attention has been directed by theoretical/computational chemists towards developing reliable and accurate means for solving dynamical quantum mechanics problems—i.e., for obtaining solutions to the time-dependent  equation—for molecular systems. Insofar as “exact” quantum methods are concerned, two traditional approaches have been used: (1) representation of the system Hamiltonian in a finite, direct-product basis set; (2) discretization of the wavefunction onto a rectilinear grid of lattice points over the relevant region of configuration space. Both approaches, however, suffer from the drawback that the computational effort scales exponentially with system dimensionality.[@bowman86; @bacic89] Recently, a number of promising new methods have emerged with the potential to alleviate the exponential scaling problem once and for all. These include various basis set optimization methods,[@poirier99qcII; @poirier00gssI; @yu02b; @wangx03b] and build-and-prune methods,[@dawes04] such as those based on wavelet techniques.[@poirier03weylI; @poirier04weylII; @poirier04weylIII]

On the other hand, a completely different approach to the exponential scaling problem is to use basis sets or grid points, that themselves evolve over time. The idea is that at any given point in time, one need sample a much smaller Hilbert subspace, or configuration space region, than would be required at all times—thus substantially reducing the size of the calculation. For basis set calculations, much 