Cornell University
Department of Physics
Phys 480/680, Astro 690 April 26, 2006
Computational Physics, Spring 2006
Homework Assignment # 9
(Due Wednesday, April 26)
Agenda and readings:
Goal: Predict bond length of H
molecule!
Readings marked NR are from Numerical Recipes: The Art of
Scientific Computing, 2
edition (in C). Readings
marked LN are from the course lecture notes to be found at
http://www.muchomas.lassp.cornell.edu/P480.
Recap:
- 04/13 Lec 21: DFT++ expressions for energy for multiple
states and for density functional theory; derivatives of real functions of complex matrices; DFT++ calculus; expression for gradient of kinetic energy
Reading: Sections 1-4.4 of
http://arxiv.org/abs/cond-mat/9909130
- 04/18 (meet at 8:00am) Lab 7: FLOP rates; Spectral solution of Poisson's equation
- 04/18 Lec 22: DFT++ expressions for gradient of all energy terms; convergence of steepest descents; preconditioning; idea behind line
minimization
Reading: NR 10.2, 10.3. 10.5
Preview of final weeks of class:
- 04/20 Lec 23: Method for line minimization; conjugate gradient algorithm
Reading: 10.6
- 04/20 Lab 8: Spectral solution of Schrödinger's equation and
Kohn-Sham equations for simple harmonic oscillator.
- 04/25 Lec 24: Further optimizations for spectral methods; ab initio pseudopotentials
- 04/27 Lec 25: FFT
Reading: 12.2
- 04/27 Lab 9: Performance of numerical minimization techniques;
preconditioner for quantum calculations, H molecule
- 05/02 Lec 26: Extraction of eigenstates from variational principle
- 05/04 Lab 10: Physics of harmonic oscillator, H2 molecule and
germanium solid
Tomas Arias
2006-04-26
