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Excitons in Time-Dependent Density-Functional Theory

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Density-Functional Methods for Excited States

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 368))

Abstract

This chapter gives an overview of the description of the optical and dielectric properties of bulk insulators and semiconductors in time-dependent density-functional theory (TDDFT), with an emphasis on excitons. We review the linear-response formalism for periodic solids, discuss excitonic exchange-correlation kernels, calculate exciton binding energies for various materials, and compare the treatment of excitons with TDDFT and with the Bethe–Salpeter equation.

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Notes

  1. 1.

    We find that the convergence of the bootstrap kernel strongly depends on the number of bands used in the iterative calculation of the kernel. The results for solid Ar, solid Ne, and LiF are obtained by calculating the bootstrap kernel with 30 bands. It turns out that some of our previous results reported in Yang and Ullrich [19], where the bootstrap kernel seemed to work very well for Ar, Ne, and LiF, were in fact not fully converged.

References

  1. Ullrich CA (2012) Time-dependent density-functional theory: concepts and applications. Oxford University Press, Oxford

    Google Scholar 

  2. Marques MAL, Maitra NT, Nogueira FMS, Gross EKU, Rubio A (2012) Fundamentals of time-dependent density functional theory. Springer, Berlin

    Book  Google Scholar 

  3. Ullrich CA, Yang ZH (2014) Brazil J Phys 44:154

    Article  Google Scholar 

  4. Hedin L (1965) Phys Rev 139:A796

    Article  Google Scholar 

  5. Aryasetiawan F, Gunnarsson O (1998) Rep Prog Phys 61:237

    Article  CAS  Google Scholar 

  6. Sham LS, Rice TM (1966) Phys Rev 144:708

    Article  CAS  Google Scholar 

  7. Hanke W, Sham L (1979) Phys Rev Lett 43:387

    Article  CAS  Google Scholar 

  8. Hanke W, Sham LS (1980) Phys Rev B 21:4656

    Article  CAS  Google Scholar 

  9. Strinati G (1982) Phys Rev Lett 49:1519

    Article  CAS  Google Scholar 

  10. Strinati G (1984) Phys Rev B 29:5718

    Article  CAS  Google Scholar 

  11. Strinati G (1988) Riv Nuovo Cimento 11:1

    Article  CAS  Google Scholar 

  12. Rohlfing M, Louie SG (1998) Phys Rev Lett 81:2312

    Article  CAS  Google Scholar 

  13. Rohlfing M, Louie S (2000) Phys Rev B 62:4927

    Article  CAS  Google Scholar 

  14. Onida G, Reining L, Rubio A (2002) Rev Mod Phys 74:601

    Article  CAS  Google Scholar 

  15. Botti S, Schindlmayr A, Del Sole R, Reining L (2007) Rep Prog Phys 70:357

    Article  Google Scholar 

  16. Turkowski V, Ullrich CA (2008) Phys Rev B 77:075204

    Article  CAS  Google Scholar 

  17. Turkowski V, Leonardo A, Ullrich CA (2009) Phys Rev B 79:233201

    Article  CAS  Google Scholar 

  18. Yang ZH, Li Y, Ullrich CA (2012) J Chem Phys 137:014513

    Article  CAS  Google Scholar 

  19. Yang ZH, Ullrich CA (2013) Phys Rev B 87:195204

    Article  CAS  Google Scholar 

  20. Yu P, Cardona M (2010) Fundamentals of semiconductors. Springer, Berlin

    Book  Google Scholar 

  21. Liang WY (1970) Phys Educ 5:226

    Article  CAS  Google Scholar 

  22. Knox RS (1963) Theory of excitons. Academic, New York

    Google Scholar 

  23. Frenkel J (1931) Phys Rev 37:17; 1276

    Google Scholar 

  24. Peierls R (1932) Ann Phys (Leipzig) 13:905

    Article  CAS  Google Scholar 

  25. Davydov AS (1948) Zh Eksperim i Teor Fiz 18:210

