  The McLachlan "minimum-distance" principle for optimizing approximate
solutions of the time-dependent Schrodinger equation is revisited, with a focus
on the local-in-time error accompanying the variational solutions. Simple,
exact expressions are provided for this error, which are then evaluated in
illustrative cases, notably the widely used mean-field approach and the
adiabatic quantum molecular dynamics. These findings pave the way for the
rigorous development of adaptive schemes that re-size on-the-fly the underlying
variational manifold and thus optimize the overall computational cost of a
quantum dynamical simulation.
