Self-consistent hybrid functional for condensed systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 89, Issue 19, 2014, Pages

  Skone, Jonathan H ^a   Govoni, Marco ^b   Galli, Giulia ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84900477658     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.89.195112     Document Type: Article

References (114)

1. P. Hohenberg, Phys. Rev. 136, B864 (1964). PHRVAO 0031-899X 10.1103/PhysRev.136.B864
2. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). PHRVAO 0031-899X 10.1103/PhysRev.140.A1133
3. R. Dreizler and E. Gross, Density Functional Theory (Springer Verlag, Berlin, 1990).
4. A. D. Becke, J. Chem. Phys. 98, 1372 (1993). JCPSA6 0021-9606 10.1063/1.464304
5. A. Seidl, A. Görling, P. Vogl, J. Majewski, and M. Levy, Phys. Rev. B 53, 3764 (1996). PRBMDO 0163-1829 10.1103/PhysRevB.53.3764
6. Though we use, as an example, the error function to partition the Coulomb interaction into long and short range, other functions could be used such as the semiclassical Thomas-Fermi screening function.
7. J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 124, 219906 (2006). JCPSA6 0021-9606 10.1063/1.2204597
8. D. Bylander and L. Kleinman, Phys. Rev. B 41, 7868 (1990). PRBMDO 0163-1829 10.1103/PhysRevB.41.7868
9. T. Yanai, D. P. Tew, and N. C. Handy, Chem. Phys. Lett. 393, 51 (2004). CHPLBC 0009-2614 10.1016/j.cplett.2004.06.011
10. E. Weintraub, T. M. Henderson, and G. E. Scuseria, J. Chem. Theory Comput. 5, 754 (2009). 10.1021/ct800530u
11. C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999). JCPSA6 0021-9606 10.1063/1.478522
12. F. M. Bickelhaupt and E. J. Baerends, in Reviews in Computational Chemistry (John Wiley & Sons, Inc., New York, 2007), pp. 1-86.
13. X. Wu, A. Selloni, and R. Car, Phys. Rev. B 79, 085102 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.79.085102
14. F. Gygi, Phys. Rev. Lett. 102, 166406 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.166406
15. F. Gygi and I. Duchemin, J. Chem. Theory Comput. 9, 582 (2013). 1549-9618 10.1021/ct3007088
16. S. Kümmel and L. Kronik, Rev. Mod. Phys. 80, 3 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.3
17. Z. D. Pozun and G. Henkelman, J. Chem. Phys. 134, 224706 (2011). JCPSA6 0021-9606 10.1063/1.3598947
18. J. C. Conesa, J. Phys. Chem. C 116, 18884 (2012). 1932-7447 10.1021/jp306160c
19. A. Alkauskas, P. Broqvist, F. Devynck, and A. Pasquarello, Phys. Rev. Lett. 101, 106802 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.106802
20. A. Alkauskas, P. Broqvist, and A. Pasquarello, Phys. Status Solidi B 248, 775 (2011). 10.1002/pssb.201046195
21. P. Broqvist, A. Alkauskas, and A. Pasquarello, Phys. Status Solidi A 207, 270 (2010). 1862-6300 10.1002/pssa.200982444
22. G. Strinati, La Rivista del Nuovo Cimento (1978-1999) 11, 1 (1988). 0393-697X 10.1007/BF02725962
23. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.601
24. L. Hedin, Phys. Rev. 139, A796 (1965). PHRVAO 0031-899X 10.1103/PhysRev.139.A796
25. M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. 55, 1418 (1985). PRLTAO 0031-9007 10.1103/PhysRevLett.55.1418