    CAS  Google Scholar 

  26. Wannier GH (1937) Phys Rev 52:191

    Article  CAS  Google Scholar 

  27. Mott NF (1938) Trans Faraday Soc 34:500

    Article  CAS  Google Scholar 

  28. Glutsch S (1994) Excitons in low-dimensional semiconductors. Springer, Berlin

    Google Scholar 

  29. Koch SW, Kira M, Khitrova G, Gibbs HM (2006) Nat Mater 5:523

    Article  CAS  Google Scholar 

  30. Scholes GD, Rumbles G (2006) Nat Mater 5:683

    Article  CAS  Google Scholar 

  31. Dresselhaus MS, Dresselhaus G, Saito R, Jorio A (2007) Annu Rev Phys Chem 58:719

    Article  CAS  Google Scholar 

  32. Wheeler DA, Zhang JZ (2013) Adv Mater 25:2878

    Article  CAS  Google Scholar 

  33. Bardeen CJ (2014) Annu Rev Phys Chem 65:127

    Article  CAS  Google Scholar 

  34. Dresselhaus G (1956) J Phys Chem Solid 1:14

    Article  Google Scholar 

  35. Elliott RJ (1957) Phys Rev 108:1384

    Article  CAS  Google Scholar 

  36. Haug H, Koch SW (2004) Quantum theory of the optical and electronic properties of solids. World Scientific, Singapore

    Google Scholar 

  37. Baerends EJ, Gritsenko OV, van Meer R (2013) Phys Chem Chem Phys 15:16408

    Article  CAS  Google Scholar 

  38. Perdew JP, Parr RG, Levy M, Balduz JL (1982) Phys Rev Lett 49:1691

    Article  CAS  Google Scholar 

  39. Perdew JP, Levy M (1983) Phys Rev Lett 51:1884

    Article  CAS  Google Scholar 

  40. Kohn W (1986) Phys Rev B 33:4331

    Article  Google Scholar 

  41. Godby RW, Schlüter M, Sham LJ (1986) Phys Rev Lett 56:2415

    Article  CAS  Google Scholar 

  42. Capelle K, Vignale G, Ullrich CA (2010) Phys Rev B 81:125114

    Article  CAS  Google Scholar 

  43. Kronik L, Stein T, Refaely-Abramson S, Baer R (2012) J Chem Theor Comput 8:1515

    Article  CAS  Google Scholar 

  44. Seidl A, Görling A, Vogl P, Majewski JA, Levy M (1996) Phys Rev B 53:3764

    Article  CAS  Google Scholar 

  45. Kümmel S, Kronik L (2008) Rev Mod Phys 80:3

    Article  CAS  Google Scholar 

  46. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) J Phys Chem 98:11623

    Article  CAS  Google Scholar 

  47. Ernzerhof M, Scuseria GE (1999) J Chem Phys 110:5029

    Article  CAS  Google Scholar 

  48. Paier J, Marsman M, Kresse G (2007) J Chem Phys 127:024103

    Article  CAS  Google Scholar 

  49. Muscat J, Wander A, Harrison NN (2001) Chem Phys Lett 342:397

    Article  CAS  Google Scholar 

  50. Heyd J, Scuseria GE, Ernzerhof M (2003) J Chem Phys 118:8207

    Article  CAS  Google Scholar 

  51. Heyd J, Peralta JE, Scuseria GE, Martin RL (2005) J Chem Phys 112:174101

    Article  CAS  Google Scholar 

  52. Gerber IC, Ángyán JC, Marsman M, Kresse G (2007) J Chem Phys 127:054101

    Article  CAS  Google Scholar 

  53. Moussa JE, Schultz PE, Chelikowsky JR (2011) J Chem Phys 136:204117

    Article  CAS  Google Scholar 

  54. Schimka L, Harl J, Kresse G (2011) J Chem Phys 134:024116

    Article  CAS  Google Scholar 

  55. Henderson TM, Paier P, Scuseria GE (2011) Phys State Solid B 248:767

    Article  CAS  Google Scholar 

  56. Marques MAL, Vidal J, Oliveira MCT, Reining L, Botti S (2011) Phys Rev B 83:035119

    Article  CAS  Google Scholar 

  57. Matsushita Y, Nakamura K, Oshiyama A (2011) Phys Rev B 84:075205

    Article  CAS  Google Scholar 

  58. Friedrich C, Betzinger M, Schlipf M, Blügel S, Schindlmayr A (2012) J Phys Condens Matter 24:293201

    Article  CAS  Google Scholar 

  59. Waroquiers D, Lherbier A, Miglio A, Stankovski M, Poncé S, Oliveira MJT, Fiantomassi M, Rignanese G-M, Gonze X (2013) Phys Rev B 87:075121

