# APPLICATION OF ORBITAL-FREE APPROACH TO SIMULATION OF MULTI ATOMIC SYSTEMS WITH VARIOUS DIRECTIONS OF INTERATOMIC BONDS

( Pp. 24-29)

More about authors

Zavodinsky Victor G.
Dr. Sci. (Phys.-Math.), Professor; leader-researcher

Khabarovsk branch at Institute of Applied Mathematics of the Far Eastern branch of the Russian Academy of Sciences

Khabarovsk, Russian Federation Gorkusha Olga A. Cand. Sci. (Phys.-Math.); senior researcher; Khabarovsk branch at Institute of Applied Mathematics of the Far Eastern branch of the Russian Academy of Sciences; Khabarovsk, Russian Federation

Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny

St. Petersburg, Russian Federation

Khabarovsk branch at Institute of Applied Mathematics of the Far Eastern branch of the Russian Academy of Sciences

Khabarovsk, Russian Federation Gorkusha Olga A. Cand. Sci. (Phys.-Math.); senior researcher; Khabarovsk branch at Institute of Applied Mathematics of the Far Eastern branch of the Russian Academy of Sciences; Khabarovsk, Russian Federation

Military Academy of Communications named after Marshal of the Soviet Union S.M. Budyonny

St. Petersburg, Russian Federation

Abstract:

On the example of the three-atomic clusters Al3, Si3 and C3 it is shown that the orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi atomic systems with both the metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found in good accordance with known data.

How to Cite:

Zavodinsky V.G., Gorkusha O.A., (2016), APPLICATION OF ORBITAL-FREE APPROACH TO SIMULATION OF MULTI ATOMIC SYSTEMS WITH VARIOUS DIRECTIONS OF INTERATOMIC BONDS. Computational Nanotechnology, 1 => 24-29.

Reference list:

Wang Y.A., Carter E.A. Orbital-free kinetic-energy density functional theory. In: Progress in Theoretical Chemistry and Physics. Kluwer, Dordrecht. 2000, 117 p.

Huajie Chen, Aihui Zhou. Orbital-Free Density Functional Theory for Molecular Structure Calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1, 1-28.

Baojing Zhou, Ligneres V.L., Carter E.A. Improving the orbital-free density functional theory description of covalent materials. Journal Chemical Physics, 2005, 122, 044103-044113.

Hung L., Carter E.A. Accurate Simulations of Metals at the Mesoscale: Explicit Treatment of 1 Million Atoms with Quantum Mechanics. Chemical Physics Letters, 2009, 475, 163-170.

Karasiev V.V., Trickey S.B. Issues and challenges in orbital-free density functional calculations. Computational Physics Communications, 2012, 183, 2519-2527.

Karasiev V.V., Chakraborty D., Shukruto O.A., Trickey S.B. Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Physical Review B, 88, 161108-161113(R).

Wesolowski T.A. Approximating the kinetic energy functional Ts : lessons from four-electron systems. Molecular Physics, 2005, 103, 1165-1167.

Kohn W., Sham J.L. Self-Consistent Equations including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133-A1138.

Hohenbeg H., Kohn W. Inhomogeneous Electron Gas, Physical Review, 1964, 136, B864-B871.

V.G. Zavodinskiy, O.A. Gorkusha. FTT, 56, 2253 (2014);

Junchao Xia, Chen Huang, Ilgyou Shin, Carter E.A. Can orbital-free density functional theory simulate molecules The Journal of Chemical Physics, 2012, 136, 084102(13).

Raghavachari K., Logovinsky V. Structure and bonding in small silicon clusters. Phys. Rev. Lett. 1985, 55, 2853-2856.

Van Orden A., Saykally R.J. Small carbon clusters: spectroscopy, structure, and energetics. Chemical Review, 1998, 98, 2313-2357.

Feng-Chuan Chuang, Wang C.Z., Ho K.H. Structure of neutral aluminum clusters Aln (2 n 23): Genetic algorithm tight-binding calculations. Phys. Rev. B, 2006 ,73, 125431(7).

Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory, Computational Physics Communications, 1999), 119, 67-98.

Perdew J.P., Zunger A. Self-interaction correction to density functional approximation for many-electron systems, Physical Review B, 1981, 23, 5048-5079.

Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method, Physical Review Letters, 1980, 45. 566-569.

Tomanek D., Schluter M.A. Structure and bonding of small semiconductor clusters. Phys. Rev. B, 1987 36, 1208-1217.

Mukhtarov A.P., Normurodov A.B., Sulaymonov N.T., Umarova F.T. Charge States of Bare Silicon Clusters up to Si8 by Non-Conventional Tight-Binding Method. Journal of nano- and electronic physics, 2015, 7, 01012(7).

Nayak S.K., Khanna S.N., Jena P.J. Evolution of bonding in AlnN clusters: A transition from nonmetallic to metallic character. Physical Review B, 1998, 57, 3787-3790.

Matr nez A., Vela A. Stability of charged aluminum clusters. Physical Review B, 1994, 49, 17464(4).

Karton A., Tarnopolsky A., Martin J.M.L. Atomization energies of the carbon clusters Cn (n 2-10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods. International Journal of Interface between Chemistry and Physics, 2009, 107, 977-1003.

Mahdi Afshar, Mahboobeh Babaei, Amir Hossein Kordbacheh. First principles study on structural and magnetic properties of small and pure carbon clusters (Cn, n 2-12) Journal of Theoretical and Applied Physics, 2014, 8, 103-108.

McCarthy M.C., Thaddeus P. Rotational spectrum and structure of Si3. Physical Review Letters, 2003, 90, 213003(4).

