Ab initio calculations for the β-tin diamond transition in silicon: Comparing theories with experiments

Physical Review B - Condensed Matter and Materials Physics

Volumn 83, Issue 7, 2011, Pages

  Sorella, Sandro ^a,b   Casula, Michele ^c   Spanu, Leonardo ^d   Dal Corso, Andrea ^a,b  

^a SISSA   (Italy)

^b DEMOCRITOS NATIONAL SIMULATION CENTER   (Italy)

^c CNRS   (France)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79961080208     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.075119     Document Type: Article

References (59)

1. R. Miletich, EMU Notes in Mineralogy: Mineral Behaviour at Extreme Conditions (7th EMU School of Mineralogy, Heidelberg, 2005).
2. J. C. Jamieson, Science SCIEAS 0036-8075 10.1126/science.139.3556.762 139, 762 (1963).
3. M. I. McMahon and R. J. Nelmes, Phys. Rev. B SCIEAS 1098-0121 10.1103/PhysRevB.47.8337 47, 8337 (1993).
4. G. A. Voronin, C. Pantea, T. W. Zerda, L. Wang, and Y. Zhao, Phys. Rev. B SCIEAS 1098-0121 10.1103/PhysRevB.68.020102 68, 020102 (2003).
5. J. Z. Hu, L. D. Merkle, C. S. Menoni, and I. L. Spain, Phys. Rev. B SCIEAS 1098-0121 10.1103/PhysRevB.34.4679 34, 4679 (1986).
6. M. Tsujino, T. Sano, N. Ozaki, O. Sakata, M. Okoshi, N. Inoue, R. Kodama, and A. Hirose, The Review of Laser Engineering, REKEDA 0387-0200 10.2184/lsj.36.1218 Supplemental Volume, 1218 (2008).
7. S. V. Ovsyannikov, V. V. Shchennikov, and A. Misiuk, JETP Lett. JTPLA2 0021-3640 10.1134/1.1830657 80, 405 (2004).
8. A. Dal Corso, A. Pasquarello, A. Baldereschi, and R. Car, Phys. Rev. B JTPLA2 1098-0121 10.1103/PhysRevB.53.1180 53, 1180 (1996).
9. In-Ho Lee and Richard M. Martin, Phys. Rev. B JTPLA2 1098-0121 10.1103/PhysRevB.56.7197 56, 7197 (1997).
10. N. Moll, M. Bockstedte, M. Fuchs, E. Pehlke, and M. Scheffler, Phys. Rev. B JTPLA2 1098-0121 10.1103/PhysRevB.52.2550 52, 2550 (1995).
11. J. P. Perdew, K. Burke, and Y. Wang, Phys. Rev. B JTPLA2 1098-0121 10.1103/PhysRevB.54.16533 54, 16533 (1996).
12. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3865 77, 3865 (1996).
13. R. G. Hennig, A. Wadehra, K. P. Driver, W. D. Parker, C. J. Umrigar, and J. W. Wilkins, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.82.014101 82 014101 (2010).
14. K. Gaál-Nagy, A. Bauer, M. Schmitt, K. Karch, P. Pavone, and D. Strauch, Phys. Status Solidi B PSSBBD 0370-1972 10.1002/(SICI)1521-3951(199 901)211:1275::AID-PSSB2753.0.CO;2-O 211, 275 (1999).
15. W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.73.33 73, 33 (2001).
16. Leonardo Spanu, Sandro Sorella, and Giulia Galli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.196401 103, 196401 (2009).
17. J. Kolorenc and L. Mitas, Phys. Rev. Lett PRLTAO 0031-9007 10.1103/PhysRevLett.101.185502 101, 185502 (2008).
18. D. Alfe, M. J. Gillan, M. D. Towler, and R. J. Needs, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.70.214102 70, 214102 (2004). (Pubitemid 40239439)
19. P. J. Reynolds, D. M. Ceperley, B. J. Alder, and W. A. Lester, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.443766 77, 5593 (1982).
20. W. Purwanto, H. Krakauer, and S. Zhang, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.80.214116 80, 214116 (2009).
21. S. Zhang and H. Krakauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.136401 90, 136401 (2003).
22. C. J. Umrigar, J. Toulouse, C. Filippi, S. Sorella, and R. G. Hennig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.110201 98, 110201 (2007). (Pubitemid 46434400)
23. H. Kwee, S. Zhang, and H. Krakauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.126404 100, 126404 (2008). (Pubitemid 351468999)
24. T. D. Beaudet, M. Casula, J. Kim, S. Sorella, and R. M. Martin, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2987716 129, 164711 (2008).
25. M. Casula, C. Attaccalite, and S. Sorella, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1794632 121, 7110 (2004).
26. P. Giannozzi, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/21/39/395502 21, 395502 (2009).