    Article  CAS  Google Scholar 

  60. Tran F, Blaha P (2009) Phys Rev Lett 102:226401

    Article  CAS  Google Scholar 

  61. Kim Y-S, Marsman M, Kresse G, Tran F, Blaha P (2010) Phys Rev B 82:205212

    Article  CAS  Google Scholar 

  62. Koller D, Tran F, Blaha P (2011) Phys Rev B 83:195134

    Article  CAS  Google Scholar 

  63. Koller D, Tran F, Blaha P (2012) Phys Rev B 85:155109

    Article  CAS  Google Scholar 

  64. Jiang H (2013) J Chem Phys 138:134115

    Article  CAS  Google Scholar 

  65. Betzinger M, Friedrich C, Blügel S, Görling A (2011) Phys Rev B 83:045105

    Article  CAS  Google Scholar 

  66. Perdew JP, Ruzsinszky A, Constantin LA, Sun J, Czonka GI (2009) J Chem Theor Comput 5:902

    Article  CAS  Google Scholar 

  67. Adler SL (1962) Phys Rev 126:413

    Article  Google Scholar 

  68. Wiser N (1963) Phys Rev 129:62

    Article  Google Scholar 

  69. Hanke W (1978) Adv Phys 27:187

    Article  Google Scholar 

  70. Del Sole R, Fiorino E (1984) Phys Rev B 29:4631

    Article  Google Scholar 

  71. Giuliani GF, Vignale G (2005) Quantum theory of the electron liquid. Cambridge University Press, Cambridge

    Book  Google Scholar 

  72. Gross EKU, Kohn W (1985) Phys Rev Lett 55:2850

    Article  CAS  Google Scholar 

  73. Botti S, Sottile F, Vast N, Olevano V, Reining L, Weissker H-C, Rubio A, Onida G, Del Sole R, Godby RW (2004) Phys Rev B 69:155112

    Article  CAS  Google Scholar 

  74. Levine ZH, Allan DC (1989) Phys Rev Lett 63:1719

    Article  CAS  Google Scholar 

  75. Del Sole R, Girlanda R (1993) Phys Rev B 48:11789

    Article  Google Scholar 

  76. Fuchs F, Rödl C, Schleife A, Bechstedt F (2008) Phys Rev B 78:085103

    Article  CAS  Google Scholar 

  77. Erhart P, Schleife A, Sadigh B, Åberg D (2014) Phys Rev B 89:075132

    Article  CAS  Google Scholar 

  78. Casida ME (1995) Recent advances in density functional methods. In: Chong DE (ed) Recent advances in computational chemistry, vol 1. World Scientific, Singapore, p 155

    Google Scholar 

  79. Gurtubay IG, Pitarke JM, Ku W, Eguiluz AG, Larson BC, Tischler J, Zschack P, Finkelstein KD (2005) Phys Rev B 72:125117

