參考文獻 |
[1] A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002). See also the three comprehensive reviews, A. Laio and F. L. Gervasio, Rep. Prog. Phys. 71, 126601 (2008); A. Barducci, M. Bonomi and M. Parrinello, Wiley Interdiscip. Rev. Comput. Mat. Sci. 1, 826 (2011); O. Valsson, P. Tiwary, and M. Parrinello, Annu. Rev. Phys. Chem. 67, 159 (2016).
[2] A. F. Voter, Phys. Rev. Lett. 78, 3908 (1997).
[3] M. M. Steiner, P. A. Genilloud, and J. W. Wilkins, Phys. Rev. B 57, 10236 (1998).
[4] J. A. Rahman and J. C. Tully, J. Chem. Phys. 116, 8750 (2002).
[5] D. Hamelberg, J. Mongan, and J. A. McCammon, ibid. 120, 11919 (2004).
[6] D. Perez, B. P. Uberuaga, Y. Shim, J. G. Amar, A. F. Voter, Annu. Rep. Comput. Chem. 5, 79 (2009).
[7] U. Doshi, D. Hamelberg, Biochim. Biophys. Acta 1850, 878 (2015).
[8] Reference 1 above has listed several program packages which can be used for metadynamics MD simulations.
[9] M. Elstner, D. Porezag, G. Jungnickel, M. Haugk, T. Frauenheim, S. Suhai, and G. Seifert, Phys. Rev. B 58, 7260 (1998).
[10] P. Koskinen, P., H. Hakkinen, G. Seifert, S. Sanna, T. Frauenheim and M. Moseler, New J. Phys. 8, 9 (2006).
[11] N. W. Ashcroft and D. Stroud, in Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic, New York, 1978), Vol. 33, p.1.
[12] Y. Zeiri, Phys. Rev. E 51, R2769 (1995).
[13] J. A. Niesse and H. R. Mayne, J. Chem. Phys. 105, 4700 (1996).
[14] D. J. Wales and J. P. Doye, J. Phys. Chem. A 101, 5111 (1997).
[15] Z. Li and H. A. Scheraga, Proc. Natl. Acad. Sci. U. S. A. 84, 6611 (1987).
[16] R. N. Barnett and U. Landman, Phys. Rev. B 48, 2081 (1993).
[17] P. Calaminici, J. M. Vasquez-Perez, and D. A. Espindola Velasco, Can. J. Chem. 91, 591 (2013).
[18] T.D. Kuhne, WIREs Comput. Mol. Sci. 4, 391 (2014).
[19] R. P. Gupta, Phys. Rev. B 23, 6265 (1981).
[20] M. W. Finnis and J. E. Sinclair, Phil Mag A 50, 45 (1984); Erratum Philos Mag A 53, 161 (1986).
[21] A. P. Sutton and J. Chen, Philos. Mag. Lett. 61, 139 (1990).
[22] T.W. Yen, T.L. Lim, T.L. Yoon and S.K. Lai, Comput. Phys. Commun. 220, 143 (2017).
[23] We checked that a replacement of the empirical potential by a DFT-based semi-empirical potential such as the parametrized DFTB theory of Fihey et al. (Ref 32 below), at only this step did not lead to the anticipated prediction of the transition size.
[24] J. L. Wang, G. H. Wang and J. J. Zhao, Phys. Rev. B 66, 035418 (2002).
[25] Y. Dong and M. Springborg, Eur. Phys. J. D 43, 15 (2007).
[26] B. Kiran, S. Balusu, H. J. Zhai, S. Yoo, X. C. Zeng, and L. S. Wang, Proc. Natl. Acad. Sci. U. S. A. 102, 961 (2005).
[27] S. Yoo and X. C. Zeng, Angew. Chem., Int. Ed. 44, 1491 (2005).
[28] J. Bai, Li. F. Cui, J. Wang, S. Yoo, X. Li, J. Jellinek, C. Koehler, T. Frauenheim, L. S. Wang, and X. C. Zeng, J. Phys. Chem. A 110, 908 (2006).
[29] Th. Frauenheim, G. Seifert, M. Elstner, Z. Hajnal, G. Jungnickel, D. Porezag, S. Suhai, and R. Scholz, Phys. Stat. Sol. (b) 217, 41 (2000).
