The most general quantum approach to obtain accurate energies and wavefunctions of bound states of electrons (in electronic structure theory) and nuclei (vibrational dynamics) is "configuration interaction" (CI). This approach typically leads to a large Hamiltonian matrix, the cost of which to obtain scales exponentially or factorially with the size of the underlying basis. This bottleneck has stimulated numerous approaches to reduce the size of the basis, which of determines the size of the H-matrix. For approaches in electronic structure, see for example refs. 1-4. Also note the recent "heat-bath" CI approach, which has also been using in vibrational CI, denoted VCI. Here we focus on vibrational dynamics, which has some prominent differences with electron motion; perhaps the biggest one is the need to obtain hundreds to thousands of eigenvalues from nuclear CI compared to a much smaller number in electronic CI.