    Article  CAS  Google Scholar 

  80. Tozer DJ, Amos RD, Handy NC, Roos BO, Serrano-Andrés L (1999) Mol Phys 97:859

    Article  CAS  Google Scholar 

  81. Tozer DJ (2003) J Chem Phys 119:12697

    Article  CAS  Google Scholar 

  82. Casida ME, Gutierrez F, Guan J, Gadea F-X, Salahub D, Daudey J-P (2000) J Chem Phys 113:7062

    Article  CAS  Google Scholar 

  83. Dreuw A, Weisman JL, Head-Gordon M (2003) J Chem Phys 119:2943

    Article  CAS  Google Scholar 

  84. Dreuw A, Head-Gordon M (2004) J Am Chem Soc 126:4007

    Article  CAS  Google Scholar 

  85. Gritsenko O, Baerends EJ (2004) J Chem Phys 121:655

    Article  CAS  Google Scholar 

  86. Autschbach J (2009) Chemphyschem 10:1757

    Article  CAS  Google Scholar 

  87. Gonze X, Ghosez P, Godby RW (1995) Phys Rev Lett 74:4035

    Article  CAS  Google Scholar 

  88. Ghosez P, Gonze X, Godby RW (1997) Phys Rev B 56:12811

    Article  CAS  Google Scholar 

  89. Reining L, Olevano V, Rubio A, Onida G (2002) Phys Rev Lett 88:066404

    Article  CAS  Google Scholar 

  90. Sottile F, Olevano V, Reining L (2003) Phys Rev Lett 91:056402

    Article  CAS  Google Scholar 

  91. Stubner R, Tokatly IV, Pankratov O (2004) Phys Rev B 70:245119

    Article  CAS  Google Scholar 

  92. Sottile F, Karlsson K, Reining L, Aryasetiawan F (2003) Phys Rev B 68:205112

    Article  CAS  Google Scholar 

  93. Tokatly IV, Pankratov O (2001) Phys Rev Lett 86:2078

    Article  CAS  Google Scholar 

  94. Tokatly IV, Stubner R, Pankratov O (2002) Phys Rev B 65:113107

    Article  CAS  Google Scholar 

  95. Hellgren M, von Barth U (2008) Phys Rev B 78:115107

    Article  CAS  Google Scholar 

  96. Hellgren M, von Barth U (2009) J Chem Phys 131:044110

    Article  CAS  Google Scholar 

  97. Talman JD, Shadwick WF (1976) Phys Rev A 14:36

    Article  CAS  Google Scholar 

  98. Görling A (1998) Phys Rev A 57:3433

    Article  Google Scholar 

  99. Görling A (1998) Int J Quant Chem 69:265

    Article  Google Scholar 

  100. Kim Y-H, Görling A (2002) Phys Rev B 66:035114

    Article  CAS  Google Scholar 

  101. Kim Y-H, Görling A (2002) Phys Rev Lett 89:096402

    Article  CAS  Google Scholar 

  102. Bruneval F, Sottile F, Olevano V, Reining L (2006) J Chem Phys 124:144113

    Article  CAS  Google Scholar 

  103. Izmaylov A, Scuseria GE (2008) J Chem Phys 129:034101

    Article  CAS  Google Scholar 

  104. Bernasconi L, Tomić S, Ferrero M, Rérat M, Orlando R, Dovesi R, Harrison NM (2011) Phys Rev B 83:195325

    Article  CAS  Google Scholar 

  105. Bernasconi L, Webster R, Tomić S, Harrison NM (2012) J Phys Conf Ser 367:012001

    Article  CAS  Google Scholar 

  106. Tomić S, Bernasconi L, Searle BG, Harrison NM (2014) J Phys Chem C 118:14478

    Article  CAS  Google Scholar 

  107. Yang ZH, Sottile F, Ullrich CA, arXiv:1501.05631

    Google Scholar 

  108. Yanai T, Tew DP, Handy NC (2004) Chem Phys Lett 393:51

    Article  CAS  Google Scholar 

  109. Vydrov OA, Scuseria GE (2006) J Chem Phys 125:234109

    Article  CAS  Google Scholar 

  110. Heyd J, Scuseria GE, Ernzerhof M (2006) J Chem Phys 124:219906

    Article  CAS  Google Scholar 

  111. Paier J, Marsman M, Kresse G (2008) Phys Rev B 78:121201 (R)

    Article  CAS  Google Scholar 

  112. Tao JM, Perdew JP, Staroverov VN, Scuseria GE (2003) Phys Rev Lett 91:146401

    Article  CAS  Google Scholar 

  113. Voorhis TV, Scuseria GE (1998) J Chem Phys 109:400

    Article  Google Scholar 

  114. Voorhis TV, Scuseria GE (2008) J Chem Phys 129:219901

    Article  CAS  Google Scholar 

  115. Becke AD, Johnson ER (2006) J Chem Phys 124:221101

    Article  CAS  Google Scholar 

  116. Nazarov VU, Vignale G (2011) Phys Rev Lett 107:216402

    Article  CAS  Google Scholar 

  117. Petersilka M, Gossmann UJ, Gross EKU (1996) Phys Rev Lett 76:1212

    Article  CAS  Google Scholar 

  118. Petersilka M, Gossmann UJ, Gross EKU (1998) In: Dobson JF, Vignale G, Das MP (eds) Electronic density functional theory: recent progress and new directions. Plenum, New York, p 177

