Cornell University

Department of Physics

Phys 480/680, Astro 690 April 24, 2002

Computational Physics, Spring 2002

Homework Assignment # 10

(Due Thursday, May 2 at 8:00 am in Computer Lab.)

Agenda and readings for the week of April 23:

Goal: Compute the bond-length of the 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 of last week:

• Lec22, 04/16 (Tue: mini-lecture, 25mins): Variational principle for Schrödinger's equation, analytic continuation for treatment of constraints.
• Lab8, 04/16 (Tue): Solving Poisson's equation in d>1 dimensions.
• Lec23, 04/18 (Thu): DFT++ representation of Schrodinger's equation; numerical minimization, steepest descents, line-minimization, preconditioning.
  Reading: NR 10.0,10.5
• Lec24, 04/23 (Tue: regular lecture only): Preconditioning as a change of variables, begin conjugate gradients
  Reading: NR 10.0,10.6
• Lec25, 04/25 (Thu: minilecture, 25mins): Finish conjugate-gradients.
• Lab9, 04/25 (Thu): Solution of Schrodinger's equation in d>1 dimensions

Preview of coming week:

• Lec26, 04/30 (Tue): Kohn-Sham equations in d>1 dimensions
• Lec27, 05/02 (Thu: minilecture, 25mins): Fast Fourier Transform Algorithm!!!
  Reading: NR 12.2
• Lab10, 05/05 (Thu): Density-functional theory of molecular mechanics of H

• Contents
• Infrastructure
  • ``physics2.c''
  • get_grad_and_E()
  • conj()
  • excVWN(), excpVWN()
  • exc(), excp()
• Coulomb potential (-Z/r)
  • evalG()
  • Nuc1(), Nuc2()
  • Debugging
• Kohn-Sham equations: full implementation of density functional theory
  • Finite-difference test
  • Kohn-Sham equations
    • Debugging
• Ab initio calculation of H bond length!
• About this document ...

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