Volume 6, Issue 4, August 2017, Page: 189-195
New Orbital Free Simulation Method Based on the Density Functional Theory
Victor Zavodinsky, Institute for Material Science, Khabarovsk, Russia
Olga Gorkusha, Khabarovsk Department, Institute of Applied Mathematics, Khabarovsk, Russia
Received: Jul. 17, 2017;       Accepted: Jul. 25, 2017;       Published: Aug. 4, 2017
DOI: 10.11648/j.acm.20170604.16      View  414      Downloads  33
A practical way to simulate multi-atomic systems without using of wave functions (orbitals) is proposed. Kinetic functionals for each type of atoms are constructed and then are used for complex systems. On examples of clusters containing Al, Si, C, and O it is shown that this method can describe structures and energies of multi-atomic systems not worse than the Kohn-Sham method but faster. Besides, it is demonstrated that the orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi-atomic systems with covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies for Si3 and C3 clusters are found in good accordance with known data.
Orbital-free, Density Functional, Hetero-Atomic Systems, Interatomic Distances, Interbonding Angles
To cite this article
Victor Zavodinsky, Olga Gorkusha, New Orbital Free Simulation Method Based on the Density Functional Theory, Applied and Computational Mathematics. Vol. 6, No. 4, 2017, pp. 189-195. doi: 10.11648/j.acm.20170604.16
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Hohenbeg H., Kohn W. Inhomogeneous electron gas, Physical Review, 1964, 136, B864-B871.
Kohn W., Sham J. L. Self-consistent equations including exchange and correlation effects. Physical Review 1965, 140, A1133-A1138.
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.
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.
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[ρ]: lessons from four-electron systems. Molecular Physics, 2005, 103, 1165-1167.
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).
Lehtomäki J., Makkonen I., Caro M. A., Harju A. and Lopez-Acevedo O. (2014) Orbital-free density functional theory implementation with the projector augmented wave method. Journal of Chemical Physics, 141 234102(7).
Zavodinsky V. G., Gorkusha O. A. Quantum-mechanical modeling without wave functions. Physics of the Solid States, 2014, 56(11), 2329-2335.
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.
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.
Beckstedte M., Kley A., Neugebauer J., Scheffler M. Density functional theory calculations for poly-atomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Computational Physics Communications, 1997, 107, 187-205.
Raghavachari K., Logovinsky V. Structure and bonding in small silicon clusters. Physical Review Letters 1985, 55, 2853-2856.
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.
Feng-Chuan Chuang, Wang C. Z., Ho K. H. Structure of neutral aluminum clusters Aln (2≤n≤23): Genetic algorithm tight-binding calculations. Physical Review B, 2006, 73, 125431(7).
Matrínez 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.
Tomanek D., Schluter M. A. Structure and bonding of small semiconductor clusters. Phys. Rev. B, 1987 36, 1208-1217.
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.
Tse J. S. Electronic structure of the dimer and trimer of aluminum. Theoretical Chemistry (Journal of Molecular Structures), 1988, 165, 21-24.
Van Orden A., Saykally R. J. Small carbon clusters: spectroscopy, structure, and energetics. Chemical Review, 1998, 98, 2313-2357.
G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 1950).
X. L. Zhu, X. C. Zeng, Structures and stabilities of small silicon clusters: Ab initiomolecular-orbital calculations of Si7–Si11. J. Chem. Phys. 2003, 118, 3558.
K. P. Huber and G. Herzberg. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules (Reinhold, New York, 1979).
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