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Application of a hybrid quantum mechanics and empirical moleculardynamics multiscale method to carbon nanotubes

  • Computational Methods
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Abstract.

We present a hybrid multiscale method for coupling quantum mechanicsto empirical molecular dynamics, which is named as hybrid energydensity method. In this approach, quantum mechanical treatment isspatially confined to a small region, surrounded by a largermolecular mechanical region. A unified expression of total energycombining quantum mechanical and molecular mechanical descriptions,is given by employing a localized energy and a weight associatedwith it on each site. And we can perform the dynamical simulationsof entire system according to the given total energy. We use thehybrid energy density method to simulate two models of carbonnanotubes (CNT): one is a long CNT with an open end, and the other along CNT containing a di-vacancy under stretching. Calculations ofthe two CNT models demonstrate that the hybrid multiscale method isrequired to accurately treat the local quantum mechanical regionwith the influence of the larger molecular mechanical region.

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References

  • G. Lu, E. Kaxiras, in Handbook of Theoreticaland Computational Nanotechnology, edited by M. Rieth, W.Schmmers (American Scientific Publishers, Stevenson Ranch, CA,2004), Chap. 22

  • S. Yip, Nature Mater. 2, 3 (2003)

  • E.B. Tadmor, M. Ortiz, R. Phillips, Philos.Mag. A 73, 1529 (1996)

    Google Scholar 

  • J. Gao, in Reviews in Computational Chemistry,edited by K.B. Libkowitz and D.B. Boyd (VCH, New York, 1996), pp.119–185

  • R.E. Rudd, J.Q. Broughton, Phys. Rev. B 58,R5893 (1998)

  • R.E. Rudd, J.Q. Broughton, Phys. Rev. B 72,144104 (2005)

    Google Scholar 

  • J.Q. Broughton, F.F. Abraham, N. Bernstein, E. Kaxiras, Phys. Rev. B 60, 2391 (1999)

    Google Scholar 

  • E. Lidorikis et al., Phys. Rev. Lett.87, 086104 (2001)

    Google Scholar 

  • M.J. Buehler, A.C.T. van Duin, W.A.Goddard III, Phys. Rev. Lett. 96, 095505 (2006)

    Google Scholar 

  • M.J. Buehler, H. Tang, A.C.T. van Duin, W.A.Goddard III, Phys. Rev. Lett. 99, 165502 (2007)

    Google Scholar 

  • N. Bernstein, D. Hess, Phys. Rev. Lett.91, 025501 (2003)

    Google Scholar 

  • N. Bernstein, D. Hess, Mater. Res. Soc.Symp. Proc. 653, Z2.7.1 (2001)

  • V.B. Shenoy et al., J. Mech. Phys. Solids47, 611 (1999)

    Google Scholar 

  • N. Govind, Y.A. Wang, A.J.R.da Silva,E.A. Carter, Chem. Phys. Lett. 295, 129 (1998)

    Google Scholar 

  • N. Choly, G. Lu, W. E, E. Kaxiras, Phys. Rev. B 71, 094101(2005)

  • P. Huang, E.A. Carter, J. Chem. Phys. 125, 084102(2006)

  • X. Zhang, G. Lu, Phys. Rev. B 76, 245111(2007)

  • G. Lu, E.B. Tadmor, E. Kaxiras, Phys. Rev. B73, 024108 (2006)

    Google Scholar 

  • T. Mordasini, W. Thiel, Chimia 52, 288 (1998)

    Google Scholar 

  • T.K. Woo et al., ACS Symp. Ser. 721, 173 (1999)

  • P. Sherwood, in Modern methods and algorithms of quantumchemistry, edited by J. Grotendorst (NIC-Directors: Princeton, 2000) Vol. 3, p. 285

  • J. Gao, D.G. Truhlar, Annu. Rev. Phys. Chem. 53,467 (2002)

    Google Scholar 

  • S. Ogata, R. Belkada, Comput. Mater. Sci. 30,189 (2004)

    Google Scholar 

  • H. Lin, D.G. Truhlar, Theor. Chem. Acc. 117,185 (2007)

    Google Scholar 

  • X. Li, W. E, J. Mech. Phys. Solids 53, 1650(2005)

  • G.J. Wagner, W.K. Liu, J. Comput. Phys. 190, 249(2003)

