Abstract
We present an introduction to Density Functional Theory. We discuss briefly the Kohn–Sham functional, the local density approximation, and some more sophisticated implementations of the theory. We present some computational examples and show how the theory can be used to provide information needed to study electron transport, focusing on the calculation of the phonon spectrum.
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References
C. Pisani, Quantum-Mechanical Ab-initio Calculation of the Properties of Crystalline Materials. Lecture Notes in Chemistry (Springer, Berlin, Heidelberg, 1996)
E. Kaxiras, Atomic and Electronic Structure of Solids (Cambridge University Press, Cambridge, 2003)
P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964)
W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965)
C. Kittel, Quantum Theory of Solids, 2nd edn. (Wiley, New York, 1987)
G.D. Mahan, Many-Particle Physics. Physics of Solids and Liquids, 3rd edn. (Kluwer, Boston, 2000)
A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (Dover, Mineola, New York, 2003)
P.A.M. Dirac, Note on exchange phenomena in the Thomas-Fermi atom. Proc. Cambridge Phil. Roy. Soc. 26, 376 (1930)
R.G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1994)
D.C. Langreth, M.J. Mehl, Beyond the local-density approximation in calculations of ground-state electronic properties. Phys. Rev. B 28, 1809 (1983)
J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671 (1992)
A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098 (1998)
A.D. Becke, A new mixing of Hartree–Fock and local density-functional theories. J. Chem. Phys. 98, 1372 (1993)
J.P. Perdew, M. Ernzerhof, K. Burke, Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 105, 9982 (1996)
J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)
G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558(R) (1993)
G. Kresse, Thesis, Technische Universität Wien, 1993
G. Kresse, J. FurthmĂĽller, Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mat. Sci. 6, 15 (1996)
G. Kresse, J. FurthmĂĽller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996)
P.E. Blöchl, Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994)
R. Car, M. Parrinello, Unified approach for molecular dynamics and density functional theory. Phys. Rev. Lett. 55, 2471 (1995)
P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 98, 11623 (1994)
S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515 (2001)
B.G. Dick, A.W. Overhauser Jr., Theory of the dielectric constants of alkali halide crystals. Phys. Rev. 112, 90 (1958)
K. Kunc, O.H. Nielsen, Phys. Commun. 17, 47 (1979)
O.H. Nielsen, W. Weber, Phys. Commun. 18, 101 (1979)
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Fischetti, M.V., Vandenberghe, W.G. (2016). Density Functional Theory. In: Advanced Physics of Electron Transport in Semiconductors and Nanostructures. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-01101-1_6
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DOI: https://doi.org/10.1007/978-3-319-01101-1_6
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