We present a method for performing time-dependent simulations of electron c
onduction through molecules. The method is based on the time-dependent Schr
odinger equation recast as a matrix equation using a basis of non-orthogona
l local orbitals. We present the basic theory and show the results of a sim
ulation of conduction through benzene 1,4-dithiolate. A comparison with exp
erimental data and with the results of the Green's function scattering theo
ry of the conductivity of a molecule is made.