Tight Binding

1
Tight Binding

• Fast quantum mechanical method (minimal basis)
• Fit to DFT calculations
• Accuracy comparable to DFT, but much faster
• 1000 atoms in minutes
• Same underlying quantities as DFT
• Hamiltonian
• Density
• Eigenvalues and Eigenvectors
• Can be used to compute many of the same
  quantities
• Energy spectrum (density of states)
• Matrix elements
• Total energy (and forces)
• Vibrational, elastic properties
• Defect energies
• Polarization, transport

picture?
2
NRL tight-binding method

• (refs?)
• TB models for much of the periodic table
• In particular
• silicon
• carbon
• silicon carbide
• charge self-consistency
• Ongoing work molecules (C-O-H)
• Successes
• CNT conduction
• Si surfaces
• a-Si vibrational properties
• SiC polytypes

pictures Si vac? SiC structures?
3
Dipole matrix elements in TB

• Implementation???
• Benefits
• Interaction with electric field
• Optical properties
• Polarization, polarizability

4
van der Waals with TB

• Native vdW implementation in TB
• Define dipole matrix elements in TB formalism
• Evaluate polarizability (like in local basis DFT)
• Evaluate non-bonded interactions
• Accurate, transferable if it works
• Capability non-bonded structure calculations for
  100s to 1000s of atoms (several intersecting
  CNTs) within hours.
• Alternative vdW additively
• Add vdW interatomic potential (derived from DFT)
  to TB total energy
• Use non-bonded interactions to correct
  equilibrium structure
• Evaluate transport given geometry

5
Transport with TB
Electron transport dependent on densities of
states, overlaps All quantities available in
TB Non-Equilibrium Greens Function (NEGF) Two
semi-infinite leads, coupled to active
part Electrical conductivity from integrals
of Hamiltonian, Greens functions Capability
Transport through array or tangle of CNTs.
Detailed information on microscopic structures
that control overall behavior.
picture of L - C - L