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A Simplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors

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Abstract

We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction-band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron bandwidth. This calculation is supplemented by the computation of the loss of ground-state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used to estimate the energy gap in the two materials. The numerical data reported here show that the methods works, in principle, but that some extension of the scheme is also necessary to obtain fully satisfactory results.

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References

  1. Harrison WA Electronic Structure and the Properties of Solids (W. H. Freeman and Company, San Francisco 1980; Dover ed., General Publ. Company, Toronto 1989)..

  2. Kohn W, Sham L (1965). Phys Rev A 140:1133

    Article  Google Scholar 

  3. Andersen OK (1975). Phys Rev B 12:3060

    Article  CAS  Google Scholar 

  4. Anisimov VI, Zaanen J, Andersen OK (1991). Phys Rev B 44:943

    Article  CAS  Google Scholar 

  5. Anisimov VI, Poteryaev AI, Korotin MA, Anokhin AO, Kotliar G (1997). J Phys Cond Matter 9:7359

    Article  CAS  Google Scholar 

  6. Lichtenstein AI, Katsnelson MI (1998). Phys Rev B 57:6884

    Article  CAS  Google Scholar 

  7. Kakehashi Y (2004). Adv Phys 53:497

    Article  CAS  Google Scholar 

  8. Hedin L (1965). Phys Rev 139(3A):796

    Article  CAS  Google Scholar 

  9. Strinati G, Mattausch HJ, Hanke W (1982). Phys Rev B 25:2867

    Article  CAS  Google Scholar 

  10. Saunders VR, Dovesi R, Roetti C, Orlando R, Zicovich-Wilson CM, Harrison NM, Doll K, Civalleri B, Bush IJ, D’Arco Ph, Llunell M (2003). CRYSTAL2003 user’s manual. Theoretical Chemistry Group, University of Torino, Italy

    Google Scholar 

  11. Shukla A, Dolg M, Stoll H, Fulde P (1996). Chem Phys Lett 262:213

    Article  CAS  Google Scholar 

  12. Shukla A, Dolg M, Stoll H, Fulde P (1998). Phys Rev B 57:1471

    Article  CAS  Google Scholar 

  13. Birkenheuer U, Izotov D (2005). Phys Rev B 71:125116

    Article  Google Scholar 

  14. Stollhoff G, Fulde P (1980). J Chem Phys 73:4548

    Article  CAS  Google Scholar 

  15. Horsch S, Horsch P, Fulde P (1984). Phys Rev B 29:1870

    Article  CAS  Google Scholar 

  16. Gräfenstein J, Stoll H, Fulde P (1997). Phys Rev B 55:13588

    Article  Google Scholar 

  17. Albrecht M, Reinhardt P, Malrieu J-P (1998). Theor Chim Acta 100:241

    Article  CAS  Google Scholar 

  18. Rubio J, Povill A, Malrieu J-P, Reinhardt P (1997). J Chem Phys 107:10044

    Article  CAS  Google Scholar 

  19. Reinhardt P, Malrieu J-P (1998). J Chem Phys 109:7632

    Article  CAS  Google Scholar 

  20. Sun JQ, Bartlett RJ (1996). J Chem Phys 104:8553

    Article  CAS  Google Scholar 

  21. Linderberg J, Öhrn Y (1973). Propagators in quantum chemistry. Academic, London

    Google Scholar 

  22. Ladik JJ (1999). Phys Rev 313:171

    CAS  Google Scholar 

  23. ross EKU, Runge E, Heinonen O (1991). Many-particle theory. Adam Hilger, Bristol

