Electronic Structure Methods based on Local Orbitals · Electronic Structure Methods based on Local...
Transcript of Electronic Structure Methods based on Local Orbitals · Electronic Structure Methods based on Local...
Electronic Structure Methods based onLocal Orbitals
• LCAO: Linear Combination of Atomic Orbitals. Matrix Elements.
• Tight-Binding Method (TB):
• basic understanding of band structures.
• Slater-Koster two-center approximation: empirical TB.
• Total Energy and Forces in TB: TB Molecular Dynamics.
• Fully self-consistent solution of the Kohn-Sham equations in
localized basis
Slater-Koster Interatomic Matrix Elements (I)
l, m, n = direction
cosines of the vector
from the left state to
the right state
l = cos θ
Es,x= l Vspσ = Vspσ cos θ
Slater-Koster LCAO Hamiltonian for ZB Slater-Koster: Two-center
approximation to the
interatomic matrix elements:
(Empirical) Tight-BindingTwo-center interatomic matrix elements fitted to reproduce
states at high-symmetry points in BZ: 6 (8) parameters for
homopolar (heteropolar) semiconductors
Fully-selfconsistent solution of the Kohn-Sham equations in localized bases
KS eqns have the same form as the Tight-Binding eqns BUT:
• The matrix elements must be computed explicitly.
• The potential must be derived self-consistently.
• Selection of orbitals: minimal basis vs overcompleteness
• Analytic basis functions: Gaussians, Slater-type
• Numerical orbitals: “confined” pseudoatomic orbitals.
FIREBALL, SIESTA, OPENMX …
Numerical Orbitals: Construction“compressed” short-range orbitals generated with confining potentials
JunqueraJunquera
• confined orbitals are more realistic in a solid.
• fewer matrix elements need to be included.