ROUGH GUIDE TO DFT (DENSITY FUNCTIONAL THEORY)

Ref: ABC of DFT, Kieran Burke (2010) web.

Born-Oppenheimer approx. -> nuclei immobile

DFT scales at most N^(1/3)

DFT calcs. electron density NOT solve wavefunction

Functional takes a function as an argument and returns a number. Does energy functional output at discreet energies (c.f. Psi(r, ..))

LDA/LSDA - Local Density Approximation
o Consider system a free gas -> simple
o Massive errors but cancel well!
o Binding energies over est.
o Bond length under est.
o Elastic const./phonon freq. under est.
o Dielectric const. over est. (~10%)
o Chemical trends good
o Van der Waals very bad
o Magnetic transition metals ok

GGA - General gradient approximation
o LDA but factors in local gradient of n(r)
o Not much more difficult than LDA computationally
o Improves LDA
o Binding energies better
o Bond length better
o Semiconductors bit better (depends)
o 3d to 5d metals similar
o Noble metals (Ag, Au, Pt) worse than LDA
o dielectric properties marginally better

Can mix LDA with other models i.e. LDA + Hartree-Foch, LDA + Hubbard. Hartree-Foch uses an arbitrary mixing ratio with LDA, Hubbard includes arbitrary choices as to what is localised and what isn't

Eigenvalues (bands) are indicitive, not great

Choosing code:
o Type of basis set
  - Plane wave basis
    Not easy to scale
    Good for periodic systems
  - Atomic orbital basis
    Good for molecules and metals
    Difficult to get systematic convergence
o Psudo potential or all electrons

LDA/GGA shortcomings:
o Mott insulators 
o Negatively charged ions
o Polarisability of molecules