This paper describes a method to do ab initio molecular dynamics in electro
nically excited systems within the random phase approximation (RPA). Using
a dynamical variational treatment of the RPA frequency, which corresponds t
o the electronic excitation energy of the system, we derive coupled equatio
ns 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. F
urthermore, we examined the computational efficiency of the method by model
ing the excited state dynamics of a one-dimensional polyene lattice. Our re
sults indicate that the present method offers a considerable decrease in co
mputational effort over a straight-forward configuration interaction (singl
es) plus gradient calculation performed at each nuclear configuration. (C)
1999 American Institute of Physics. [S0021-9606(99)01413-0].