    Google Scholar 

  24. Albrecht M, Fulde P (2002). Phys Stat Sol (b) 234:313

    Article  CAS  Google Scholar 

  25. Stoll H (1992). Chem Phys Lett 191:548

    Article  CAS  Google Scholar 

  26. Stoll H (1992). Phys Rev B 46:6700

    Article  CAS  Google Scholar 

  27. Stoll H (1992). J Chem Phys 97:8449

    Article  CAS  Google Scholar 

  28. Gräfenstein J, Stoll H, Fulde P (1993). Chem Phys Lett 215:610

    Article  Google Scholar 

  29. Albrecht M, Fulde P, Stoll H (2000). Chem Phys Lett 319:355

    Article  CAS  Google Scholar 

  30. Roetti C, Dovesi R, von Arnim M, Alsheimer W, Birkenheuer U (2002). The CRYSTAL-MOLPRO interface. MPI-PKS, Dresden

    Google Scholar 

  31. Borrmann W, Fulde P (1987). Phys Rev B 35:9569

    Article  Google Scholar 

  32. Zicovich-Wilson CM, Dovesi R, Saunders VR (2001). J Chem Phys 115:9708

    Article  CAS  Google Scholar 

  33. Fulde P (1995). Electron correlations in molecules and solids, 3rd edn. .Springer series in solid-state sciences, vol 100, Springer, Berlin

    Book  Google Scholar 

  34. MOLPRO (Version 2002.6). is a package of ab initio programs designed by Werner H-J, Knowles PJ. The authors are Amos RD, Bernhardsson A, Berning A, Celani P, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Hampel C, Hetzer G, Knowles PJ, Korona T, Lindh R, Lloyd AW, McNicholas SJ, Manby FR, Meyer W, Mura ME, Nicklaß A, Palmieri P, Pitzer R, Rauhut G, Schütz M, Schumann U, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T, Werner H-J

  35. Bezugly V, Birkenheuer U (2004). Chem Phys Lett 399:57

    Article  CAS  Google Scholar 

  36. Saunders VR, Dovesi R, Roetti C, Causá M, Harrison NM, Orlando R, Zicovich-Wilson CM, Doll K, Civalleri B (2001). CRYSTAL200x user’s manual. Theoretical Chemistry Group, University of Torino, Italy

    Google Scholar 

  37. Dunning Jr TH (1989). J Chem Phys 90:1007

    Article  CAS  Google Scholar 

  38. Bergner A, Dolg M, Kuechle W, Stoll H, Preuss H (1993). Mol Phys 80:1431

    Article  CAS  Google Scholar 

  39. Baranek P, Zicovich-Wilson CM, Roetti C, Orlando R, Dovesi R (2001). Phys Rev B 64:125102

    Article  Google Scholar 

  40. Werner H-J, Knowles PJ (1985). J Chem Phys 82:5053

    Article  CAS  Google Scholar 

  41. Knowles PJ, Werner H-J (1985). Chem Phys Lett 115:259

    Article  CAS  Google Scholar 

  42. Werner H-J, Knowles PJ (1988). J Chem Phys 89:5803

    Article  CAS  Google Scholar 

  43. Knowles PJ, Werner H-J (1988). Chem Phys Lett 145:514

    Article  CAS  Google Scholar 

  44. Werner H-J, Knowles PJ (1990). Theor Chim Acta 78:175

    Article  CAS  Google Scholar 

  45. Pulay P (1983). Chem Phys Lett 100:151

    Article  CAS  Google Scholar 

  46. Ashcroft NW, Mermin ND (1976). Solid State Physics. Saunders College, Philadelphia, Tab. 27.3

    Google Scholar 

  47. Godby RW, Schlüter M, Sham LJ (1987). Phys Rev B 36:6497

    Article  CAS  Google Scholar 

  48. Orlando R, Dovesi R, Roetti C, Saunders VR (1990). J Phys Condens Matter 2:7769

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187, Dresden, Germany

    U. Birkenheuer & P. Fulde

  2. Universität Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    H. Stoll

Authors
  1. U. Birkenheuer
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  2. P. Fulde
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  3. H. Stoll
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Correspondence to P. Fulde.

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Dedicated to J.-P. Malrieu on the occasion of his 60th birthday

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Birkenheuer, U., Fulde, P. & Stoll, H. A Simplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors. Theor Chem Acc 116, 398–403 (2006). https://doi.org/10.1007/s00214-006-0091-7

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