A numerical method is given for effecting nonlinear local density functional evolution. Within a given time interval, Chebyshev quadrature points are used to sample the evolving orbitals. An implicit equation coupling wave functions at the different time points is then set up. The equation is solved iteratively using the "direct inversion in iterative space" acceleration technique. Spatially, the orbitals are represented on a Fourier grid combined with soft pseudopotentials. The method is first applied to the computation of the (3)Pi (g) adiabatic potential energy curves of Al-2. Next, the electronic dynamics of a toy molecular wire is studied. The wire consists of a C2H4 molecule connected via sulfur atoms to two gold atoms, the "electrodes." The molecule is placed in a homogeneous electric field and a dynamical process of charge transfer is observed. By comparing the transient with that of a resistance-capacitance circuit, an effective Ohmic resistance and capacitance is estimated for the system. (C) 2001 American Institute of Physics.