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 MNSMS  Vol.5 No.2 , April 2015
New Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles
Abstract: Development of the orbital-free (OF) approach of the density functional theory (DFT) may result in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A key problem on this way is calculation of the kinetic energy. We demonstrate how it is possible to create the OF kinetic energy functionals using results of Kohn-Sham calculations for single atoms. Calculations provided with these functionals for dimers of sp-elements of the C, Si, and Ge periodic table rows show a good accordance with the Kohn-Sham DFT results.
Cite this paper: Zavodinsky, V. and Gorkusha, O. (2015) New Orbital-Free Approach for Density Functional Modeling of Large Molecules and Nanoparticles. Modeling and Numerical Simulation of Material Science, 5, 39-47. doi: 10.4236/mnsms.2015.52004.
References

[1]   Hohenberg, H. and Kohn, W. (1964) Inhomogeneous Electron Gas. Physical Review, 136, B864-B871.
http://dx.doi.org/10.1103/PhysRev.136.B864

[2]   Wang, Y.A. and Carter, E.A. (2000) Orbital-Free Kinetic-Energy Density Functional Theory. In: Schwartz, S.D., Ed., Progress in Theoretical Chemistry and Physics, Kluwer, Dordrecht.

[3]   Chen, H.J. and Zhou, A.H. (2008) Orbital-Free Density Functional Theory for Molecular Structure Calculations. Numerical Mathematics: Theory, Methods and Applications, 1, 1-28.

[4]   Zhou, B.J., Ligneres, V.L. and Carter, E.A. (2005) Improving the Orbital-Free Density Functional Theory Description of Covalent Materials. Journal of Chemical Physics, 122, Article ID: 044103. http://dx.doi.org/10.1063/1.1834563

[5]   Hung, L. and Carter, E.A. (2009) Accurate Simulations of Metals at the Mesoscale: Explicit Treatment of 1 Million Atoms with Quantum Mechanics. Chemical Physics Letters, 475, 163-170.
http://dx.doi.org/10.1016/j.cplett.2009.04.059

[6]   Karasiev, V.V. and Trickey, S.B. (2012) Issues and Challenges in Orbital-Free Density Functional Calculations. Computational Physics Communications, 183, 2519-2527.
http://dx.doi.org/10.1016/j.cpc.2012.06.016

[7]   Karasiev, V.V., Chakraborty, D., Shukruto, O.A. and Trickey S.B. (2013) Nonempirical Generalized Gradient Approximation Free-Energy Functional for Orbital-Free Simulations. Physical Review B, 88, 161108-161113(R).
http://dx.doi.org/10.1103/PhysRevB.88.161108

[8]   Wesolowski, T.A. (2005) Approximating the Kinetic Energy Functional Ts[ρ]: Lessons from Four-Electron Systems. Molecular Physics, 103, 1165-1167.
http://dx.doi.org/10.1080/00268970512331339341

[9]   Watson, S.C. and Carter, E.A. (2000) Linear-Scaling Parallel Algorithms for the First Principles Treatment of Metals. Computational Physics Communications, 128, 67-92.
http://dx.doi.org/10.1016/S0010-4655(00)00064-3

[10]   Ho, G.S., Ligneres, V.L. and Carter, E.A. (2008) Introducing PROFESS: A New Program for Orbital-Free Density Functional Theory Calculations. Computational Physics Communications, 179, 839-854.
http://dx.doi.org/10.1016/j.cpc.2008.07.002

[11]   Lehtomaki, 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 Chemical Physics, 141, 234102.

[12]   Τhоmas, L.Η. (1926) The Calculation of Atomic Field. Proceedings of the Cambridge Philosophical Society, 23, 542- 548.

[13]   Fermi, E. (1927) Un metodo statistico per la determinazione di alcune prioprietà dell’atomo. Rendiconti Academia Dei Lincei, 6, 602-607.

[14]   Von Weizsacker, C.F. (1935) Zur Theorie de Kernmassen. Zeitschrift für Physik, 96, 431-458.
http://dx.doi.org/10.1007/BF01337700

[15]   Sarry, A.M. and Sarry, M.F. (2012) To the Density Functional Theory. Physics of Solid State, 54, 1315-1322.
http://dx.doi.org/10.1134/S1063783412060297

[16]   Bobrov, V.B. and Trigger, S.A. (2013) The Problem of the Universal Density Functional and the Density Matrix Functional Theory. Journal of Experimental and Theoretical Physics, 116, 635-640.
http://dx.doi.org/10.1134/S1063776113040018

[17]   Zavodinsky, V.G. and Gorkusha, O.A. (2012) A Simple Quantum Mechanics Way to Simulate Nanoparticles and Nanosystems without Calculation of Wave Functions. ISRN Nanomaterials, 2012, Article ID: 531965.

[18]   Zavodinsky, V.G. and Gorkusha, O.A. (2014) A Practical Way to Develop the Orbital-Free Density Functional Calculations. Physics Science International Journal, 4, 880-891.
http://dx.doi.org/10.9734/PSIJ/2014/10415

[19]   Kohn, W. and Sham, J.L. (1965) Self-Consistent Equations including Exchange and Correlation Effects. Physical Review, 140, A1133-A1138. http://dx.doi.org/10.1103/PhysRev.140.A1133

[20]   Fuchs, M. and Scheffler, M. (1999) Ab Initio Pseoudopotentials for Electronic Structure Calculations of Poly-Atomic Systems Using Density-Functional Theory. Computational Physics Communications, 119, 67-98.
http://dx.doi.org/10.1016/S0010-4655(98)00201-X

[21]   Beckstedte, M., Kley, A., Neugebauer, J. and Scheffler, M. (1997) Density-Functional Theory Calculations for Poly- Atomic Systems: Electronic Structure, Static and Elastic Properties and ab Initio Molecular Dynamics. Computational Physics Communications, 107, 187-205.
http://dx.doi.org/10.1016/S0010-4655(97)00117-3

[22]   Perdew, J.P. and Zunger, A. (1981) Self-Interaction Correction to Density Functional Approximation for Many-Elec- tron Systems. Physical Review B, 23, 5048-5079.
http://dx.doi.org/10.1103/PhysRevB.23.5048

[23]   Ceperley, D.M. and Alder, B.J. (1980) Ground State of the Electron Gas by a Stochastic Method. Physical Review Letters, 45, 566-569.
http://dx.doi.org/10.1103/PhysRevLett.45.566

 
 
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