?
[30] Th. Frauenheim, G. Seifert, M. Elstner, Th. Niehaus, C. Kohler, M. Amkreutz, M. Sternberg, Z. Hajnal, Aldo Di Carlo and S. Suhai, J. Phys.: Condens. Matter 14, 3015 (2002).
[31] T. W. Yen and S. K. Lai, J. Chem. Phys. 142, 084313 (2015).
[32] A. Fihey, C. Hettich, J. Touzeau, F. Maurel, A. Perrier, C. Kohler, B. Aradi and T. Frauenheim, J. Comput. Chem. 36, 2075 (2015).
[33] V. Makinen, P. Koskinen, and H. Hakkinen, Eur. Phys. J. D 67, 1 (2013).
[34] P. Koskinen, and V. Makinen, Comput. Mat. Sci. 47, 237 (2009).
[35] P. Gruene, B. Butschke, J. T. Lyon, M. Rayner and A. Fiekicke, Z. Phys. Chem. 228, 337 (2014).
[36] P. Koskinen, H. Hakkinen, B. Huber, B. von Issendorff, and M. Moseler, Phys. Rev. Lett. 98, 015701 (2007).
[37] W. M. C. Foulkes and R. Haydock, Phys. Rev. B 39, 12520 (1989).
[38] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
[39] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[40] A very recent work by Gaus et al. [M. Gaus, A. Goez, and M. Elstner, J. Chem. Theory Comput. 9, 338 (2013)] has expanded δn(r) up to third order.
[41] P. Koskinen, H. Hakkinen, G. Seifert, S. Sanna, T. Frauenheim and M. Moseler, New J. Phys. 8, 9 (2006).
[42] L. F. L. Oliveira, N. Tarrat, J. Cuny, J. Morillo, D. Lemoine, F. Spiegelman, and M. Rapacioli, J. Phys. Chem. A 120, 8469 (2016).
[43] S. K. Lai, W. D. Lin, K. L. Wu, W. H. Li, and K. C. Lee, J. Chem. Phys. 121, 1487 (2004).
[44] S. K. Lai, P. J. Hsu, K. L. Wu, W. K. Liu and M. Iwamatsu, J. Chem. Phys. 117, 10715 (2002).
[45] A. Barducci, G. Bussi, M. Parrinello, Phys. Rev. Lett. 100, 02063 (2008).
[46] M. Bonomi, D. Branduardi, G. Bussi, C. Camilloni, D. Provasi, P. Raiteri, D. Donadio, F. Marinelli, F. Pietrucci, R.A. Broglia and M. Parrinello, Comput. Phys. Commun. 180, 1961 (2009).
[47] M. Bonomi, A. Barducci and M. Parrinello, J Comput Chem 30, 1615 (2009).
[48] S.K. Lai and Wafa Maftuhin, National Central University M.Sc. thesis, unpublished (2018).
[49] S.K. Lai and Nurulia Sinta Rahmani, National Central University M.Sc. thesis, unpublished (2018).
[50] D. Liu and J. Nocedal, Math. Program. 45, 503 (1989)
[51] A. Vargas, G. Santarossa, M. Iannuzzi, and A. Baiker, Phys. Rev. B 80, 195421 (2009).
[52] G. Rossi, A. Rapallo, C. Mottet, A. Fortunelli, F. Baletto, and R. Ferrando, Phys. Rev. Lett. 93, 105503 (2004).
[53] E.M. Fernandez, J.M. Soler, I.L. Garzon, L.C. Balbas, Phys. Rev. B 70, 165403 (2004).
[54] B. Assadollahzadeh and P. Schwerdtfeger, J. Chem. Phys. 131, 064306 (2009).
[55] A. V. Walker, J. Chem. Phys. 122, 094310 (2005).
[56] X. B. Li, H.Y. Wang, X. D. Yang and Z. H. Zhu, J. Chem. Phys. 126, 084505 (2007).
[57] G. Zanti and D. Peeters, Theor. Chem. Acc. 132, 1300 (2013).
[58] P. J. Hsu, S. A. Cheong, and S. K. Lai, J Chem. Phys. 140, 204905 (2014). |