Abstract
In condensed matter the motion of the electrons is determined by the electric field generated by the nuclei and their mutual interaction. The conditions for neglecting the vibrations of the nuclei around their fixed positions are discussed. The arrangement of the nuclei rules the symmetry and classification of electronic states. The strength of the electron-nucleus interaction is used to distinguish valence and core electrons.
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References
M. Born, R. Oppenheimer, Quantum theory of the molecules. Ann. d. Physik 84, 457–484 (1927)
M. Born, K. Huang, Dynamic Theory of Crystal Lattices (Oxford University Press, Oxford, 1954)
E.G. Brovman, Yu.M. Kagan, Phonons in non-transition metals, in Dynamical Properties of Solids, vol. I, ed. by G.K. Horton, A.A. Maradudin (North-Holland, Amsterdam, 1974), pp. 191–301
F. Bechstedt, Principles of Surface Physics (Springer, Berlin, 2003)
K. Seino, F. Bechstedt, P. Kroll, Tunneling of electrons between Si nanocrystals embedded in a SiO\(_2\) matrix. Phys. Rev. B 86, 075312 (2012)
A. Hermann, Ab initio Untersuchung eines molekularen \(\pi \)-Elektronensystems auf der Si(001)-Oberfläche. Diploma thesis, Friedrich-Schiller-Universität Jena (2004)
F. Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–560 (1928)
Ch. Kittel, Introduction to Solid State Physics (Wiley, Hoboken, 2005)
M. Born, Th. von Kármán, Über Schwingungen in Raumgittern. Z. Physik 13, 297–309 (1912)
M. Fuchs, M. Scheffer, Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density functional theory. Comput. Phys. Commun. 119, 67–98 (1999)
G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996)
G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 11–50 (1996)
X. Xonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Riganese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roay, M. Mikami, Ph Ghosez, J.-Y. Raty, D.C. Allan, First-principles computation of material properties: the ABINIT software project. Comput. Mater. Sci. 25, 478–492 (2002)
P. Gianozzi, 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, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009)
R.M. Martin, Electronic Structure. Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004)
P.E. Blöchl, Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994)
G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999)
J.M. Soler, E. Artacho, J.D. Gale, A. GarcÃa, J. Junquera, P. Ordejón, D. Sánchez-Portal, The SIESTA method for ab initio order-\(N\) materials simulation. J. Phys. Condens. Matter 14, 2745–2780 (2002)
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Bechstedt, F. (2015). Born-Oppenheimer Approximation. In: Many-Body Approach to Electronic Excitations. Springer Series in Solid-State Sciences, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44593-8_1
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DOI: https://doi.org/10.1007/978-3-662-44593-8_1
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