  This paper describes a method to do ab initio molecular dynamics in
electronically excited systems within the random phase approximation (RPA).
Using a dynamical variational treatment of the RPA frequency, which corresponds
to the electronic excitation energy of the system, we derive coupled equations
of motion for the RPA amplitudes, the single particle orbitals, and the nuclear
coordinates. These equations scale linearly with basis size and can be
implemented with only a single holonomic constraint. Test calculations on a
model two level system give exact agreement with analytical results.
Furthermore, we examined the computational efficiency of the method by modeling
the excited state dynamics of a one-dimensional polyene lattice. Our results
indicate that the present method offers a considerable decrease in
computational effort over a straight-forward configuration interaction
(singles) plus gradient calculation performed at each nuclear configuration.
