1. 2/16/2015PHY 752 Spring 2015 -- Lecture 141 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 14: 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

2. 2/16/2015PHY 752 Spring 2015 -- Lecture 142 Note: Take-home exam scheduled for the week of March 2 nd.

3. 2/16/2015PHY 752 Spring 2015 -- Lecture 143 Numerical methods for solving the Kohn-Sham equations

4. 2/16/2015PHY 752 Spring 2015 -- Lecture 144 Self-consistent solution Numerical methods for solving the Kohn-Sham equations

5. 2/16/2015PHY 752 Spring 2015 -- Lecture 145 Numerical methods for solving the Kohn-Sham equations – Consider the case of a single atom, choosing the coordinate system at the center of the nucleus. We will further assume that the atom is spherically symmetric, averaging over the multiplet configurations.

6. 2/16/2015PHY 752 Spring 2015 -- Lecture 146 Kohn-Sham equations for spherical atom

7. 2/16/2015PHY 752 Spring 2015 -- Lecture 147 Kohn-Sham equations for spherical atom -- continued

8. 2/16/2015PHY 752 Spring 2015 -- Lecture 148 Kohn-Sham equations for spherical atom -- continued

9. 2/16/2015PHY 752 Spring 2015 -- Lecture 149 Kohn-Sham equations for spherical atom -- continued Notes on numerical integration of differential equations

10. 2/16/2015PHY 752 Spring 2015 -- Lecture 1410 Digression on numerical integration N=4N=8Exact  9.549150289.76979549.869604404  34.5491503137.900800239.47841762 Numerical results from second-order approximation: Numerical results from Numerov approximation: N=4Exact  9.8630976259.869604404  39.0458162039.47841762