275:. Augmented plane wave method (APW) is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice. The basic approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region and constant in the interstitial region. Wave functions (the augmented plane waves) are constructed by matching solutions of the
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within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method. Many modern electronic structure methods employ the approximation. Among them APW method, the linear muffin-tin orbital method (LMTO)
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of a radial Schrödinger equation. Such use of functions other than plane waves as basis functions is termed the augmented plane-wave approach (of which there are many variations). It allows for an efficient representation of single-particle wave functions in the vicinity of the atomic cores where
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experienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the potential is approximated as a constant. Continuity of the potential between the atom-centered spheres and interstitial region is enforced.
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I Turek, J Kudrnovsky & V Drchal (2000). "Disordered Alloys and Their
Surfaces: The Coherent Potential Approximation". In Hugues Dreyssé (ed.).
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In the interstitial region of constant potential, the single electron wave functions can be expanded in terms of
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they can vary rapidly (and where plane waves would be a poor choice on convergence grounds in the absence of a
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In its simplest form, non-overlapping spheres are centered on the atomic positions. Within these regions, the
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Slater, J. C. (1937). "An
Augmented Plane Wave Method for the Periodic Potential Problem".
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Computational
Quantum Mechanics for Materials Engineers: The EMTO Method and Applications
296:. This method has been adapted to treat random materials as well, where it is called the
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methods. One application is found in the variational theory developed by
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Slater, J. C. (1937). "Wave
Functions in a Periodic Potential".
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Electronic
Structure and Physical Properties of Solids
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Electronic
Structure: Basic Theory and Applications
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may be too technical for most readers to understand
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450:Kaoru Ohno, Keivan Esfarjani, Yoshiyuki (1999).
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480:: CS1 maint: multiple names: authors list (
292:and N. Rostoker (1954) referred to as the
132:Multi-configurational self-consistent field
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59:Learn how and when to remove this message
43:, without removing the technical details.
383:Introduction to Condensed Matter Physics
154:Time-dependent density functional theory
116:Semi-empirical quantum chemistry methods
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166:Linearized augmented-plane-wave method
162:Orbital-free density functional theory
682:KKR coherent potential approximation.
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41:make it understandable to non-experts
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564:Introduction to the Theory of Metals
298:KKR coherent potential approximation
271:. The approximation was proposed by
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598:Impurity Scattering in Metal Alloys
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136:Quantum chemistry composite methods
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259:. It is most commonly employed in
120:Møller–Plesset perturbation theory
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625:Kuon Inoue; Kazuo Ohtaka (2004).
381:Duan, Feng; Guojun, Jin (2005).
251:is a shape approximation of the
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453:Computational Materials Science
170:Projector augmented wave method
592:Joginder Singh Galsin (2001).
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208:Korringa–Kohn–Rostoker method
742:Electronic structure methods
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363:Local-density approximation
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200:Empty lattice approximation
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737:Electronic band structures
569:Cambridge University Press
534:Cambridge University Press
385:. Vol. 1. Singapore:
184:Nearly free electron model
98:Modern valence bond theory
526:Richard P Martin (2004).
265:electronic band structure
177:Electronic band structure
147:Density functional theory
124:Configuration interaction
752:Condensed matter physics
192:Muffin-tin approximation
105:Molecular orbital theory
94:Generalized valence bond
495:Vitos, Levente (2007).
196:k·p perturbation theory
718:10.1103/PhysRev.92.603
437:10.1103/PhysRev.51.846
90:Coulson–Fischer theory
747:Computational physics
277:Schrödinger equation
75:Electronic structure
710:1953PhRv...92..603S
561:U Mizutani (2001).
429:1937PhRv...51..846S
358:Kronig–Penney model
353:Kohn–Sham equations
317:spherical harmonics
263:simulations of the
140:Quantum Monte Carlo
112:Hartree–Fock method
83:Valence bond theory
305:screened potential
261:quantum mechanical
158:Thomas–Fermi model
677:978-3-540-67238-8
642:978-3-540-20559-3
628:Photonic Crystals
611:978-0-306-46574-1
578:978-0-521-58709-9
547:978-0-521-78285-2
512:978-1-84628-950-7
467:978-3-540-63961-9
396:978-981-238-711-0
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594:"Appendix C"
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280:and various
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348:Bloch waves
313:plane waves
290:Walter Kohn
731:Categories
666:. p.
369:References
294:KKR method
247:muffin-tin
476:cite book
49:July 2018
664:Springer
633:Springer
602:Springer
458:Springer
343:Band gap
332:See also
319:and the
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425:Bibcode
77:methods
35:Please
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