a parameter associated to the system modes (the first and the second modes), such i=1,2 λ i ≤ L s . (iii) L m , a parameter which controls the coupling between the system and bath modes, such i=1,n λ i ≤ L m . Furthermore, the Smolyak parameters are subject to other constraints: L m ≥ L s ≥ L b and L m ≤ L s + L b . This approach enables us to tune the basis set expansion of the system part (the first two modes) and the bath part (the remaining modes). With this system-bath separation, D λ coefficients are obtained from the transformation between the first and the second Smolyak scheme. Furthermore, to improve the integration, the value of Smolyak parameter associated to the grid, L G , can be larger than L m and typically,