The purpose of this page is to provide some introduction and a place to get more information. As I write my dissertation, I will begin to slowly increase the amount of information provided, include both references, manuscripts, and some tutorials. I have found that the introduction to DFT has been somewhat frustrating when I started by graduate career because much of the theory is confusing, which might be surprising to some because I have a background in mathematics before getting into computational materials science.
Some good websites at the current time include:
The Sherrill Group. Notes on Computational Chemistry.
John Kitchen. "Modeling materials using density functional theory"
The application of density functional theory (DFT) calculations has become a ubiquitous tool for materials modelling problems in physics, chemistry, materials science, and multiple branches of engineering.
Let us first motivate Density Functional Theory by motivating the evolution of solving the quantum mechanical problems to introduce terminology and introduce problems with previous approaches.
Schroedinger's Equation.[1]
Time Dependent Schroedinger's Equation
Time Independent Schroedinger's Equation
Born-Oppenheimer Approximation[2]
Hartree-Fock Equation.
Slater Determinant, a determinant of one-particle orbitals first used by Heisenberg and Dirac in 1926, trivially satisfies the antisymmetric property of the exact solution and hence is a suitable ansatz for applying the variational principle.
The theoretical foundations of DFT consist of the Hohenberg-Kohn Theorems[4] and the Khon-Sham equations[5]. In short, DFT finds the electronic ground state (T=0) structure by solving for the electron density consistent with that ground state. A discussion of this approach is too short for a google sites article, but I will provide a more complete explanation shortly.
[1] Schrödinger, Erwin. "An undulatory theory of the mechanics of atoms and molecules." Physical Review 28.6 (1926): 1049.
[2] Born, Max, and Robert Oppenheimer. "Zur quantentheorie der molekeln." Annalen der Physik 389.20 (1927): 457-484.
[3] Slater, John C. "The theory of complex spectra." Physical Review 34.10 (1929): 1293.
[4] Hohenberg, Pierre, and Walter Kohn. "Inhomogeneous electron gas." Physical review 136.3B (1964): B864.
[5] Kohn, Walter, and Lu Jeu Sham. "Self-consistent equations including exchange and correlation effects." Physical review 140.4A (1965): A1133.
There are essentially two flavors of DFT which are dependent upon the basis sets.
Plane wave codes take a physicists approach to making calculations, by expanding the Kohn-Sham orbitals in terms of plane-waves, up to a certain maximum kinetic energy. With the plane-wave approach, if the system modeled is periodic as typically is the case in materials science, then the plane-wave approach is more efficient because the problem is solved using Fourier techniques in reciprocal space.
CASTEP
Quantum Espresso (QE)
VASP
ABINIT
This approach uses localized orbitals, which provides more freedom with the choice of boundary conditions because periodicity does not necessarily need to be enforced.
NWChem
Most DFT system scale O(N3), but linear-scaling DFT scales as O(N) for large systems. For smaller systems, less than 50 atoms, linear scaling DFT will not be faster than standard DFT. Introduces additional approximations on top of DFT. While accuracy is usually well-controllable, meaning you can get arbitrarily close to the "true-DFT" result, this requires some experience. It's much easier to get garbage with LS-DFT than DFT if you are not careful.
ONETEP
SIESTA
CONQUEST
BigDFT
Paolo Giannozzi, "Notes on Pseudopotential Generation", http://www.quantum-espresso.org/wp-content/uploads/Doc/pseudo-gen.pdf
For structural electronic convergence, convergence with respect to the kinetic energy cutoff, the kpoint-mesh, and the smearing parameters are necessary, and should be done before embarking on solutions. In addition, convergence with respect to the supercell is also important.
[1] R. Zeller. "Spin-Polarized DFT Calculations and Magnetism." Computational Nanoscience: Do It Yourself!, J. Grotendorst, S. Blugel, D. Marx (Eds.), John von Neumann Institute for Computing, Julich, NIC Series, 31 ( 2006) 419-445. Link.
[2]
Includes a calculation of O2 dimers.
https://www.vasp.at/vasp-workshop/slides/handsonI.pdf
https://www.vasp.at/vasp-workshop/slides/handsonIV.pdf
https://www.vasp.at/vasp-workshop/slides/magnetism.pdf
http://kitchingroup.cheme.cmu.edu/dft-book/dft.html
This is a pretty good online tutorial to VASP
http://kitchingroup.cheme.cmu.edu/dft-book/dft.pdf
http://chemistry.tcd.ie/staff/people/gww/gw_new/research/methodology/occupation_matrix_control_in_vasp.pdf
https://www.vasp.at/vasp-workshop/slides/optionic.pdf
[1] W. Setyawan, S. Curtarolo. "High-throughput electronic band structure calculations: challenges and tools." Computational Materials Science. 49:2 (2010) 299-312. http://www.sciencedirect.com/science/article/pii/S0927025610002697