An efficient method is presented for performing molecular quantum dynamics calculations using the (3f-3) Cartesian components of the (f-1) Jacobi vectors, where f is the number of atoms. Coriolis coupling is treated exactly, but with two extra degrees of freedom, relative to coordinates that explicitly separate rotation from vibration. On the other hand, the Cartesian approach has several appealing advantages: (1) code scalability, (2) simple kinetic energies, and (3) minimal CPU requirements (for a given basis size). Our approach combines the phase space optimized discrete variable representation method, which mitigates the effect of the larger dimensionality, together with a version of the symmetry adapted Lanczos method that can exploit both rotational and permutation-inversion symmetry to reduce the effective level degeneracy, and the required number of Lanczos iterations. Results are presented for a three-dimensional calculation of the bound rovibrational levels of the neon dimer. (C) 2003 American Institute of Physics.