26. W. G. Aulbur, L. Jönsson, and J. W. Wilkins, Solid State Phys. 54, 1 (2000).
27. H.-V. Nguyen, T. A. Pham, D. Rocca, and G. Galli, Phys. Rev. B 85, 081101 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.081101
28. T. A. Pham, H.-V. Nguyen, D. Rocca, and G. Galli, Phys. Rev. B 87, 155148 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.155148
29. Y. Ping, D. Rocca, and G. Galli, Phys. Rev. B 87, 165203 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.165203
30. F. Bruneval and M. Gatti, in Topics in Current Chemistry (Springer, Berlin, 2014), pp. 1-37.
31. M. A. L. Marques, J. Vidal, M. J. T. Oliveira, L. Reining, and S. Botti, Phys. Rev. B 83, 035119 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.83.035119
32. J. E. Moussa, P. A. Schultz, and J. R. Chelikowsky, J. Chem. Phys. 136, 204117 (2012). JCPSA6 0021-9606 10.1063/1.4722993
33. S. Botti, F. Sottile, N. Vast, V. Olevano, L. Reining, H.-C. Weissker, A. Rubio, G. Onida, R. Del Sole, and R. W. Godby, Phys. Rev. B 69, 155112 (2004). PRBMDO 1098-0121 10.1103/PhysRevB.69.155112
34. T. Shimazaki and Y. Asai, Chem. Phys. Lett. 466, 91 (2008). CHPLBC 0009-2614 10.1016/j.cplett.2008.10.012
35. S. Refaely-Abramson, S. Sharifzadeh, M. Jain, R. Baer, J. B. Neaton, and L. Kronik, Phys. Rev. B 88, 081204 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88. 081204
36. T. Shimazaki and Y. Asai, J. Chem. Phys. 130, 164702 (2009). JCPSA6 0021-9606 10.1063/1.3119259
37. T. Shimazaki and Y. Asai, J. Chem. Phys. 132, 224105 (2010). JCPSA6 0021-9606 10.1063/1.3431293
38. In the Penn model [114] the static dielectric constant is approximated as (Equation presented), where (Equation presented) is the plasmon frequency and (Equation presented) is the energy gap.
39. D. Koller, P. Blaha, and F. Tran, J. Phys.: Condens. Matter 25, 435503 (2013). JCOMEL 0953-8984 10.1088/0953-8984/25/43/435503
40. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.77.3865
41. Convergence of the sc-hybrid scheme is achieved when (Equation presented). In the present scheme (Equation presented) is only evaluated at the end of each converged self-consistent field (SCF) calculation; in principle one could instead evaluate (Equation presented) at each step of the SCF procedure in an attempt to reduce the overall number of SCF iterations, but this would be prohibitively expensive.
42. R. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993). PRBMDO 0163-1829 10.1103/PhysRevB.47.1651
43. R. Resta, Rev. Mod. Phys. 66, 899 (1994). RMPHAT 0034-6861 10.1103/RevModPhys.66.899
44. S. Baroni, S. de Gironcoli, and A. Dal Corso, Rev. Mod. Phys. 73, 515 (2001). RMPHAT 0034-6861 10.1103/RevModPhys.73.515
45. M. Rérat, R. Orlando, and R. Dovesi, J. Phys.: Conf. Ser. 117, 012016 (2008). 1742-6596 10.1088/1742-6596/117/1/012016
46. B. G. Johnson and M. J. Frisch, Chem. Phys. Lett. 216, 133 (1993). CHPLBC 0009-2614 10.1016/0009-2614(93)E1238-C
47. J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Int. J. Quantum Chem. 16, 225 (1979). IJQCB2 0020-7608 10.1002/qua.560160825
48. G. J. B. Hurst, M. Dupuis, and E. Clementi, J. Chem. Phys. 89, 385 (1988). JCPSA6 0021-9606 10.1063/1.455480
49. R. Orlando, M. Ferrero, M. Rérat, B. Kirtman, and R. Dovesi, J. Chem. Phys. 131, 184105 (2009). JCPSA6 0021-9606 10.1063/1.3263919
50. R. Dovesi, R. Orlando, B. Civalleri, C. Roetti, V. R. Saunders, and C. M. Zicovich-Wilson, Zeitschrift für Kristallographie 220, 571 (2005).
