To summarize, in the Smolyak scheme, several direct-products, S DP λ , are used and due to the constraint on λ, those direct-products are small. Indeed, when one λ i is large (for instance equal to L s ), all the other ones are equal to zero. In the direct-product approach, one large direct-product is used, S DP Ls with all λ i being equal to L s . Furthermore, the Smolyak scheme overcomes the usual exponential scaling with system size (it becomes polynomial of degree L), which is the main advantage of the approach with respect to the standard direct-product one. As the direct-product approach, the Smolyak schemes are able to use the full grid, therefore, the diabatic-to-adiabatic transformation of the density is possible. In the present study, this feature will be used to analyse the wavepacket density along the propagation. In particular, the adiabatic populations and other properties will be calculated.