These criteria involve the PES itself, but also involve the density of the wave function and targets the PES domains that are critical for the accuracy of the final predictions. The grid domains and grid mesh for the SPs are in the ADGA iteratively determined based on convergence of energy-like integrals over the PES and wave function densities. Furthermore, the time-independent ADGA method (denoted here TI-ADGA to spell out the difference to TD-ADGA) has been based on the mode-coupling expansion of the potential, where the PES is expanded in a set mode-combinations (MCs) and by truncating the set of included MCs an approximate PES is obtained with potential for significant reductions in computational time. Truncation to include only terms coupling less than a given number n of modes gives rise to a standard approach known under many names, including the n-mode representation, high-dimensional model representations (HDMR), many-body expansion and pair approximation. It is the sub-PES for the different MCs that in the TI-ADGA PES are adaptively constructed using reduced one-mode densities from a vibrational self consistent field (VSCF) wave function to guide the placement of SP calculations. These sub-PES are typically of sufficient low dimensionality to be comparatively easy to fit, and methods for using arbitrary one-mode fit functions in a sum of products approach are available. In this manner the TI-ADGA PES is constructed in accordance with the need of the time-independent wave function, and the computational cost and accuracy can be controlled by a few logical variables and convergence thresholds.