51. H. Ehrenreich, The Optical Properties of Solids: Proceedings of the International School of Physics "Enrico Fermi", Varenna, edited by J. Tauc. (Academic Press, New York, 1966), p. 106.
52. W. Hanke, Adv. Phys. 27, 287 (1978). ADPHAH 0001-8732 10.1080/00018737800101384
53. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, New York, 2003).
54. S. L. Adler, Phys. Rev. 126, 413 (1962). PHRVAO 0031-899X 10.1103/PhysRev.126.413
55. N. Wiser, Phys. Rev. 129, 62 (1963). PHRVAO 0031-899X 10.1103/PhysRev.129.62
56. E. K. U. Gross, E. Runge, and O. Heinonen, Many-Particle Theory (Taylor & Francis, London, 1991).
57. J. Paier, M. Marsman, and G. Kresse, Phys. Rev. B 78, 121201(R) (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.121201
58. The explicit calculation of the perturbed orbitals comes at the expense of evaluating unoccupied KS orbitals that enter the expression of the functional derivatives. Within DFPT applied to semilocal functionals, the calculations of empty orbitals is avoided by utilizing projection techniques [44].
59. F. Bruneval, F. Sottile, V. Olevano, R. Del Sole, and L. Reining, Phys. Rev. Lett. 94, 186402 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.186402
60. F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys. 7, 3297 (2005). PPCPFQ 1463-9076 10.1039/b508541a
61. D. Rappoport and F. Furche, J. Chem. Phys. 133, 134105 (2010). JCPSA6 0021-9606 10.1063/1.3484283
62. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevB.89.195112 for additional information on the localized Gaussian basis sets used, the pseudopotentials used in plane-wave calculations, the (Equation presented)-point convergence for the polarizabilities, and a comparison of plane-wave and Gaussian basis set results.
63. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, J. Phys.: Condens. Matter 21, 395502 (2009). JCOMEL 0953-8984 10.1088/0953-8984/21/39/395502
64. A. R. Tackett, A. W. Holzwarth, and G. E. Matthews, Comput. Phys. Commun. 135, 329 (2001). CPHCBZ 0010-4655 10.1016/S0010-4655(00)00244-7
65. http://www.quantum-espresso.org/pseudopotentials/.
66. J. A. Van Vechten, Phys. Rev. 182, 891 (1969). PHRVAO 0031-899X 10.1103/PhysRev.182.891
67. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, Berlin, 2001).
68. J. R. DeVore, JOSA 41, 416 (1951). 10.1364/JOSA.41.000416
69. K. V. Rao and A. Smakula, J. Appl. Phys. 36, 2031 (1965). JAPIAU 0021-8979 10.1063/1.1714397
70. M. Giehler, M. Ramsteiner, O. Brandt, H. Yang, and K. H. Ploog, Appl. Phys. Lett. 67, 733 (1995). APPLAB 0003-6951 10.1063/1.115208
71. J. Plendl, L. Mansur, S. Mitra, and I. Chang, Solid State Commun. 7, 109 (1969). SSCOA4 0038-1098 10.1016/0038-1098(69)90704-2
72. M. Hutchins, O. Abu-Alkhair, M. El-Nahass, and K. A. El-Hady, Mater. Chem. Phys. 98, 401 (2006). MCHPDR 0254-0584 10.1016/j.matchemphys.2005.09.052
73. J. Chen, Z. H. Levine, and J. W. Wilkins, Appl. Phys. Lett. 66, 1129 (1995). APPLAB 0003-6951 10.1063/1.113835
74. M. Balog, M. Schieber, M. Michman, and S. Patai, Thin Solid Films 41, 247 (1977). THSFAP 0040-6090 10.1016/0040-6090(77)90312-1
75. S. Shokhovets, R. Goldhahn, G. Gobsch, S. Piekh, R. Lantier, A. Rizzi, V. Lebedev, and W. Richter, J. Appl. Phys. 94, 307 (2003). JAPIAU 0021-8979 10.1063/1.1582369
76. N. Ashkenov, B. N. Mbenkum, C. Bundesmann, V. Riede, M. Lorenz, D. Spemann, E. M. Kaidashev, A. Kasic, M. Schubert, M. Grundmann, G. Wagner, H. Neumann, V. Darakchieva, H. Arwin, and B. Monemar, J. Appl. Phys. 93, 126 (2003). JAPIAU 0021-8979 10.1063/1.1526935
77. R. H. French, H. Müllejans, and D. J. Jones, J. Am. Ceram. Soc. 81, 2549 (2005). JACTAW 0002-7820 10.1111/j.1151-2916.1998.tb02660.x
