Excited States from Time-Dependent Density Functional Theory - Reviews in Computational Chemistry - page 145

Figure 17 Ring geometry for gauge transformation of electric fields. Black dots
represent a conducting molecule while gray dots represent the electrically conducting
leads. ( Top panel ) Single molecule in a bias electric field attached to semi-infinite leads.
( Middle panel ) Same system with periodic boundary conditions, while the lower panel
shows how the middle panel can be imagined as a ring with the electric field gauge
transformed to a magnetic one.

propagating KS orbitals in the semi-infinite leads, and using an iterative pro-
cedure to get the correct initial state, the authors were able to find a steady-
state current.
An alternative TDDFT formulation for electron transport uses periodic
boundary conditions and includes dissipation. 371 In the Landauer-B ¨ ttiker
formalism, dissipation effects arising from electron-electron interaction and
electron-phonon interaction can be neglected because the molecule is smaller
than the scattering length. However, there would be scattering in the leads.
Imagine a molecule in the ring geometry of Figure 17, with a spatially constant
electric field; via a gauge transformation, the electric field can be replaced by a
constant time-dependent magnetic field through the center of the ring. If no
dissipation exists, the electrons keep accelerating indefinitely and never reach
a steady state.
In the classical Boltzmann equation for electron transport, scattering is
included via a dissipation term using , the average collision time. A master

equation approach is basically a generalization of the Boltzmann equation
to a fully quantum mechanical system. The master equation is based on the

t