In many processes, the impact of nuclear quantum phenomena cannot be neglected if a physically correct simulation is aimed for . This quantum description of the nuclear motion is usually obtained by mapping the system onto a grid, thus implying a discretisation of the configuration space. As a consequence, all quantities take the form of high-order tensors. Unfortunately, multidimensional representations imply an exponential scaling of data and the concomitant number of operations with system size as well as the difficulty of computing multidimensional integrals .
Solutions to these issues, in particular when considering the representation of the potential energy surface, exist in the form of tensor-decomposition schemes. We present the recently developed the Multigrid POTFIT (MGPF) algorithm  which alleviates the exponential scaling by avoiding the calculations on the full grid. Moreover, we introduceour latest improvements to the algorithm which provide numerical stability and higher accuracy through the use of non-product grids for combined modes .
We illustrate the power of the MGPF algorithm in conjunction with the Multiconfiguration Time-Dependent Hartree (MCTDH) method in the case of the full-dimensional (9D) study of the vibrational structure  and the computation of the infrared spectrum  of the hydrated hydroxide complex (H3O2-).
 Fabien Gatti (Ed.) in Molecular Quantum Dynamics From Theory to Applications. Springer (2014).
 H.-D. Meyer, F. Gatti, G. A. Worth (Eds.) Multidimensional Quantum Dynamics: MCTDH Theory and Applications, Wiley (2009).
 D. Peláez, H.D. Meyer, The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems, J. Chem. Phys., 138, 014108 (2013).
 D. Peláez, H.D. Meyer (in preparation)
 D. Peláez, K. Sadri, H.-D. Meyer, Full-dimensional MCTDH/MGPF study of the ground and lowest lying vibrational states of the bihydroxide complex, Spectrochimica Acta Part A,119, 42 (2014).
 D. Peláez, H.D. Meyer, On the infrared absorption spectrum of the hydrated hydroxide (H3O2-) cluster anion, Chem. Phys., (in press) (2016).