Lecture Notes
Lecture 01 : Variational principle (updated 25/02/2009)
Micheal Springborg, Methods of Electronic Structure Calculation : Chapter 5
Lecture 02 : Fundamental concepts in solid states (updated 02/03/2009)
Charles Kittel , Introduction to Solid State Physics : Chapters 1 and 2
Richard Martin , Electronic Structure : Chapter 4
Micheal Springborg , Methods of Electronic Structure Calculation : Chapter 19
Otfried Madelung , Introduction to Solid State Theory : Chapter 2
Octave code for TB model :
Download here
Lecture 03 : The many-body Hamiltonian and the functional derivative (updated 09/03/2009)
Lecture 04 : Hartree-Fock theory (updated 15/03/2009)
Micheal Springborg, Methods of Electronic Structure Calculation : Chapter 9
Philip Phillips, Advanced Solid State Physics : Chapter 4
Lecture 05 : Total energy in terms of density (old)
Lecture 06 : The Hohenberg-Kohn theorem and Kohn-Sham equations (updated 06/04/2009)
Walter Kohn : Nobel Lecture
P. Hohenberg and . Kohn : Phys Rev 136 B864(1964)
W. Kohn and J. Sham : Phys Rev 140 A1133 (1965)
R. Stowasser and R. Hoffmann : What do Kohn-Sham Orbitals and Eigenvalues Mean?, Journal of the Americal Chemical Society, 121, 3414 (1999)
Lecture 07 : Planewave expansion (old)
Lecture 08 : The pseudopotential (updated 03/05/2009)
Efthimios Kaxiras, Atomic and Electronic Structure of Solids : Chapter 2.7
Hamann, Schluter and Chiang : Phys Rev Lett, 43, 1494 (1979)
Kleinman and Bylander : Phys Rev Lett 48 1425
D. Vanderbilt : Phys Rev B 41 7892 (1990)
Lecture 09 : Brillioun zone integration (old)
Lecture 10 : Self-consistent solution of the Kohn-Sham equations (old)
Lecture 11 : Iterative diagonalization methods (old)
Lecture 12 : Exchange and correlation (old)
Homework Octave codes for DFT coding session on 25/05/09 Problem : One-dimensional system under a harmonic potential.
The XC funcional : Calmels and Gold, PRB 52 10841 (1995)
integrate.m : General function for interating a function f on a discrete domain x.
get_Vxc.m : Exchange-correlation potential for a one-dimensional nanowire of radius R_0 and a given density n(x).
hermite.m : Generate Hermite functions of up to order N on a domain x.
initialize_density.m : Initialize the density (i.e. make an initial guess) to a Gaussian over the domain x and for Ne electrons.
get_VH.m : Get the Hartree potential for a given density n and over a domain x.
get_hamiltonian.m : Put together all terms of the Hamiltonian and obtain it as a matrix in the Hermite function representation.
main.m : The driver routine for all the subroutines, where the scf calculation is carried out.
Practice example : Try to do the following
octave:1> x=-10:0.01:10;
Take-home final : Due on 19/06/2009 here .