforge.net

Chin Li Cheung, Andrea Kurtz, Hongkun Park, Charles M. Lieber. Diameter-controlled synthesis of carbon nanotubes. J. Phys. Chem. B. 2002. No. 106. Pp. 2429-2433.

Eletskiy A.V. Uglerodnye nanotrubki. UFN. 1997. № 167 (9). S. 945-972.

Ching-Hwa Kiang, Goddard III W.A., Beyers R., Bethune D.S. Carbon nanotubes with single-layer walls. In: Carbon nanotubes. M. Endo, S. Iijima, M.S. Dresselhaus (eds). Oxford OX5 l GB, U.K.: Pergamon, Elsevier Science Ltd; The Boulevard, Langford Lane, Kidlington, 1996. Pp. 47-58.

Zavodinsky V.G., Gorkusha O.A., Kuzmenko A.P. Energetics of carbon nanotubes with open edges: Modeling and experiment. Nanosystems: Physics, Chemistry, Mathematics. 2017. No. 8 (5). Pp. 635-640.

Kohn W., Sham J.L. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965. Vol. 140. Pp. A1133-A1138.

Hohenberg H., Kohn W. Inhomogeneous electron gas. Phys. Rev. 1964. Vol. 136. Pp. B864-B871.

Perdew J.P., Zunger A.S. Self-interaction correction to density functional approximation for many-electron systems. Physical Review. 1981. No. 23. Pp. 5048-5079.

Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method. Physical Review. 1980. No. 45. Pp. 566-569.

Perdew J.P., Wang Y. Accurate send simple density functional for the electronic exchange energy. Physical Review. 1986. No. 33. Pp. 8800-8802.

Zavodinsky V.G., Gorkusha O.A. On a possibility to develop a fullpotential orbital-free modeling approach. Nanosystems: Physics, Chemistry, Mathematics, 2019. No. 10 (4). Pp. 402-409.

Zavodinskiy V.G., Gorkusha O.A. Polnoelektronnyy bezorbital nyy metod modelirovaniya atomnykh sistem: pervyy shag. Computational Nanotechnology. 2019. T. 6. № 3. C. 80-85.

Polnoelektronnyy paket dlya modelirovaniya atomov i molekul. URL: http://elk.sourceforge.net

Keywords:

quantum modeling, density functional theory, orbital-free approach, carbon nanotubes.

## Related Articles

Development of Functional Nanomaterials Based on Nanoparticles and Polymer Nanostructures Pages: 11-17 DOI: 10.33693/2313-223X-2021-8-2-11-17 Issue №19121

Energetics and Elastic Properties of Large Nano-objects: Orbital-free Approach on the Basis of the Density Functional Theory

orbital-free approach
all-electron potential
density functional theory
modeling
nanomaterials

Show more