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Theoretical Methods

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Vibrational Properties of Defective Oxides and 2D Nanolattices

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Density functional theory provides an efficient and robust method for (approximately) solving the many-body Schrödinger equation of quantum mechanics. Solving this equation is one of the central problems in solid states physics and quantum chemistry since they are potentially able to provide some fundamental understanding as well as predict, in some instances, the properties of atoms, molecules and solids, enabling to describe a large variety of experimental observations.

If in some cataclysm all scientific knowledge were to be destroyed and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made of atoms, little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see there is an enormous amount of information about the world, if just a little imagination and thinking are applied.

Richard P. Feynman

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References

  1. I.N. Levine, Quant. Chem. (Chaps. 1, 2, 8) (2008)

    Google Scholar 

  2. M. Born, J.R. Oppenheimer, Ann. Phy. 84, 457 (1927)

    Article  ADS  MATH  Google Scholar 

  3. A. Szabo, N.S. Ostlund, Modern quantum chemistry: introduction to advanced electronic structure (Dover Publications, 1996)

    Google Scholar 

  4. R.R. Martin, Electronic structure: basic theory and practical methods (Cambridge University Press, Cambridge, 2004)

    Book  Google Scholar 

  5. G. Goulub, C. Van Loan, Matrix computations (Johns Hopkins University Press, Baltimore, 1989)

    Google Scholar 

  6. W. Kohn, Nobel lectures, chemistry 1996–2000 (1999)

    Google Scholar 

  7. W. Koch, M.C. Holthausen, A chemist’s guide to density functional theory (2001)

    Google Scholar 

  8. P. Hohenberg, W. Kohn, Phys. Rev. 136(3B), B864 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  9. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45, 566 (1980)

    Article  ADS  Google Scholar 

  10. E.P. Wigner, Phys. Rev. 46, 1002 (1934)

    Article  ADS  Google Scholar 

  11. E.P. Wigner, Trans. Faraday Soc. 34, 678 (1938)

    Article  Google Scholar 

  12. A.D. Becke, Phys. Rev. A 38, 3098 (1988)

    Article  ADS  Google Scholar 

  13. J.P. Perdew, Y. Wang, Phys. Rev. B 45, 13244 (1992)

    Article  ADS  Google Scholar 

  14. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    Article  ADS  Google Scholar 

  15. A.D. Becke, J. Chem. Phys. 98, 1372 (1993)

    Article  ADS  Google Scholar 

  16. A.D. Becke, J. Chem. Phys. 98, 5648 (1993)

    Article  ADS  Google Scholar 

  17. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988)

    Article  ADS  Google Scholar 

  18. P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Chem. Phys. 98, 11623 (1998)

    Article  Google Scholar 

  19. M. Ernzerhof, G.E. Scuseria, J. Chem. Phys. 110, 5029 (1999)

    Article  ADS  Google Scholar 

  20. J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

    Article  ADS  Google Scholar 

  21. M. Dion, H. Rydberg, E. Schroeder, D.C. Langreth, B.I. Lundqvis, Phys. Rev. Lett. 92, 246401 (2004)

    Article  ADS  Google Scholar 

  22. Y. Zhang, W. Yang, Phys. Rev. Lett. 80, 890 (1998)

    Article  ADS  Google Scholar 

  23. J.M. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Junquera, P. Ordejon, D. Sanchez-Portal, J. Phys. Condens. Matter 14, 2745 (2002)

    Article  ADS  Google Scholar 

  24. C. Kittel, Introduction to solid state physics (1996)

    Google Scholar 

  25. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. 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, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. Seitsonen, A. Smogunov, P. Umari, R. Wentzcovitch, J. Phys. Condens. Matter 21(39), 395502 (2009)

    Google Scholar 

  26. X. Gonze, J.M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.M. Rignanese, L. Sindic, M. Verstraete, G. ZÃt’erah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Ghosez, J.Y. Raty, D.C. Allan, Comput. Mater. Sci. 25, 478 (2002)

    Google Scholar 

  27. J.C. Slater, Phys. Rev. 51, 846 (1937)

    Article  ADS  Google Scholar 

  28. J. Grotendorst, S. Blugel, D. Marx, Comput. Nanosci. 31, 71 (2006)

    Google Scholar 

  29. D.H. Hamalm, M. Schluter, C. Chiang, Phys. Rev. Lett. 43, 1494 (1979)

    Article  ADS  Google Scholar 

  30. G.B. Bachelet, D.H. Hamalm, M. Schluter, Phys. Rev. B 26, 4199 (1982)

    Article  ADS  Google Scholar 

  31. N. Troullier, J.L. Martins, Phys. Rev. B 43, 1993 (1990)

    Article  ADS  Google Scholar 

  32. S. Goedecker, M. Teter, J. Hutter, Phys. Rev. B 54, 1703 (1996)

    Article  ADS  Google Scholar 

  33. C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58, 3641 (1998)

    Article  ADS  Google Scholar 

  34. D. Vanderbilt, Phys. Rev. B 41, 7892 (1990)

    Article  ADS  Google Scholar 

  35. D.D. Koelling, Sol. Stat. Commun. 53, 1019 (1985)

    Article  ADS  Google Scholar 

  36. S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)

    Article  ADS  Google Scholar 

  37. P. Giannozzi, S. Baroni, Handbook of materials modelling (2005) (pp. 189–208)

    Google Scholar 

  38. H. Hellmann, Einführung in die quantenchemie (1937)

    Google Scholar 

  39. R.P. Feynman, Stat. Mech. 249 (1972)

    Google Scholar 

  40. E.N. Zein, Fiz. Tverd. Tela 26, 3024 (1984)

    Google Scholar 

  41. S. Baroni, P. Giannozzi, A. Testa, Phys. Rev. Lett. 58, 1861 (1987)

    Article  ADS  Google Scholar 

  42. X. Gonze, Phys. Rev. A 52, 1096 (1995)

    Article  ADS  Google Scholar 

  43. T.M. Yin, M.L. Cohen, Phys. Rev. B 26, 3259 (1980)

    Article  ADS  Google Scholar 

  44. M. Lazzeri, F. Mauri, Phys. Rev. Lett. 90, 036401 (2003)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany

    Emilio Scalise

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  1. Emilio Scalise
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Correspondence to Emilio Scalise .

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Scalise, E. (2014). Theoretical Methods. In: Vibrational Properties of Defective Oxides and 2D Nanolattices. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07182-4_2

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