Orbital-Free Pseudopotential Approach for Simulation of Multi-Atomic Systems with Covalent Bonds

Authors

  • Victor Zavodinsky  Instutute for Materials Science/FEBRAS, Khabarovsk, Russia
  • Olga Gorkusha  Khabarovsk Department/Instutute of Applied Mathematics/FEBRAS, Khabarovsk, Russia

Keywords:

Orbital-Free, Density Functional, Covalent Bonding, Angular Bond Dependence

Abstract

We showed that the use of the restriction principle for the interatomic density (following from the Paulie's principle) allows us to describe correctly angular dependences of the interatomic bonding in polyatomic systems in the framework of the orbital-free version of the density functional theory. On the example of the three- and four-atomic clusters of aluminum, silicon, and carbon we show that an 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. In particular, the equilateral triangle is favorable for the Al3 cluster; the Si3 trimer is characterized by the isosceles triangle with angles of 80 and 50 degrees, and three atoms of carbon built the linear chain. Calculated equilibrium interatomic distances and the values of binding energy are compared with known data.

References

  1. 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.
  2.  Huajie Chen, Aihui Zhou. Orbital-Free Density Functional Theory for Molecular Structure Calculations. Numerical Mathematics: Theory, Methods and Applications, 2008, 1, 1-28.
  3. 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.
  4. Karasiev V.V., Trickey S.B. Issues and challenges in orbital-free density functional calculations. Computational Physics Communications, 2012, 183, 2519-2527.
  5. 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, 2013, 88, 161108-161113(R). 
  6. Wesolowski T.A. Approximating the kinetic energy functional Ts[ρ]: lessons from four-electron systems. Molecular Physics, 2005, 103, 1165-1167.
  7. 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.
  8. 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).
  9. Lehtomäki, J., Makkonen, I., Caro, M.A., Harju, A. and Lopez-Acevedo O. Orbital-free density functional theory implementation with the projector augmented wave method. Journal Chemical Physics, 2014 141, 234102(7).
  10. Kohn W., Sham J.L. Self-Consistent Equations including Exchange and Correlation Effects. Physical Review 1965, 140, A1133-A1138.
  11. Hohenbeg H., Kohn W. Inhomogeneous Electron Gas, Physical Review, 1964, 136, B864-B871.
  12. Τhоmas, L.Η. The calculation of atomic field, Proceeding Cambridge Philosophical Society, 1926, 23, 542-548.
  13. Fermi E. Un metodo statistico per la determinazione di alcune prioprietà dell'atomo, Rendiconti Academia Dei Lincei, 1927, 6, 602-607.
  14. Von Weizsacker, C.F. Zur Theorie de Kernmassen, Zeitschrift für Physik, 1935, 96, 431-458.
  15. Sarry, A.M. and Sarry, M.F. To the density functional theory. Physics of Solid State, 2012, 54(6), 1315–1322.
  16. Bobrov, V.B. and Trigger, S.A. The problem of the universal density functional and the density matrix functional theory. Journal of Experimental and Theoretical Physics, 2013, 116(4), 635–640.
  17. Zavodinsky V.G., Gorkusha O.A. Quantum-Mechanical Modeling without Wave Functions. Physics of the Solid States, 2014, 56(11), 2329-2335.
  18. Zavodinsky V.G., Gorkusha O.A. New Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles. Modeling and Numerical Simulation of Material Science, 2015, 5, 39-46.
  19. Carling K.M., Carter E.A. Orbital-free density functional theory calculations of the properties of Al, Mg and Al-Mg crystalline phases. Modelling and simulation in materials science and engineering, 2003, 11, 339–348.
  20. Raghavachari K., Logovinsky V. Structure and bonding in small silicon clusters. Physics Review Letteers, 1985, 55, 2853-2856.
  21. Van Orden A., Saykally R.J. Small carbon clusters: spectroscopy, structure, and energetics. Chemical Review, 1998, 98, 2313-2357.
  22. Chuang F.-C., Wang C.Z., Ho K.H. Structure of neutral aluminum clusters Aln (2≤n≤23): Genetic algorithm tight-binding calculations. Physics Review B, 2006 ,73, 125431(7).
  23. 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.
  24. Perdew J.P., Zunger A. Self-interaction correction to density functional approximation for many-electron systems, Physical Review B, 1981, 23, 5048-5079.
  25. Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method, Physical Review Letters, 1980, 45. 566-569.
  26. 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).
  27. Tomanek D., Schluter M.A. Structure and bonding of small semiconductor clusters. Physics Review B, 1987 36, 1208-1217.
  28. Martínez A., Vela A. Stability of charged aluminum clusters. Physical Review B, 1994, 49, 17464(4).
  29. Kumar V., Sundararajan V, Ab initio molecular-dynamics studies of doped magic clusters and their interaction with atoms, Physical Review B, 1998, 57, 4939-4942.
  30. Herzberg G. Spectra of Diatomic Molecules. (Van Nostrand, New York, 1950).
  31. Chelikowsky J.R., Chou M.Y. Ab initio pseudopotential-local density description of the structural properties of small carbon clusters. Physical Review B, 37, 6504-6507.
  32. Fougere P.F., Nesbet R.K. Electronic Structure of C2. Journal of Chemical Physics, 1966, 44, 285-297.
  33. Huber K.P., Herzberg G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules (Reinhold, New York, 1979).
  34. McCarthy M.C., Thaddeus P. Rotational spectrum and structure of Si3. Physical Review Letteers, 2003, 90, 213003(4).
  35. 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.
  36. Rohlfing C.M., Raghavachari K. Electronic structures and photoelectron spectra of Si3 and Si4 . Journal of Chemical Physics, 1992, 96, 2114-2117.
  37. Yang S.H., Drabold D.A., Adams J.B., Sachdev A. First-principles local-orbital density-functional study of Al clusters. Phys. Rev. B. 1993, 47, 1567-1576.
  38. Chuang F.-C., 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).
  39. Tse J.S. Electronic structure of the dimer and trimer of aluminum. Theoretical Chemistry (J. Mol. Structures), 1988, 165, 21-24.
  40. Fuentealba P. Static dipole polarizabilities of small neutral carbon clusters Cn (n<8) Physical Review A, 1998, 58, 4232-4234.
  41. 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.
  42. Drowart J., Burns R.P., DeMaria G., Inghram M.G. Mass spectrometric study of carbon vapor. Journal of Chemical. Physics, 1959, 31, 1131(1).
  43. Rubio A., Alonso J.A., Blase X., Balbas L.C., Louie S.G. Ab initio photoabsorption spectra and structures of small semiconductor and metal clusters. Physical Review Letters, 1996, 77, 247(4).
  44. Drabold D.A., Wang R., Dow J.D. Efficient ab initio molecular-dynamics simulation of carbon. Physical Review B. 1991, 43, 5132-5134.

International Journal of Scientific Research in Science and Technology

Downloads

Published

2017-12-31

Issue

Volume 2, Issue 3, May-June-2016

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Victor Zavodinsky, Olga Gorkusha, " Orbital-Free Pseudopotential Approach for Simulation of Multi-Atomic Systems with Covalent Bonds, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 2, Issue 3, pp.244-251, May-June-2016.