The Kohn-Sham Equation for Deformed Crystals
Author | : Weinan E |
Publisher | : American Mathematical Soc. |
Total Pages | : 109 |
Release | : 2013-01-25 |
ISBN-10 | : 9780821875605 |
ISBN-13 | : 0821875604 |
Rating | : 4/5 (05 Downloads) |
Download or read book The Kohn-Sham Equation for Deformed Crystals written by Weinan E and published by American Mathematical Soc.. This book was released on 2013-01-25 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.