In variational calculations of rotational-vibrat ional energy levels of polyatomic molecules the total wave-function is typ ically represented as a linear combination of basis functions. The size of the multidimensionaldirect-product basis grows exponentially with the num ber of atoms. As a result\, the memory requirements forvariational calcula tions become prohibitive for molecules with more than 4-5 atoms - this is often referred to asthe curse of dimensionality [1].Here we propose a meth od which circumvents the problem of the exponential scaling of the basis s et size.This is achieved through the collocation approach [2]\, in which t he Schrodinger equation is solved at a set ofpoints\, avoiding the need fo r an accurate multidimensional quadrature.The new collocation method has t he following advantages: 1) the size of the matrix eigenvalue problem isth e size of the required pruned (non-direct product) polynomial-type basis\; 2) it requires solving a regular\, andnot a generalized matrix eigenvalue problem\; 3) accurate results are obtained even if quadrature points andw eights are not good enough to yield a nearly exact overlap matrix\; 4) the potential matrix is diagonal\; 5)the matrix-vector products required to c ompute eigenvalues and eigenvectors can be evaluated by doing sumssequenti ally\, despite the fact that the basis is pruned\; 6) unlike in popular MC TDH and tensor rank-reductionmethods\, here no sum-of-product form of the potential energy surface (PES) is required.To achieve these advantages we use sets of nested Leja grid points and special hierarchical basis functio ns.Matrix-vector products needed for iterative eigensolvers are inexpensiv e because transformation matrices be-tween the basis and the grid\, and th eir inverses\, are lower triangular. Vibrational energy levels of CH2NH ar ecalculated with the new method.

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:swheatle@ist.ac.at SUMMARY:Overcoming the curse of dimensionality: a hierarchical collocation method for solving the rotational-vibrational SchrÃ¶dinger equation for po lyatomic molecules URL:https://talks-calendar.app.ist.ac.at/events/1415 END:VEVENT END:VCALENDAR