    Chapter  Google Scholar 

  119. Karimi S, Ullrich CA (2014) Phys Rev B 90:245304

    Google Scholar 

  120. Kohn W (1959) Phys Rev 115:809

    Article  Google Scholar 

  121. des Cloiseaux J (1964) Phys Rev 135:A685; A698

    Google Scholar 

  122. Kohn W (1996) Phys Rev Lett 76:3168

    Article  CAS  Google Scholar 

  123. Zhang W, Drabold DA (2001) Phys Rev B 63:233109

    Article  CAS  Google Scholar 

  124. Taraskin SN, Drabold DA, Elliott SR (2002) Phys Rev Lett 88:196405

    Article  CAS  Google Scholar 

  125. Stefanucci G, van Leeuwen R (2013) Nonequilibrium many-body theory of quantum systems. Cambridge University Press, Cambridge

    Book  Google Scholar 

  126. Adragna G, Del Sole R, Marini A (2003) Phys Rev B 68:165108

    Article  CAS  Google Scholar 

  127. Marini A, Del Sole R, Rubio A (2003) Phys Rev Lett 91:256401

    Article  CAS  Google Scholar 

  128. Sottile F, Marsili M, Olevano V, Reining L (2007) Phys Rev B 76:161103

    Article  CAS  Google Scholar 

  129. Gatti M, Olevano V, Reining L, Tokatly IV (2007) Phys Rev Lett 99:057401

    Article  CAS  Google Scholar 

  130. Varsano D, Marini A, Rubio A (2008) Phys Rev Lett 101:133002

    Article  CAS  Google Scholar 

  131. Sagmeister S, Ambrosch-Draxl C (2009) Phys Chem Chem Phys 11:4451

    Article  CAS  Google Scholar 

  132. Sharma S, Dewhurst JK, Sanna A, Gross EKU (2011) Phys Rev Lett 107:186401

    Article  CAS  Google Scholar 

  133. Sharma S, Dewhurst JK, Gross EKU (2014) Top Curr Chem 347:235

    Article  CAS  Google Scholar 

  134. Trevisanutto PE, Terentjevs A, Constantin LA, Olevano V, Della Sala F (2013) Phys Rev B 87:205143

    Article  CAS  Google Scholar 

  135. Constantin LA, Pitarke JM (2007) Phys Rev B 75:245127

    Article  CAS  Google Scholar 

  136. Corradini M, Del Sole R, Onida G, Palummo M (1998) Phys Rev B 57:14569

    Article  CAS  Google Scholar 

  137. Perdew JP, Wang Y (1992) Phys Rev B 45:13244

    Article  Google Scholar 

  138. Tretiak S, Igumenshchev K, Chernyak V (2005) Phys Rev B 71:033201

    Article  CAS  Google Scholar 

  139. Kilina S, Badaeva E, Piryatinski A, Tretiak S, Saxena A, Bishop AR (2009) Phys Chem Chem Phys 11:4113

    Article  CAS  Google Scholar 

  140. Wong BM (2009) J Phys Chem C 113:21921

    Article  CAS  Google Scholar 

  141. Zimmerman PM, Bell F, Casanova D, Head-Gordon M (2011) J Am Chem Soc 133:19944

    Article  CAS  Google Scholar 

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Acknowledgments

This work was supported by NSF grant DMR-1408904. We thank Lucia Reining and Francesco Sottile for many helpful discussions. C.U. thanks the ETSF-Palaiseau group for its hospitality and the Ecole Polytechnique for its support during an extended visit in 2014.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Missouri, Columbia, MO, 65211, USA

    Carsten A. Ullrich & Zeng-hui Yang

  2. Department of Physics, Temple University, Philadelphia, PA, 19122, USA

    Zeng-hui Yang

Authors
  1. Carsten A. Ullrich
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  2. Zeng-hui Yang
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Corresponding author

Correspondence to Carsten A. Ullrich .

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Editors and Affiliations

  1. Institut de Chimie Radicalaire, Université d'Aix-Marseille, Marseille, France

    Nicolas Ferré

  2. Inst. für Physikalische und Theoretische Chemie, Universität Bonn, Bonn, Germany

    Michael Filatov

  3. Institut für Physikalische und Theoretische Chemie, Goethe-Universität Frankfurt am Main, Frankfurt, Germany

    Miquel Huix-Rotllant

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Ullrich, C.A., Yang, Zh. (2014). Excitons in Time-Dependent Density-Functional Theory. In: Ferré, N., Filatov, M., Huix-Rotllant, M. (eds) Density-Functional Methods for Excited States. Topics in Current Chemistry, vol 368. Springer, Cham. https://doi.org/10.1007/128_2014_610

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