By increasing the number of eigenstates used in the average, a larger domain of the PES is explored as the higher energy of the higher lying states leads to a wider distribution of the wavefunction. The averaging with the lower energy states ensures that the averaged density does not contain any nodes within the potential boundaries. Similar to Eq. 21, multi-dimensional averaged densities, ρ mn ave (q), are approximated as a simple product of the VSCF densities for the individual modes.