Energetics and Elastic Properties of Large Nano-objects: Orbital-free Approach on the Basis of the Density Functional Theory
( Pp. 11-17)
More about authors
Zavodinsky Victor G.
doktor fizikomatematicheskih nauk, professor; veduschiy nauchnyy sotrudnik
Institute of Applied Mathematics of the Russian Academy of Sciences
Khabarovsk, Russian Federation Gorkusha Olga A. kandidat fizikomatematicheskih nauk; starshiy nauchnyy sotrudnik
Institute of Applied Mathematics of the Russian Academy of Sciences
Khabarovsk, Russian Federation
Institute of Applied Mathematics of the Russian Academy of Sciences
Khabarovsk, Russian Federation Gorkusha Olga A. kandidat fizikomatematicheskih nauk; starshiy nauchnyy sotrudnik
Institute of Applied Mathematics of the Russian Academy of Sciences
Khabarovsk, Russian Federation
Abstract:
Cohesive energy Ecoh and bulk modulus B of large nanosystems Cn, Sin, Aln и Tin, were calculated in the workframe of the all-electron version of the orbital-free approach on the basis of the density functional theory: number of atoms n was varied up to 4096 for carbon and silicon, 23 328 for aluminum, and 2662 for titanium. Nanosystems were taken as fragments of corresponding crystals. It was found that Ecoh and B tend to their values known for bulk materials. Therefore, it was convincingly shown that our orbital-free approach could be used successfully for study mechanical properties of large nanosystems.
How to Cite:
Zavodinsky V.G., Gorkusha O.A., (2021), ENERGETICS AND ELASTIC PROPERTIES OF LARGE NANO-OBJECTS: ORBITAL-FREE APPROACH ON THE BASIS OF THE DENSITY FUNCTIONAL THEORY. Computational Nanotechnology, 2: 11-17. DOI: 10.33693/2313-223X-2021-8-2-11-17
Reference list:
Hohenberg H., Kohn W. Inhomogeneous electron gas // Physical Review. 1964. No. 136. Pp. B864-B871.
Perdew J.P., Zunger A.S. Self-interaction correction to density functional approximation for many-electron systems // Physical Review. 1981. No. 23. Pp. 5048-5079.
Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method // Physical Review. 1980. No. 45. Pp. 566-569.
Thomas L.H. The calculation of atomic eld // Proc. Cambr. Phil. Soc. 1927. No. 23. Pp. 542-548.
Fermi E. Un metodo statistic per la determinazione lcune priorieta dell atomo // Rend. Accad. Lincei. 1927. No. 6. Pp. 602-607.
v. Weizsacker C.F. Theorie de Kernmassen // Z. Physik. 1935. No. 96. Pp. 431-458.
Kohn W., Sham J.L. Self-consistent equations including exchange and correlation effects // Phys. Rev. 1965. No. 40. Pp. A1133-A1138.
Gomez S., Gonzalez L.E., Gonzalez D.J. et al. Orbital free ab initio molecular dynamic study of expanded liquid Cs // Non-Cryst. Solids. 1999. No. 250-252. Pp. 163-167.
Wang Y.A., Carter E.A. Orbital-free kinetic-energy density functional theory. In: Theoretical methods in condensed phase chemistry. Schwartz, S.D.: Springer, Dordrecht, 2002. Pp. 117-184.
Huajie Chen, Aihui Zhou. Orbital-free density functional theory for molecular structure calculations // Numerical Mathematics: Theory, Methods and Applications. 2008. No. 1. Pp. 1-28.
Hung L., Carter E.A. Accurate simulations of metals at the mesoscale: Explicit treatment of 1 million atoms with quantum mechanics // Chem. Phys. Lett. 2009. No. 475. Pp. 163-170.
Karasiev V.V., Chakraborty D., Trickey S.B. Progress on new approaches to old ideas: Orbital-free density functionals. In: Many-electron approaches in physics, chemistry and mathematics. Mathematical physics studies. V. Bach, S.L. Delle (eds.). Schwartz, S.D.: Springer, Dordrecht, 2014. Pp. 113-135.
