Communication: Favorable dimensionality scaling of rectangular collocation with adaptable basis functions up to 7 dimensions

We show that by using a rectangular collocation method with a small basis of parameterized functions, it is possible to compute a vibrational spectrum by solving the Schrodinger equation in 7D from a small number of ab initio calculations without a potential surface. The method is ideal for spectra of molecules adsorbed on a surface. In this paper, it is applied to calculate experimentally relevant energy levels of acetic acid adsorbed on the (101) surface of anatase TiO2. In this case, to obtain levels of experimental accuracy, increasing the number of dimensions from 4 to 7 increases the number of required potential points from about 1000 to about 10 000 and the number of basis functions from 126 to 792: the scaling is very attractive.