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.
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