Sarry A.M., Sarry M.F. To the density functional theory // Physics of Solid State. 2012. No. l54 (6). Pp. 1315-1322.
Bobrov V.B., Trigger S.A. The problem of the universal density functional and the density matrix functional theory // J. Exper. Theor. Phys. 2013. No. 116 (4). Pp. 635-640.
Zavodinsky V.G., Gorkusha O.A. On a possibility to develop a full-potential orbital-free modelling approach // Nanosystems: Physics, Chemistry, Mathematics. 2019. No. 9 (4). Pp. 402-409.
Zavodinskiy V.G., Gorkusha O.A. Polnoelektronnyy bezorbital nyy metod modelirovaniya atomnykh sistem: pervyy shag // Computational nanotechnology. 2019. T. 6. № 3. S. 72-76.
Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory // Comp. Phys. Commun. 1999. No. 119. Pp. 67-98.
Houqian Sun, Yun Ren, Zhaofeng Wu, Ning Xu. Density functional calculation of the growth, electronic and bonding properties of titanium clusters Tin (n 2-20) // Computational and Theoretical Chemistry. 2015. No. 1062. Pp. 74-83.
Waschi H.P., Stoll H., Preu H. Ab-initio and PCILO calculations of diamond clusters and the corresponding saturated hydrocarbons // Z. Naturforsch. 1978. No. 83. Pp. 358-365.
Robertson J. Diamond-like amorphous carbon // Materials Science and Engineering R. 2002. No. 37. Pp. 129-281.
Ahlrichs R., Elliott S.D. Clusters of aluminium, a density functional study // Phys. Chem. Chem. Phys. 1999. No. 1. Pp. 13-21.
Kiohara V.O., Carvalho E.F.V., Paschoal C.W.A. et al. DFT and CCSD(T) electronic properties and structures of aluminum clusters: Alnx (n 1-9, x 0, 1) // Chemical Physics Letters. 2013. No. 568-569. Pp. 42-48.
Wei S.H., Zeng Zhi, You J.Q. et al. A density-functional study of small titanium clusters // J. Chem. Phys. 2000. No. 113. Pp. 11127-11133.
Tomanek D.S. Calculation of magic numbers and the stability of small Si clusters // Phys. Rev. Lett. 1986. No. 56 (10). Pp. 1055-1058.
Xiaolei Zhu, Zeng X.C. Structures and stabilities of small silicon clusters: Ab initio molecular-orbital calculations of Si7-Si11 // Journal of Chemical Physics. 2003. Vol. 118. No. 8. Pp. 3558-3570.
Zavodinskiy V.G., CHibisov A.N., Gnidenko A.A., Aleynikova M.A. Teoreticheskoe issledovanie uprugikh svoystv malykh nanochastits s razlichnymi tipami mezhatomnykh svyazey // Mekhanika kompozitsionnykh materialov i konstruktsiy. 2005. T. 11. № 3. S. 337-346.
Vakhrushev A.V., SHushkov A.A. Modelirovanie uprugoy reaktsii nanochastits na silovoe vozdeystvie // Izvestiya Instituta matematiki i informatiki. 2006. № 2 (36). S. 125-128.
Gerard C., Pizzagalli L. Mechanical behavior of nanoparticles: Elasticity and plastic deformation mechanisms // Journal Pramana of Indian Academy of Sciences. Physics. 2015. Vol. 84. No. 6. Pp. 1041-1048.
Nysten B., Fr tigny Ch., Cuenot S. Elastic modulus of nanomaterials: Resonant contact-AFM measurement and reduced-size effect // Proc. SPIE Conf. Vol. 5766: Testing, Reliability, and Application of Micro- and Nano-Material Systems III (SPIE, Bellingham, 2005). R.E. Geer, N. Meyendorf, G.Y. Baaklini, B. Michel (eds.). Pp. 78-88.