27. K. Schwarzland and P. Blaha, Comput. Mater. Sci. CMMSEM 0927-0256 10.1016/S0927-0256(03)00112-5 28, 259 (2003).
28. F. Gygi, computer code qbox (2010) [http://eslab.ucdavis.edu/software/ qbox/].
29. S. Sorella, computer code turborvb (2010) [http://turborvb.qe-forge.org/] .
30. M. Casula, C. Filippi, and S. Sorella, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.100201 95, 100201 (2005). (Pubitemid 41505791)
31. J. R. Trail and R. J. Needs, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1888569 122, 174109 (10) (2005). (Pubitemid 40665966)
32. M. Burkatzki, C. Filippi, and M. Dolg, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2741534 126, 234105 (2007). (Pubitemid 47141464)
33. N. Troullier and J. L. Martins, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.43.1993 43, 1993 (1991).
34. The pseudopotentials not available in the semilocal Gaussian form, as those generated by the atomic pwscf code, have been fitted by a series of Gaussian functions. The discrepancy in the transition pressure obtained by the fitted pseudopotentials is less than 0.15 GPa from the original one.
35. M. Casula and S. Sorella, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1604379 119, 6500 (2003).
36. M. Capello, F. Becca, M. Fabrizio, and S. Sorella, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.77.144517 77, 144517 (2008).
37. S. Azadi, C. Cavazzoni, and Sandro Sorella, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.82.125112 82, 125112 (2010).
38. T. H. Dunning Jr., J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.456153 90, 1007 (1989).
39. K. A. Peterson and T. H. Dunning Jr., J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1520138 117, 10548 (2002).
40. M. Casula, S. Moroni, S. Sorella, and C. Filippi, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3380831 132, 154113 (2010).
41. It is clear that with the PBC + APBC average of the KZK corrected energies we can reduce the error on the final transition pressure well below the 20 meV/atom threshold reached in Ref. 13.
42. P. E. Blöchl, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.50. 17953 50, 17953 (1994).
43. G. Kresse and D. Joubert, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.59.1758 59, 1758 (1999).
44. d = 2. 0 (d is local). The nonlocal channels are fitted at the eigenvalue and at 6. 0 Ry for s and p. The unbound d channel is at ε = - 0. 3 Ry.
45. M. Methfessel and A. T. Paxton, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.40.3616 40, 3616 (1989).
46. Early attempts to generate PPs at the QMC level were done in Ref. 59.
47. V. V. Brazhkin, A. G. Lyapin, S. V. Popova, and R. N. Voloshin, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.51.7549 51, 7549 (1995).
48. L. Kleinman and D. M. Bylander, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.1425 48, 1425 (1982).
49. P. E. Blöchl, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.41.5414 41, 5414 (1990).
50. S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.42.3503 42, 3503 (1990).
51. L. Mitáš, E. L. Shirley, and D. M. Ceperley, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.460849 95, 3467 (1991).
52. C. J. Umrigar (private communication).
53. J. P. Perdew and A. Zunger, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.23.5048 23, 5048 (1981).
54. M. Hill, ed., Properties of Crystallin Silicon (INSPEC, London, 1999).
55. M. T. Yin and M. L. Cohen, Phys. Rev. B JCPSA6 1098-0121 10.1103/PhysRevB.26.5668 26, 5668 (1982).
56. K. P. Esler, R. E. Cohen, B. Militzer, J. Kim, R. J. Needs, and M. D. Towler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.185702 104, 185702 (2010).
57. R. Maezono, N. D. Drummond, A. Ma, and R. J. Needs, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.82.035107 82, 184108 (2010).
58. M. Casula, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.74.161102 74, 161102 (2006). (Pubitemid 44654524)
59. G. B. Bachelet, D. M. Ceperley, and M. G. B. Chiocchetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.2088 62, 2088 (1989).