Agenda and Readings

[Note: The abbreviations for the readings are NR =Numerical Recipes, CN = class notes]

Goal: Implement variational solution to Schrodinger's equation and Kohn-Sham equations using steepest descents.

We highly recommend you go over the readings before the corresponding lecture...

Recap:

Lec 18 11/03 (Tue) Discrete Fourier Transforms (DFTs): standard ordering of indices for Discrete Fourier Transforms; aliasing/Nyquist frequency. Readings: NR 12.0-12.1
Lec 19 11/05 (Thu) Fourier inversion theorem; Variational principle, analytic continuation for constraints, minimization by steepest descents. Readings: NR 12.0-12.2, 10.6
Lec 20 11/10 (Tue) DFT++ expressions for energy and gradient for multiple states and for density functional theory. Readings: Sections 1-4 of http://arxiv.org/abs/cond-mat/9909130 .

Upcoming:

Lec 21 11/12 (Thu) Convergence of steepest descents; preconditioning; preview of improved minimization methods. Readings: NR 10.5-10.6
Lab 7 11/12 (Thu) Spectral solution of Poisson’s equation
Semifinals and Thanksgiving: 11/16-11/27

Lec 22 12/01 (Tue) Details behind line minimization; motivation for conjugate gradients; begin conjugate gradient algorithm. Readings: NR 10.2-10.3, 10.5-10.6, 10.7-10.8

Preview:

Lec 23 12/03 (Thu) Finish conjugate gradients; finite difference test, finite difference derivative and machine precision; begin extraction of eigenstates from variational principle. Readings: NR 12.2
Lab 8 12/03 (Thu) Spectral solution of Schrödinger’s equation