Qiong Wu, Wei-shou Miao, Yi-du Zhang et al. Mechanical properties of nanomaterials: A review // Nanotechnol. Rev. 2020. No. 9. Pp. 259-273.
Lunyakov YU.V., Balagan S.A. Modul uprugosti kremnievykh i germanievykh fullerenov Si60 i Ge60 // Fizika tverdogo tela. 2015. T. 57. Vyp. 6. S. 1058-1063.
Magomedov M.N. Zavisimost uprugikh svoystv ot razmera i formy nanokristalov almaza, kremniya i germaniya // ZHurnal tekhnicheskoy fiziki. 2014. T. 84. Vyp. 11. C. 80-90.
Zavodinsky V.G., Kuyanov I.A., Holavkin M.N. Soft elastic behavior of nanometer silicon particles: Computer simulation // Phys. of Low-Dim. Struct. 1999. No. 9/10. Pp. 49-56.
Perdew J.P., Zunger A.S. Self-interaction correction to density functional approximation for many-electron systems // Physical Review. 1981. No. 23. Pp. 5048-5079.
Ceperley D.M., Alder B.J. Ground state of the electron gas by a stochastic method // Physical Review. 1980. No. 45. Pp. 566-569.
Thomas L.H. The calculation of atomic eld // Proc. Cambr. Phil. Soc. 1927. No. 23. Pp. 542-548.
Fermi E. Un metodo statistic per la determinazione lcune priorieta dell atomo // Rend. Accad. Lincei. 1927. No. 6. Pp. 602-607.
v. Weizsacker C.F. Theorie de Kernmassen // Z. Physik. 1935. No. 96. Pp. 431-458.
Kohn W., Sham J.L. Self-consistent equations including exchange and correlation effects // Phys. Rev. 1965. No. 40. Pp. A1133-A1138.
Gomez S., Gonzalez L.E., Gonzalez D.J. et al. Orbital free ab initio molecular dynamic study of expanded liquid Cs // Non-Cryst. Solids. 1999. No. 250-252. Pp. 163-167.
Wang Y.A., Carter E.A. Orbital-free kinetic-energy density functional theory. In: Theoretical methods in condensed phase chemistry. Schwartz, S.D.: Springer, Dordrecht, 2002. Pp. 117-184.
Huajie Chen, Aihui Zhou. Orbital-free density functional theory for molecular structure calculations // Numerical Mathematics: Theory, Methods and Applications. 2008. No. 1. Pp. 1-28.
Hung L., Carter E.A. Accurate simulations of metals at the mesoscale: Explicit treatment of 1 million atoms with quantum mechanics // Chem. Phys. Lett. 2009. No. 475. Pp. 163-170.
Karasiev V.V., Chakraborty D., Trickey S.B. Progress on new approaches to old ideas: Orbital-free density functionals. In: Many-electron approaches in physics, chemistry and mathematics. Mathematical physics studies. V. Bach, S.L. Delle (eds.). Schwartz, S.D.: Springer, Dordrecht, 2014. Pp. 113-135.
Sarry A.M., Sarry M.F. To the density functional theory // Physics of Solid State. 2012. No. l54 (6). Pp. 1315-1322.
Bobrov V.B., Trigger S.A. The problem of the universal density functional and the density matrix functional theory // J. Exper. Theor. Phys. 2013. No. 116 (4). Pp. 635-640.
Zavodinsky V.G., Gorkusha O.A. On a possibility to develop a full-potential orbital-free modelling approach // Nanosystems: Physics, Chemistry, Mathematics. 2019. No. 9 (4). Pp. 402-409.
Zavodinskiy V.G., Gorkusha O.A. Polnoelektronnyy bezorbital nyy metod modelirovaniya atomnykh sistem: pervyy shag // Computational nanotechnology. 2019. T. 6. № 3. S. 72-76.
Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory // Comp. Phys. Commun. 1999. No. 119. Pp. 67-98.