Liu B., Lu Z.Y., Pan B., Wang C.Z., Ho K. M., Shvartsburg A.A., Jarrold M.F. Ionization of medium-sized silicon clusters and the geometries of the cations. Journal of Chemical Physics, 1998, 109, 9401-9409.

Raghavachari K., Rohlfing C.M. Bonding and stabilities of small silicon clusters: A theoretical study of Si7-Si10. Journal of Chemical Physics, 1988, 89, 2219-2234.

V.G. Zavodinsky, O.A. Gorkusha. A practical way to develop the orbital-free density functional calculations. Physical Science International Journal, 2014, 4(6), 880-891;

V.G. Zavodinskiy, O.A. Gorkusha. Na puti k modelirovaniyu bol shikh nanosistem na atomnom urovne. Computational nanotechnology, 2014, 1, 11-16;

V.G. Zavodinsky O.A. Gorkusha. A new Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles. Modeling and Numerical Simulation of Material Science, 2015, 5, 39-47.

Huajie Chen, Aihui Zhou. Orbital-Free Density Functional Theory for Molecular Structure Calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1, 1-28.

Baojing Zhou, Ligneres V.L., Carter E.A. Improving the orbital-free density functional theory description of covalent materials. Journal Chemical Physics, 2005, 122, 044103-044113.

Hung L., Carter E.A. Accurate Simulations of Metals at the Mesoscale: Explicit Treatment of 1 Million Atoms with Quantum Mechanics. Chemical Physics Letters, 2009, 475, 163-170.

Karasiev V.V., Trickey S.B. Issues and challenges in orbital-free density functional calculations. Computational Physics Communications, 2012, 183, 2519-2527.

Karasiev V.V., Chakraborty D., Shukruto O.A., Trickey S.B. Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Physical Review B, 88, 161108-161113(R).

Wesolowski T.A. Approximating the kinetic energy functional Ts : lessons from four-electron systems. Molecular Physics, 2005, 103, 1165-1167.

Kohn W., Sham J.L. Self-Consistent Equations including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133-A1138.

Hohenbeg H., Kohn W. Inhomogeneous Electron Gas, Physical Review, 1964, 136, B864-B871.

V.G. Zavodinskiy, O.A. Gorkusha. FTT, 56, 2253 (2014);

Junchao Xia, Chen Huang, Ilgyou Shin, Carter E.A. Can orbital-free density functional theory simulate molecules The Journal of Chemical Physics, 2012, 136, 084102(13).

Raghavachari K., Logovinsky V. Structure and bonding in small silicon clusters. Phys. Rev. Lett. 1985, 55, 2853-2856.

Van Orden A., Saykally R.J. Small carbon clusters: spectroscopy, structure, and energetics. Chemical Review, 1998, 98, 2313-2357.

Feng-Chuan Chuang, Wang C.Z., Ho K.H. Structure of neutral aluminum clusters Aln (2 n 23): Genetic algorithm tight-binding calculations. Phys. Rev. B, 2006 ,73, 125431(7).

Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory, Computational Physics Communications, 1999), 119, 67-98.

Perdew J.P., Zunger A. Self-interaction correction to density functional approximation for many-electron systems, Physical Review B, 1981, 23, 5048-5079.

Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method, Physical Review Letters, 1980, 45. 566-569.

Tomanek D., Schluter M.A. Structure and bonding of small semiconductor clusters. Phys. Rev. B, 1987 36, 1208-1217.

Mukhtarov A.P., Normurodov A.B., Sulaymonov N.T., Umarova F.T. Charge States of Bare Silicon Clusters up to Si8 by Non-Conventional Tight-Binding Method. Journal of nano- and electronic physics, 2015, 7, 01012(7).

Nayak S.K., Khanna S.N., Jena P.J. Evolution of bonding in AlnN clusters: A transition from nonmetallic to metallic character. Physical Review B, 1998, 57, 3787-3790.

Matr nez A., Vela A. Stability of charged aluminum clusters. Physical Review B, 1994, 49, 17464(4).

Karton A., Tarnopolsky A., Martin J.M.L. Atomization energies of the carbon clusters Cn (n 2-10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods. International Journal of Interface between Chemistry and Physics, 2009, 107, 977-1003.

Mahdi Afshar, Mahboobeh Babaei, Amir Hossein Kordbacheh. First principles study on structural and magnetic properties of small and pure carbon clusters (Cn, n 2-12) Journal of Theoretical and Applied Physics, 2014, 8, 103-108.

McCarthy M.C., Thaddeus P. Rotational spectrum and structure of Si3. Physical Review Letters, 2003, 90, 213003(4).

Liu B., Lu Z.Y., Pan B., Wang C.Z., Ho K. M., Shvartsburg A.A., Jarrold M.F. Ionization of medium-sized silicon clusters and the geometries of the cations. Journal of Chemical Physics, 1998, 109, 9401-9409.

Raghavachari K., Rohlfing C.M. Bonding and stabilities of small silicon clusters: A theoretical study of Si7-Si10. Journal of Chemical Physics, 1988, 89, 2219-2234.

V.G. Zavodinsky, O.A. Gorkusha. A practical way to develop the orbital-free density functional calculations. Physical Science International Journal, 2014, 4(6), 880-891;

V.G. Zavodinskiy, O.A. Gorkusha. Na puti k modelirovaniyu bol shikh nanosistem na atomnom urovne. Computational nanotechnology, 2014, 1, 11-16;

V.G. Zavodinsky O.A. Gorkusha. A new Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles. Modeling and Numerical Simulation of Material Science, 2015, 5, 39-47.

Keywords:

Modeling, the density functional, butalbitalin approach, the trimers, covalent bonds.

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