78. D. R. Lide, CRC Handbook of Chemistry and Physics, 90th ed. (CRC Press/Taylor and Francis, Boca Raton, FL, 2010).
79. M. Bass, C. DeCusatis, V. Enoch, J Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd ed. (McGraw Hill Professional, New York, 2009).
80. G. P. Johari and S. J. Jones, Proc. R. Soc. London A 349, 467 (1976). 1364-5021 10.1098/rspa.1976.0085
81. A. C. Sinnock and B. L. Smith, Phys. Rev. 181, 1297 (1969). PHRVAO 0031-899X 10.1103/PhysRev.181.1297
82. W. Schulze and D. M. Kolb, J. Chem. Soc., Faraday Trans. 2 70, 1098 (1974). JCFTBS 0300-9238 10.1039/f29747001098
83. M. Shishkin and G. Kresse, Phys. Rev. B 75, 235102 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.75.235102
84. M. Shishkin, M. Marsman, and G. Kresse, Phys. Rev. Lett. 99, 246403 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.246403
85. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2005).
86. B. Monemar, Phys. Rev. B 8, 5711 (1973). 0556-2805 10.1103/PhysRevB.8. 5711
87. W. Choyke, D. Hamilton, and L. Patrick, Phys. Rev. 133, A1163 (1964). PHRVAO 0031-899X 10.1103/PhysRev.133.A1163
88. Y. Tezuka, S. Shin, T. Ishii, T. Ejima, S. Suzuki, and S. Sato, J. Phys. Soc. Jpn. 63, 347 (1994). JUPSAU 0031-9015 10.1143/JPSJ.63.347
89. G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett. 53, 2339 (1984). PRLTAO 0031-9007 10.1103/PhysRevLett.53.2339
90. C. D. Clark, P. J. Dean, and P. V. Harris, Proc. R. Soc. A 277, 312 (1964). 1364-5021 10.1098/rspa.1964.0025
91. J. van Elp, J. L. Wieland, H. Eskes, P. Kuiper, G. A. Sawatzky, F. M. F. de Groot, and T. S. Turner, Phys. Rev. B 44, 6090 (1991). PRBMDO 0163-1829 10.1103/PhysRevB.44.6090
92. G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras- Martínez, R. C. Powell, and J. E. Greene, Phys. Rev. B 50, 8433 (1994). PRBMDO 0163-1829 10.1103/PhysRevB.50.8433
93. J. van Elp, R. H. Potze, H. Eskes, R. Berger, and G. A. Sawatzky, Phys. Rev. B 44, 1530 (1991). PRBMDO 0163-1829 10.1103/PhysRevB.44.1530
94. J. Meyer, M. Kröger, S. Hamwi, F. Gnam, T. Riedl, W. Kowalsky, and A. Kahn, Appl. Phys. Lett. 96, 193302 (2010). APPLAB 0003-6951 10.1063/1.3427430
95. M. Levinshtein, S. L. Rumyantsev, and M. S. Shur, Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, and SiGe (Wiley, New York, 2001).