  • H.S. Park, W.K. Liu, Computer Methods in Applied Mechanicsand Engineering 193, 1733 (2004)

  • S.Q. Tang, T.Y. Hou, W.K. Liu, J. Comput.Phys. 231, 57 (2006)

    Google Scholar 

  • C. Woodward, S.I. Rao, Phys. Rev. Lett. 88, 216402 (2002)

    Google Scholar 

  • C.Y. Wang, X. Zhang, Curr. Opin. Solid state mater. Science 10, 2 (2006)

    Google Scholar 

  • S. Iijima, Nature, 354, 56 (1991)

  • Articles on nanotubes in Phys. World 13, 29 (2000)

  • R.H. Baughman, A.A. Zakhidov, W.A. de Heer,Science 297, 787 (2002)

    Google Scholar 

  • P. Hohenberg, W. Kohn, Phys. Rev. 136, B864(1964); W. Kohn, L.J. Sham, Phys. Rev. 140, A1133(1965)

  • J. Tersoff, Phys. Rev. B 37, 6991(1988)

  • M.S. Daw, M.I. Baskes, Phys. Rev. B 29, 6443(1984)

  • M. Born, J.R. Oppenheimer, Ann. Physik84, 457 (1927)

    Google Scholar 

  • R.M. Martin, in Electronic structure: basic theoryand pratical methods (Cambridge Univ. Press, Cambridge, 2004),Sect. 19.1

  • V. Heine, in Solid State Phys. 35, 92 (1980)

  • R.A. Deegan, J. Phys. C 1, 763 (1968)

  • C.M. Varma, W. Weber, Phys. Rev. Lett. 39, 1094 (1977)

    Google Scholar 

  • A.R. Mackintosh, O.K. Andersen, in Electronsat the Fermi Surface edited by M. Springgord. (Cambridge Univ. Press,London and New York, 1980), Sect. 3.1

  • W. Kohn, Phys. Rev. Lett. 76, 3168 (1996)

    Google Scholar 

  • S. Goedecher, Rev. Mod. Phys. 71, 1085 (1999)

    Google Scholar 

  • M. Tuckerman, B.J. Berne, G.J. Martyna, J. Chem. Phys. 97, 1990(1992)

  • B. Delly, J. Chem. Phys. 92, 508 (1990); B. Delly,J. Quant. Chem. 69, 423 (1998)

  • J.P. Perdew, K. Burke, M. Ernzerhof, Phy. Rev. Lett.77, 3865 (1996)

    Google Scholar 

  • D.W. Brenner, Phys. Rev. B 42, 9458 (1990)

    Google Scholar 

  • D.B. Mawhinney, V. Naumenko, A. Kuznetsova, J.T. Yates Jr., J.Liu, R.E. Smalley, Chem. Phys. Lett. 324, 213 (2000)

    Google Scholar 

  • R. Andrews, D. Jacques, D. Qian, E.C. Dickey, Carbon 39,1681 (2001)

    Google Scholar 

  • B. Ni, S.B. Sinnott, Phys. Rev. B 61, R16343 (2000)

  • M. Terrones, F. Banhart, N. Grobert, J.-C. Charlier, H. Terrones, P. Ajayan, Phys. Rev. Lett. 89, 075505 (2002)

    Google Scholar 

  • M. Bockrath et al., Science 297, 283(2001)

  • M. Sammalkorpi, A. Krasheninnikov, A. Kuronen, K. Nordlund, K.Kaski1, Phys. Rev. B 70, 245416 (2004)

    Google Scholar 

  • C. Gomez-Navarro et al. Nature Mater. 4,534 (2005)

  • S. Zhang et al, Phys. Rev. B 71, 115403(2005)

  • Z. Li, C.Y. Wang, X. Zhang, S.H. Ke, W. Yang, J. Phys.: Condens. Matter 20, 345225 (2008)

    Google Scholar 

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Zhang, X., Wang, CY. Application of a hybrid quantum mechanics and empirical moleculardynamics multiscale method to carbon nanotubes. Eur. Phys. J. B 65, 515 (2008). https://doi.org/10.1140/epjb/e2008-00366-7

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  • DOI: https://doi.org/10.1140/epjb/e2008-00366-7

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