1. 2/18/2015PHY 752 Spring 2015 -- Lecture 151 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 15: Reading: Chapter 10 in MPM Numerical Realizations of Density functional theory 1.Electronic structure of atoms 2.Integration of the radial equations 3.Frozen core approximation 4.Extension of formalism to multi-center analysis

2. 2/18/2015PHY 752 Spring 2015 -- Lecture 152 Note: Take-home exam scheduled for the week of March 2 nd.

3. 2/18/2015PHY 752 Spring 2015 -- Lecture 153

4. 2/18/2015PHY 752 Spring 2015 -- Lecture 154

5. 2/18/2015PHY 752 Spring 2015 -- Lecture 155 Kohn-Sham equations for spherical atom

6. 2/18/2015PHY 752 Spring 2015 -- Lecture 156 Self-consistent solution Numerical methods for solving the Kohn-Sham equations

7. 2/18/2015PHY 752 Spring 2015 -- Lecture 157 Example for carbon

8. 2/18/2015PHY 752 Spring 2015 -- Lecture 158 Results for carbon r (Bohr) P nl (r) 1s 2s 2p

9. 2/18/2015PHY 752 Spring 2015 -- Lecture 159 n core (r) n val (r) r (Bohr) n r 2 /4 

10. 2/18/2015PHY 752 Spring 2015 -- Lecture 1510 Example for Cu 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 r (Bohr) n core (r) n vale (r) n r 2 /4 

11. 2/18/2015PHY 752 Spring 2015 -- Lecture 1511 r (Bohr) 4s 4p 3d 3s 3p Results for Copper P nl (r)

12. 2/18/2015PHY 752 Spring 2015 -- Lecture 1512 Frozen core approximation Example for Cu 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 r (Bohr) n core (r) n vale (r) n r 2 /4 

13. 2/18/2015PHY 752 Spring 2015 -- Lecture 15b13 Systematic study of frozen core approximation in DFT http://journals.aps.org/prb/abstract/10.1103/PhysRevB.21.2222

14. 2/18/2015PHY 752 Spring 2015 -- Lecture 1514 Variational relations for DFT in frozencore approximation (Kohn-Sham formulation)

15. 2/18/2015PHY 752 Spring 2015 -- Lecture 1515 Practical solution to Kohn-Sham equations for single particle orbitals:

16. 2/18/2015PHY 752 Spring 2015 -- Lecture 1516 Practical solution of Kohn-Sham equations in solids

17. 2/18/2015PHY 752 Spring 2015 -- Lecture 1517 Muffin tin potential construction http://journals.aps.org/pr/abstract/10.1103/PhysRev.51.846 Augmented Plane Wave (APW) approximation

18. 2/18/2015PHY 752 Spring 2015 -- Lecture 1518 Muffin tin potential construction http://www.jara.org/de/research/jara-hpc/forschung/details/simlab-ai/performance-modeling-for-linear-algebra-in-fleur/

19. 2/18/2015PHY 752 Spring 2015 -- Lecture 1519 Muffin tin model continued: Problems with APW and KKR Green’s function schemes 1.Difficult numerically to find Kohn-Sham energies  i 2.Potential form unrealistic especially for covalent materials  Linearized equations – O. K. Andersen http://journals.aps.org/prb/abstract/10.1103/PhysRevB.12.3060

20. 2/18/2015PHY 752 Spring 2015 -- Lecture 1520

21. 2/18/2015PHY 752 Spring 2015 -- Lecture 1521 Modern software based on LAPW method -- http://www.wien2k.at/

22. 2/18/2015PHY 752 Spring 2015 -- Lecture 1522 http://elk.sourceforge.net/ http://exciting-code.org/