The concrete realization of the general idea pursued here is what we term the time-dependent adaptive density-guided approach (TD-ADGA) for PES construction. The TD-ADGA is a time-dependent generalization of the adaptive density-guided approach (ADGA) that has been applied for more than a decade for constructing PESs for anharmonic vibrational computations. Essential to the ADGA approach is the concept of adaptively constructing the PES. In ADGA SPs are added to a grid until certain convergence criteria are satisfied.