96. S. Sayan, T. Emge, E. Garfunkel, X. Zhao, L. Wielunski, R. A. Bartynski, D. Vanderbilt, J. S. Suehle, S. Suzer, and M. Banaszak-Holl, J. Appl. Phys. 96, 7485 (2004). JAPIAU 0021-8979 10.1063/1.1803107
97. L. Roskovcová and J. Pastrňák, Czech. J. Phys. B 30, 586 (1980). CZLIA6 0011-4626 10.1007/BF01596307
98. Ü. Özgür, Y. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doǧan, V. Avrutin, S.-J. Cho, and H. Morkoç, J. Appl. Phys. 98, 041301 (2005). 10.1063/1.1992666
99. M. E. Innocenzi, R. T. Swimm, M. Bass, R. H. French, A. B. Villaverde, and M. R. Kokta, J. Appl. Phys. 67, 7542 (1990). JAPIAU 0021-8979 10.1063/1.345817
100. R. Whited, C. J. Flaten, and W. Walker, Solid State Commun. 13, 1903 (1973). SSCOA4 0038-1098 10.1016/0038-1098(73)90754-0
101. G. Baldini and B. Bosacchi, Phys. Status Solidi B 38, 325 (1970). PSSBBD 0370-1972 10.1002/pssb.19700380132
102. S.-i. Nakai and T. Sagawa, J. Phys. Soc. Jpn. 26, 1427 (1969). JUPSAU 0031-9015 10.1143/JPSJ.26.1427
103. M. Piacentini, D. W. Lynch, and C. G. Olson, Phys. Rev. B 13, 5530 (1976). 0556-2805 10.1103/PhysRevB.13.5530
104. K. Kobayashi, J. Phys. Chem. 87, 4317 (1983). JPCHAX 0022-3654 10.1021/j100244a065
105. N. Schwentner, F. J. Himpsel, V. Saile, M. Skibowski, W. Steinmann, and E. E. Koch, Phys. Rev. Lett. 34, 528 (1975). PRLTAO 0031-9007 10.1103/PhysRevLett.34.528
106. R. H. French, J. Am. Ceram. Soc. 73, 477 (1990). JACTAW 0002-7820 10.1111/j.1151-2916.1990.tb06541.x
107. S. D. Kevan, Studies in Surface Science and Catalysis: Angle-Resolved Photoemission (Elsevier, Amsterdam, 1992), Vol. 74.
108. I. Jiménez, L. J. Terminello, D. G. J. Sutherland, J. A. Carlisle, E. L. Shirley, and F. J. Himpsel, Phys. Rev. B 56, 7215 (1997). PRBMDO 0163-1829 10.1103/PhysRevB.56.7215
109. J. Furthmüller, G. Cappellini, H.-C. Weissker, and F. Bechstedt, Phys. Rev. B 66, 045110 (2002). PRBMDO 0163-1829 10.1103/PhysRevB.66.045110
110. F. J. Himpsel, L. J. Terminello, D. A. Lapiano-Smith, E. A. Eklund, and J. J. Barton, Phys. Rev. Lett. 68, 3611 (1992). PRLTAO 0031-9007 10.1103/PhysRevLett.68.3611
111. L. Tjeng, A. Vos, and G. Sawatzky, Surf. Sci. 235, 269 (1990). SUSCAS 0039-6028 10.1016/0039-6028(90)90802-F
112. L. Schimka, J. Harl, and G. Kresse, J. Chem. Phys. 134, 024116 (2011). JCPSA6 0021-9606 10.1063/1.3524336
113. Notable exceptions are CoO and NiO, for which the sc-hybrid and the (Equation presented) hybrid were not as similar because the convergence in the sc-hybrid is not achieved until five and nine iterations, respectively, for CoO and NiO.
114. D. R. Penn, Phys. Rev. 128, 2093 (1962). PHRVAO 0031-899X 10.1103/PhysRev.128.2093