Houqian Sun, Yun Ren, Zhaofeng Wu, Ning Xu. Density functional calculation of the growth, electronic and bonding properties of titanium clusters Tin (n 2-20) // Computational and Theoretical Chemistry. 2015. No. 1062. Pp. 74-83.
Waschi H.P., Stoll H., Preu H. Ab-initio and PCILO calculations of diamond clusters and the corresponding saturated hydrocarbons // Z. Naturforsch. 1978. No. 83. Pp. 358-365.
Robertson J. Diamond-like amorphous carbon // Materials Science and Engineering R. 2002. No. 37. Pp. 129-281.
Ahlrichs R., Elliott S.D. Clusters of aluminium, a density functional study // Phys. Chem. Chem. Phys. 1999. No. 1. Pp. 13-21.
Kiohara V.O., Carvalho E.F.V., Paschoal C.W.A. et al. DFT and CCSD(T) electronic properties and structures of aluminum clusters: Alnx (n 1-9, x 0, 1) // Chemical Physics Letters. 2013. No. 568-569. Pp. 42-48.
Wei S.H., Zeng Zhi, You J.Q. et al. A density-functional study of small titanium clusters // J. Chem. Phys. 2000. No. 113. Pp. 11127-11133.
Tomanek D.S. Calculation of magic numbers and the stability of small Si clusters // Phys. Rev. Lett. 1986. No. 56 (10). Pp. 1055-1058.
Xiaolei Zhu, Zeng X.C. Structures and stabilities of small silicon clusters: Ab initio molecular-orbital calculations of Si7-Si11 // Journal of Chemical Physics. 2003. Vol. 118. No. 8. Pp. 3558-3570.
Zavodinskiy V.G., CHibisov A.N., Gnidenko A.A., Aleynikova M.A. Teoreticheskoe issledovanie uprugikh svoystv malykh nanochastits s razlichnymi tipami mezhatomnykh svyazey // Mekhanika kompozitsionnykh materialov i konstruktsiy. 2005. T. 11. № 3. S. 337-346.
Vakhrushev A.V., SHushkov A.A. Modelirovanie uprugoy reaktsii nanochastits na silovoe vozdeystvie // Izvestiya Instituta matematiki i informatiki. 2006. № 2 (36). S. 125-128.
Gerard C., Pizzagalli L. Mechanical behavior of nanoparticles: Elasticity and plastic deformation mechanisms // Journal Pramana of Indian Academy of Sciences. Physics. 2015. Vol. 84. No. 6. Pp. 1041-1048.
Nysten B., Fr tigny Ch., Cuenot S. Elastic modulus of nanomaterials: Resonant contact-AFM measurement and reduced-size effect // Proc. SPIE Conf. Vol. 5766: Testing, Reliability, and Application of Micro- and Nano-Material Systems III (SPIE, Bellingham, 2005). R.E. Geer, N. Meyendorf, G.Y. Baaklini, B. Michel (eds.). Pp. 78-88.
Qiong Wu, Wei-shou Miao, Yi-du Zhang et al. Mechanical properties of nanomaterials: A review // Nanotechnol. Rev. 2020. No. 9. Pp. 259-273.
Lunyakov YU.V., Balagan S.A. Modul uprugosti kremnievykh i germanievykh fullerenov Si60 i Ge60 // Fizika tverdogo tela. 2015. T. 57. Vyp. 6. S. 1058-1063.
Magomedov M.N. Zavisimost uprugikh svoystv ot razmera i formy nanokristalov almaza, kremniya i germaniya // ZHurnal tekhnicheskoy fiziki. 2014. T. 84. Vyp. 11. C. 80-90.
Zavodinsky V.G., Kuyanov I.A., Holavkin M.N. Soft elastic behavior of nanometer silicon particles: Computer simulation // Phys. of Low-Dim. Struct. 1999. No. 9/10. Pp. 49-56.
Keywords:
orbital-free approach, all-electron potential, density functional theory, modeling, nanomaterials.
