Home Page for Computational Physics 2006

(Cornell Phys 480, Phys 680 and Astro 690)

Announcements:

• Prof. Arias's new baby has arrived!

Course Hours

• Prof. Arias office hours: 522 Clark Hall, Tue 2-3pm
• TA office hours: Rock B3, Wed 4-6pm

Important links

• Books and original articles on density-functional theory:
  • Books:
    • Density-Functional Theory of Atoms and Molecules (International Series of Monographs on Chemistry, No 16) by Robert G. Parr, Weitao Yang.
    • A Chemist's Guide to Density Functional Theory, 2nd Edition, by Wolfram Koch, Max C. Holthausen.
  • Original articles:
    • "Inhomogeneous Electron Gas," by P. Hohenberg and W. Kohn, Physical Review 136, B864-B871 (1964).
    • "Self-Consistent Equations Including Exchange and Correlation Effects," by W. Kohn and L. J. Sham, Physical Review 140, A1133-A1138 (1965).
    • "Correlation Energy of an Electron Gas at High Density," by M. Gell-Mann and K.A. Brueckner, Physical Review 106, 364-368 (1957).
    • "New algebraic formulation of density functional calculation,'' by Sohrab Ismail-Beigi and T.A. Arias, Computer Physics Communications 128:1-2, 1-45 (June 2000).

• Free versions of Numerical Recipes on line
  • Cornell's access to Numerical Recipes for free!
  • Numerical Recipes book on line!
  • Cut and paste versions of Numerical Recipes utilities and header file

• On-line version of "What Every Computer Scientist Should Know About Floating-Point Arithmetic".

• US National Institute of Standards and Technology project on the electronic structure of atoms

• On-line Hartree-Fock calculator

Class Handouts

Course Information
[HTML Postscript PDF ]

Lecture Notes

• Overview of quantum mechanics of material systems (density functional theory)
  [ HTML, Postscript, PDF ]

• Numerical Integration of functions
  [HTML, Postscript, PDF ]

Animations

• Animation of integration of the one-dimensional Schrodinger equation as a function of energy
  [HTML/MPEG]

  This movie is from a web based quantum mechanics course which has a variety of other interesting animations.

Problem Sets

• Problem Set # 1: Numerical integration --- potential energy terms in atoms
  [HTML Postscript PDF ]
  

• Problem Set # 2: Solution of ODE's --- Poisson's equation in atoms and a simple Schrondinger solver
  [HTML Postscript PDF ]
  

• Problem Set # 3: Root finding -- Automated, high precision Schrodinger solver for energies of atomic states
  [HTML Postscript PDF ]
  

• Problem Set # 4: Matching method; packaging -- Automated, high precision Schrodinger solver for wave functions of atoms; full set of routines needed for self-consistent atomic calculations
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

  Typo: The last sentence in Section 4.1 ("interpolate()") should read

  • For the special endpoint cases, k=1 and k=N-1, you may take f[-2]=0 and f[N+2]=0, respectively.
  Not,
  • For the special endpoint cases, k=1 and k=N-1, you may take f[-1]=0 and f[N+1]=0, respectively.

  Compiling hint for Problem Set 4:
  The grader from 2003 hit some issues in getting his code to compile. If you are having problems, you may want to try the following: When copying from the "nrutil.c" file to "p480.c", there are two versions of the tensor routines; make sure to copy the ANSI versions (they were first in his file). To compile, he needed to copy the macro lines

  #define NR_END 1
  #define FREE_ARG char*

  that are needed by free_d3tensor(). He also needed to add the header file

  #include <stddef.h>

  to define "size_t" in d3tensor().

• Problem Set # 5: Exchange and correlation energy functionals; implementation of self-consistency; density functional theory of atoms
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 6: Optimization of atomic code, FLOP counting of inner loop operations, cache optimization, ATLAS LAPACK, Octave --
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 7: Spectral solution of PDE's; expressive software: Poisson's equation in a single line of octave code; solution of Schrodinger's equation in three dimensions using spectral methods and steepest descents
  [HTML Postscript PDF ]

• Problem Set # 8: line minization, preconditioning, conjugate gradients; density-functional theory, quantum dots
  [HTML Postscript PDF ]

• Problem Set # 9: Computation of the bond-length of the hydrogen molecule, with your own code built from scratch!!!
  [HTML Postscript PDF ]

• Problem Set # 10: Computation of the binding energy and bonds (electron distribution) in the bonds of a germanium crystal, again with your own code built from scratch!!!
  [HTML Postscript PDF ]

  Errata:

  • There is a bug in our latex-to-html converter, and the Appendix which contains the function "ppm.m" doesn't appear in the HTML version for cutting and pasting. We've put copies of the display functions "ppm.m" and "smooth.m" in Prof. Arias's directory on the physics educational computing cluster in the directory /home/Faculty/muchomas/P480/Octave. You may copy these files directly from there if you wish.
  • Note that for some example code fragements where we say "along the lines of", the variable names may differ from yours, particularly for internal function variables, for which we have no way of knowing the name you have chosen.